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Managerial Economics
Rational Decision Criteria
Richard A. Stanford
Copyright 2011 by Richard A. Stanford
All rights reserved. No part of this book may be reproduced, stored, or transmitted by any means—whether auditory, graphic, mechanical, or electronic—without written permission of the author, except in the case of brief excerpts used in critical articles and reviews.
CONTENTS
PART A. ECONOMICS AND DECISION MAKING
Chapter 1. The Economic Nature of Decision Making
-- Appendix 1A. Forms of Enterprise Organization
Chapter 2. The Goals of the Enterprise
Chapter 3. Economic Method and Modeling
Chapter 4. Modeling the Decision Context
--Appendix 4A. Inferences about Regression Models
PART B. TOOLS OF ANALYSIS
Chapter 5. The Analysis of Value and Risk
-- Appendix 5A. Marginal Utility and Risk
Chapter 6. The Marginal in Decision Analysis
-- Appendix 6A. Calculus and the Marginal
-- Appendix 6B. Optimization by Linear Programming
PART C. THEORETICAL FOUNDATIONS
Chapter 7. Consumer Behavior and Demand
-- Appendix 7A. Preference and Indifference
Chapter 8. Elasticity and Demand Specification
-- Appendix 8A. The Economic Functions of Marketing
Chapter 9. Production in the Short Run
-- Appendix 9A. The Horizontal Slice Approach
Chapter 10. Production in the Long Run
Chapter 11. Costs in the Short Run
Chapter 12. Costs in the Long Run
PART D. THE COMPETITIVE ENVIRONMENT
Chapter 13. The Competitive Environment
-- Appendix 13A. Price Changes in Competitive Markets
Chapter 14. Pure Monopoly
Chapter 15. Monopolistic Competition
Chapter 16. Oligopolistic Competition
-- Appendix 16A. More on the Kinked Demand Curve
Chapter 17. Extending the Models
-- Appendix 17A. A Mathematical Model Of Price Discrimination
-- Appendix 17B. Joint Products Produced In Variable Proportions
Chapter 18. Challenges to the Theory of the Firm
PART E. THE MACROECONOMIC SETTING
Chapter 19. The Firm in Society
Chapter 20. Ethical Dimensions of Managerial Decisions
Chapter 21. The Role of the Government
Chapter 22. Reallocation of Resources by Government
Chapter 23. Government and Macroeconomic Instability
Chapter 24. International Commerce
Chapter 25. The Multinationalization of Enterprise
Chapter 26. Opportunities in Developing Economies
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PREFACE
In the microeconomic analysis the theory of the firm, various aspects of the operations of a business firm are elaborated with mathematical models that for classroom illustration purposes are rendered both algebraically and graphically.
Models in all of their possible formats (tabular, functional notation, graphic, equation, computer statement) constitute the primary instructional vehicles employed in economics texts to convey to students understandings of the functioning of economic mechanisms. Modeling is the chief analytical vehicle employed by those economists who are pushing the frontiers of economic knowledge. Models, ranging from the highly simplified to the extremely complex, are designed in both the private and the public sectors to forecast the future courses of economic phenomena.
Managerial economics, the applied side of the microeconomic theory of the firm, is about the criteria for rational decision making by managers of business enterprises. The criteria elaborated here for business enterprises can also be applied to non-commercial decision settings, including government agencies, eleemosynary institutions, the home, and one's personal life.
The chapters in Part A introduce managerial decision making within the theory of the firm and describe the process of modeling a business firm.
Part B provides an overview of the tools of analysis that are employed in analysis of value, risk, and marginal relationships.
The chapters in part C lay out the theoretical foundations of the theory of the firm: consumer behavior, demand, production, and cost.
Part D elaborates the competitive environment ranging from purely competitive markets through monopolistic and oligopolistic competition to pure monopoly.
Part E surveys the macroeconomic setting within which business enterprises must operate.
Richard A. Stanford
Summer, 2011
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PART A. ECONOMICS AND DECISION MAKING
CHAPTER 1. THE ECONOMIC NATURE OF DECISION MAKING
Managerial economics is about the criteria for rational decision making by managers of business enterprises. The criteria elaborated here for business enterprises can also be applied to non-commercial decision settings, including government agencies, eleemosynary institutions, the home, and one's personal life. Before we proceed to an examination of these decision criteria, we shall review the essential economic nature of decision making in order to establish the fundamental principles upon which decision criteria may be based.
As noted in a first Principles of Economics course, the world is characterized by scarcity rather than abundance. Human beings need certain things for survival, and they want to possess or consume a much larger variety of amenities. If all of these things were abundantly available, each person could simply gather as much as he or she wished, and still leave enough for everyone else to do likewise. Managerial decision making would require little more than determining the time sequence of acquisition.
In regard to most of the things that humans consume, scarcity is the rule and abundance is the exception. A scarcity of something means that the total of human wants for it exceeds the quantity of it available for human consumption. As a result, one person simply cannot take all that he or she might want without consequences for other persons. Something may be said to be scarce when its price exceeds zero (P greater than 0). The price may be expressed and paid in non-pecuniary terms as well as in money. There are a few things that have essentially zero prices, e.g., common air and the water available from a water fountain.[1]
Some other things are available in greater quantities than people wish to consume. The quantities of such items so exceed simple abundance that their effective prices are negative (P less than 0). People would not pay positive prices to acquire more of such things, but they might be willing to pay others to get rid of them. Such superabundancies may be regarded as nuisance goods (an obvious contradiction in terms), or "bads." Examples include garbage, sewage, and any of the other kinds of environmental pollutants that have become troublesome.
It is because of scarcity that humans have to make choices. The "economic problem" is the juxtaposition of productive resource scarcity against human want insatiability. In attempting to resolve the economic problem, humans must make choices in how to use their scarce resources as efficiently as possible in the satisfaction of human wants. Making choices is the essence of decision making, and making decisions is the central function of management. The management of any human activity is ultimately an exercise in economizing. Managerial economics focuses upon the criteria for making rational economic decisions in regard to the use of scarce resources.
The Nature of the Firm
Economic opportunities lie in the possibilities for supplying other humans with goods and services made with scarce resources. Opportunities may also be found in the removal or disposal of nuisance goods ("bads"). Productive opportunities are enhanced by specialization and division of labor. People have found that they can consume larger quantities of scarce goods and services when they specialize in the functions that they perform best, trading the fruits of their efforts to others in exchange for the things that they can produce most effectively.The organization of individual capabilities into firms or enterprises can further enhance productive ability relative to that which individuals alone can achieve. The business firm accomplishes such enhanced productivity by serving as a vehicle for organizing the specialization and division of labor. R. H. Coase has noted ("The Nature of the Firm," Economica, New Series, Vol. IV (1937), p. 393) that firms governed by hierarchical, authoritarian control usually can accomplish resource reallocations more efficiently (i.e., at lower costs) than can be achieved by human interaction through market mechanisms on a purely personal level. Coase notes that commercial enterprises may also function as "players" on their own account in market interactions.
The management of such commercial enterprises involves the exercise of authority, usually from a top level of responsibility downward through progressively lower levels of responsibility and function. The decisions made by the manager of the enterprise encompass both the acquisition of scarce resources from outside the enterprise, and the efficient allocation of those resources within the enterprise. Thus, the management of a commercial enterprise ultimately is an exercise in economizing. The motives, behavior, legitimacy of authority, criteria for successful decision making, and consequences of operations constitute the heart of a study of managerial economics.
The Variety of Managerial Settings in the Modern Firm
Managerial decision making necessarily occurs within any of the organizational forms that modern business enterprises may take. Appendix 1A describes in some detail the three principal forms, proprietorship, partnership, and corporation. Our purpose in this section is to survey the ranges of decision settings in the larger, more complex commercial enterprises. In most cases this means the corporation since both size and organizational complexity are severely limited in both proprietorships and partnerships. Even so, some of the following remarks may be applicable to aspects of decision making in the simpler organizational forms.The modern corporation is characterized by a pyramidal, hierarchical organization. A manager may be situated in any setting ranging from that of a shop floor foreman, through lower and middle management echelons, to vice presidential and CEO (chief executive officer) positions. A manager may serve in all of these positions at one time or another with progression through the managerial career. The manager may also be placed in staff rather than line positions. A line position is so called because the manager is in a direct line of authority between the top level decision maker and those employees who carry out the essential business of the firm. A staff position, although it is not in the direct line of authority, provides supplemental services or analyses that enable managers to exercise authority more efficiently. Such staff positions include those in accounting, data processing, communications, statistical analysis, marketing, financial analysis and services, personnel, and transportation, among others. Even though a staff officer is not in the direct line of authority over the essential business of the firm, he or she still must manage the resources under his or her control.
Every business firm has at least one office or plant, and many firms establish multiple places of business, each of which must be directed by an office or plant manager. Such multiple sites may be organized by function or by geographical region. Depending upon the mission of the office or plant, multiple tiers of managerial responsibility and authority may be established at each site. Managers at every site and at every tier are responsible for the efficient allocation of the resources assigned to them.
Corporate operations sometimes become so extensive and complex that a single management team (or bureaucracy) cannot effectively oversee all of the operations of the business. One possible remedy to this problem has been the divisionalization of the firm's operations. Divisionalization allows the establishment of separate management teams to direct the operations of the multiple divisions. The chief operating officer of the division may have a title such as division director, vice president for the division, or even president of the division. Whatever the title, the division manager reports ultimately to the CEO of the corporation. There may emerge multiple tiers of managerial organization within the divisions of a corporation. The divisions may be organized along staff function lines, or by geographic regions if operations are widely dispersed geographically (including internationally). A division may also have multiple offices or plants assigned to it.
Corporate divisions are occasionally "spun off" from the main corporation and constituted as separate corporations that are wholly or partially owned by the parent firm as subsidiaries. A subsidiary relationship may also come into existence when one firm acquires a controlling ownership interest in another firm, but chooses to preserve the acquired firm's corporate identity. Because of the ownership relationship, the management of the acquiring firm can dictate policy to the management of the acquired firm. If the acquiring firm has never conducted business operations or for some reason ceases physical operations but continues to direct the operations of one or more subsidiary operating companies, it may be referred to as a holding company.
The internal structures of enterprises, and their divisions and subsidiary relationships as well, may be organized horizontally, vertically, or in conglomeration. As is common in the automobile and other American industries, numerous divisions of the same enterprise may perform parallel or identical functions, and may even be directed to compete with one another. This constitutes a horizontal structure. In other cases, the multiple plants or divisions of a firm may perform different functions in a vertical sequence ranging from the extraction of raw materials through the refinement of ores and the production of basic shapes, the fabrication of parts, various stages of assembly, and distribution through jobber, wholesale, and retail outlets. The multiple plants, divisions, and subsidiaries of a corporation may be conglomerated in the sense that the functions performed or items produced are unrelated to one another, but are linked in the corporate family for financial or distributional reasons.
Whatever the structure of a firm and its affiliated entities, any line or staff officer of the firm, or any plant, division, or subsidiary manager, must make economic choices in the use of the scarce resources that are assigned to his or her control. It is in this sense that managerial decision making in any of its settings is ultimately an exercise in economizing.
Strategic and Tactical Decision Making
Strategic management is concerned with the fundamental direction of the organization's activity, i.e., the businesses that the organization intends to pursue and desired levels of achievement in those lines of business. Such decisions, by their very natures, must be made at the highest policy making level of the organization. The time frame is from the present to as far into the future as the organization's time horizon. The organization's time horizon is limited to that of its least visionary policy maker who constrains the enthusiasm of its would-be innovators.By virtue of the fact that such directional decision making covers the long run and is laden with risk, it should be understood to be entrepreneurial rather than managerial in nature. Although the language of the business administration literature stresses strategic management, it should be more properly understood to be strategic entrepreneurship. In the late twentieth century, the term "entrepreneurship" has come to be associated with new, small, "start-up" business ventures that are highly risky. Entrepreneurship often is not perceived to occur in established or "going" concerns, especially if they have attained large size in terms of assets, employment, market share, or volume of sales.
Strategic entrepreneurship may occur at any level in any organization, whether a new local venture or a well-established multinational enterprise. In a new venture, entrepreneurship is exercised by the founder of the firm. To the extent that fundamental change is initiated at the board room level of an established enterprise, the function of the governing board is almost purely entrepreneurial since the board must assume the risks of its innovational decisions. If proposals for change are devised at lower levels in the administrative organization and only submitted to the governing board for approval, it is the site of the innovative proposal that is the true locus of entrepreneurship. However, in its approval the governing board assumes a substantial portion of the risk of the proposed innovation, and in effect shares risk with the proposer of the strategic change.
There is some confusion over the meanings of the terms "goals" and "objectives." We shall take the term goal to refer to an ultimate end that the organization at its highest policy making level determines to try to achieve. The term objective is taken to refer to desirable intermediate situations or levels of performance to be achieved in pursuit of the ultimate goals of the organization. By their nature then, goals are long-term and strategic in orientation, whereas objectives are more short-term, immediate, and partial in nature.
In military parlance, the term "tactic" is usually juxtaposed to "strategy" in referring to an action that is taken "in the field" by a specific unit to accomplish a limited objective in pursuit of a strategic goal of the organization. The term "tactic" and its various derivative forms are rarely used in discussions of strategic management. However, decisions taken at various levels in the administrative organization to implement an approved strategic change are oriented toward specific objectives (such as a target volume of sales or share of the market) rather than ultimate goals (such as a required return on investment in a particular line of business), and are thus essentially tactical in nature. In a new venture, goals and objectives may coincide, and strategic and tactical decision making may converge in the mind of the founding entrepreneur.
In the established enterprise, tactical decision making at various administrative levels must confront choices that involve risks. A modicum of entrepreneurship may therefore be exercised by the mid-level manager in the tactical decisions that must be made. However, tactical decisions that involve simply deciding upon increases or decreases in activities already in progress belong to the realm of managerial decision making. It is possible that nearly all of the decisions that must be made in a new business venture are strategic and entrepreneurial rather than tactical and managerial.
A prime example of strategic decision making is found in the international business arena. It is not uncommon for corporations to engage in international transactions or operations, but proprietorships and partnerships may do so as well. By its very nature, much of the business decision making concerning the international realm is entrepreneurial because of the inherent risks attendant upon extending operations into other countries. But once international operations have become established, tactical managerial decision making is required to adjust levels and rates of operations.
The Nature of the Decision Problem
Managers of business firms may make a myriad of decisions every day. Some of the decisions are trivial in the sense that the consequences of them do not matter very much. The consequences of other decisions, for example, what employee health insurance plan to adopt or whether to add or drop a product line from the company's product mix, may be monumental.We shall assume as an operating premise that human beings are basically interested in their own welfare. Rational human behavior consists of trying to maximize the value of some positive quantity, or to minimize the value of something perceived as having negative connotations. Although human nature is culturally influenced, we shall also presume that human beings are more-or-less materialistic, i.e., more is better than less, and hedonistic, i.e., that pain and displeasure are to be avoided or minimized. We consider in Chapter 2 whether these behavior premises truly are viable foundations upon which to erect models of managerial decision making.
Human approaches to decisions may be categorized as capriciousness, conditioned response, and deliberate, reasoned choice. The more trivial the consequences of the decision, the less time and effort are devoted to the decision process. Sometimes people seem to act without engaging in any apparent decision-making process. The choices underlying such actions may have been nearly automatic, based upon an implicit summing-up of the current circumstance compared with the decision maker's accumulated stock of past experiences under similar circumstances. Occasionally, however, human beings indulge themselves in a capricious action (an act without deliberate choice), even when the consequences may be non-trivial. If a capricious action constitutes a "bad" decision, the actor must suffer the consequences.
Dimensions of the Decision Problem
Multiple Goals. The decision maker may be confronted with a multiplicity of goals. Since it is technically not possible to try to maximize simultaneously the values of multiple conflicting goals, the decision maker has to choose one of the goals for primary pursuit. The other goals, expressed as minimum or maximum acceptable values, can then be regarded as constraints on the pursuit of the primary goal. The object of the decision is to maximize the value of the primary goal, subject to realization of satisfactory levels of subordinate goals. The problems and possibilities with respect to multiple goals are elaborated in Chapter 2.Multiple Strategies. With respect to any single goal, a decision involves multiple possible courses of action, or strategies. If there were no alternatives, no decision would be required other than selecting the goal for pursuit. The deliberate approach to decision making involves the identification of all possible courses of action and the benefits and costs likely to result from each of the alternatives. The rational choice is the alternative that yields the greatest relative positives or the largest sum of net benefits (positives less negatives), given the decision maker's set of preferences.
Marginal Changes. In many cases, the choices are not mutually-exclusive alternative courses of action; rather they involve more or less of the same course of action. The range of possible alternatives includes larger or smaller quantities to be selected. Typically, the decision problem is to select some quantity that is an alternative to the present one. Assuming that the alternative quantities are arrayed from smallest to largest, or vice-versa, choosing to shift from one to another involves additions to or subtractions from benefits or costs. Economists speak of such additions and subtractions as incremental changes, or marginal changes if they are the smallest possible changes that can be made. The rational choice in such cases is to make a quantitative change that will yield the greatest marginal benefit relative to marginal cost.
Multiple Outcomes. Often the possible alternative courses of action can be identified, but each decision alternative may have several outcome possibilities. If the decision maker can in some meaningful sense assess the probability of the occurrence of each possible outcome for each of the alternative courses of action, he may then compute the expected value of each alternative.[2] The presumption here is that the sum of the probabilities of the possible outcomes is 100 percent. Each outcome may itself be a net difference between benefit and cost. Other things remaining the same, the rational decision then is the choice of the alternative that promises the largest expected value of possible outcomes.
An extension of the expected value concept may be employed in decision situations that unfold in stages such that subsequent stages depend upon what happens in previous stages. In such cases, the probability of occurrence of an ultimate outcome is a conditional probability, i.e., the product of the probabilities of the final outcome and all prior stages. Such a situation can best be visualized with a "decision tree," an example of which is illustrated in Figure 1-1. In this hypothetical situation the decision maker has to decide whether to develop a major shopping center anchored by two department stores, or a small strip shopping center with no department stores. In Figure 1-1, the decision point is represented by the box on the left side of the tree. The circles in the diagram indicate non-decision outcome branches. There is a 60 percent chance that if a major center is built, the county will construct a 4-lane approach road to the center, but a 40 percent chance that the existing 2-lane road will have to do. But if a small strip is constructed, there is only a 20 percent chance of construction of a 4-lane. Beyond the estimated completion of the project, there is a 20 percent chance that the economy will boom, a 50 percent chance of normal economic conditions, and a 30 percent chance of recession.
The expected values of the decision branches may be computed from the information in columns (4) through (6) of Figure 1-1. Column (4) shows the conditional probabilities computed as the products of the probabilities of conditions along the branches to the respective stems of the tree; the sum of the probabilities for each decision branch is 100 percent. Column (5) contains the best available estimates of the first-year revenue flows that will occur under the different conditions. Column (6) reveals the expected values of the first-year revenue flows. The sum of the expected values of the revenue flows for each branch reveals the expected value (a conditional probability-weighted average of the outcomes) of each of the respective decision branches. Real-world decision settings may be far more complicated than illustrated in this example, and may involve multiple decision points as well numerous states of nature. Other things remaining the same, the decision branch with the largest expected value is the decision choice.
Risk. Other things may not be the same, however, if the range of outcome variability differs from one alternative to another. It is typical for decision alternatives to have different expected values, but even if two decision alternatives have approximately the same expected values, one may have a wider range of possible outcome variability than the other. Risk is inherent in the dispersion of possible outcomes about the mean of all such outcomes.
To illustrate, suppose that decision alternatives A and B may each result in any of five possible outcomes with probabilities of occurrence as indicated in Table 1-1. It is readily apparent that the possible outcomes for alternative A span a narrower range than do those of alternative B even though each has an expected value of $900. Figure 1-2 employs bar-charts in panel (a) to illustrate the probability distributions of the outcomes of the two alternatives.[3] The standard deviation of a probability distribution is used as a measure of risk on the assumption that probability distributions tend to be normally distributed about their means as illustrated by the smooth probability distribution curves drawn in panel (b) of Figure 1-2. If this assumption is valid, then the mean of the distribution plus and minus one, two. and three standard deviations contains, respectively, 68.26, 95.44, and 99.74 percent of the outcomes in the distribution. The decision alternative with the wider range of outcome variability, i.e., greater standard deviation, is said to be the riskier of the two. If the expected values are equal, the lower-risk decision alternative would be preferred by most people. Since standard deviation of alternative A is only 238.7 while that of alternative B is 402.5, alternative A is the lower-risk alternative.
Figure 1-2. Probability distributions of two decision alternatives.
However, when the expected values of two decision alternatives differ substantially, so also will their standard deviations be of different magnitudes, and will therefore not serve as a reliable basis for comparing risks. In such cases, the decision maker may compute a coefficient of variation for each decision alternative[4] The decision alternative with the smaller coefficient of variation is the less-risky alternative.
It is not uncommon for a decision alternative with a higher expected value of outcomes also to be riskier in the sense of having a wider range of outcome possibilities. In addition to assessing the riskiness of the decision alternatives, the decision maker must also be able rationally to make comparisons of the expected values of outcomes (or returns) in light of their comparative risks. Since a decision maker might be willing to trade off risk for return (i.e., expected value), he must be able to decide whether the higher expected value of a decision alternative is adequate compensation for the additional risk that must be assumed. A decision preference function is described in Appendix 2B.
Imperfect Knowledge. Only rarely does a decision maker have perfect knowledge of a decision environment, the possible alternative courses of action that may be taken, or the range of outcomes that may result from each choice. Where multiple outcomes are possible, a risky situation is said to exist if the decision maker can both identify all of the possible outcomes and meaningfully assess the probabilities of occurrence of each of the possible outcomes. An uncertain situation occurs if the decision maker either cannot identify some of the outcomes, or cannot meaningfully estimate the probabilities of their occurrence. The decision maker may attempt to deal with uncertainty by seeking additional information about outcomes or their probabilities of occurrence. But after all available information is acquired and there is a persisting aura of uncertainty, the decision still has to be made.
Decision theorists have suggested a number of decision rules for situations involving uncertainty, i.e., where outcomes cannot be identified or their probabilities of occurrence cannot be meaningfully assessed. The two that seem to be most useful are the maximin and the minimax regret decision rules. In the former, the objective is to identify the worst-case outcomes of all of the decision strategies under consideration, and then choose the one that yields the least-negative effects, i.e., the best of the worst-case scenarios. This is an extremely conservative approach that is most appropriate to the need to avoid ultimate failure of the enterprise. Its prime deficiency is that it considers only failure states, and does not take into account the possibilities of success.
The minimax regret rule requires that the decision maker perceive the best possible outcome of the decision strategies, and then compute the regret associated with all other strategies as the difference between each and the best of the alternate strategies. The strategy of choice then is the one that minimizes the regret that follows from failure to select the best outcome.
The Time Dimension. Economists refer to a time frame during which some matters can be changed (e.g., the number of workers employed), but others cannot (e.g., the size of plant or the number of assembly lines) as the short run. Short-run decisions usually affect the current situation or the immediate future. The long run is a period long enough so that any- and everything can be changed. Long-run decisions usually have their impacts only after the passage of some time, and do not affect current operations in any significant sense. Most short-run decisions within the business enterprise are to increase or decrease something already being done and thus require marginal comparisons of benefits and costs. Long-run decisions usually affect the scale of the enterprise's operations, and often involve starting something new or stopping some operation currently under way. Given the sharpest possible contrast, short-run decisions are "more-or-less," whereas long-run decisions are "go-no go" decisions.
Entrepreneurial Decisions. Finally, we may distinguish between managerial and entrepreneurial decisions. The managerial context involves making relatively low-risk, routine decisions in regard to processes that change in smooth, continuous fashion, about which much can be known or discovered, and to which marginal analysis is applicable. In contrast, the entrepreneurial decision is risk-laden because it involves innovative discontinuities in operations, about which little can be known in advance, and to which marginal analysis is less likely to be applicable. As a general rule, short-run decisions are often managerial in nature, whereas long-run decisions tend to be entrepreneurial. Managerial decisions are matters of doing more or less of something already in process, whereas entrepreneurial decisions involve starting or stopping activities or significantly altering the structure, scope, or pace of extant processes.
Looking Ahead
This brief survey of the range of settings for managerial decision making and the dimensions of the decision problem should convey something of the magnitude of the task before us in identifying the criteria for rational decision making in a variety of contexts. The study of managerial economics is, in effect, applied microeconomic analysis. But it is much more than an application of economic principles. Managerial economics brings together economic theory, the methodology of modeling relationships, the statistical process of function specification, and the application of algebra, geometry, and calculus to the decision process. In addition, we shall have occasion to touch upon the subject matters of marketing, finance, accounting, organizational behavior, and international trade. The next chapter is devoted to an examination of the motives of decision makers and the patterns of decision making that follow.
Chapter 1 Endnotes
[1]We must make qualifications in regard to each of these examples. If someone wishes to breathe air of any particular quality or purity, he or she will have to go to some lengths to acquire it, and such pure air then is not a so-called "free good." The water that any one of us can "freely" drink from a water fountain does in fact cost the larger society of which the drinker is a member something to acquire it, to transport it to the site, and to cool it to a desirable temperature.
[2]The expected value is a probability-weighted average of the possible outcomes for each decision alternative,
[3]A common measure of risk associated with a decision alternative is the standard deviation (s) of the alternative's possible outcomes,
[4]The coefficient of variation v is the ratio of the standard deviation to its respective expected value,
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APPENDIX 1A. FORMS OF ENTERPRISE ORGANIZATION
Copyright 2011 by Richard A. Stanford
Commercial enterprises, and thus the settings for managerial decision making, range from the very simple to the highly complex. The simplest form of an enterprise or firm is the proprietorship, exemplified by the baby sitter, the lawn boy, the news agent, the self-employed repair person, the consultant, and the bazaar trader in a developing country. Because a proprietorship coincides with the identity of its owner, its life comes to an end when the owner expires; its financial resources are limited to personal fortune plus any amounts that can be borrowed from relatives, friends, or banks; and the personal fortune of the owner is fully exposed to any liability incurred in the operations of the enterprise. Within the proprietorship there is virtually no possibility of specializing or dividing managerial authority or responsibility.
Even with these limitations and negatives, the proprietorship form of commercial organization has two very significant positive aspects. Tax and other legal reporting requirements are minimal, and the proprietor retains full authority over all of the resources at his or her command, answering to no one other than spouse and civil authorities. Within these limits the proprietor may choose to pursue any goal or engage in any activity or behavior desired, including profit, charity, social responsibility, or leisure. It is because of these two positives that the vast majority of commercial enterprises throughout the world are organized as proprietorships. In the United States, around three-fourths of the nearly 20 million business firms are proprietorships. This proportion may approach 100 percent in some developing countries.
The partnership form of commercial organization relieves some of the limitations of the proprietorship, but aggravates others. Because two or more principals are involved in the firm, there is some possibility of specialization and division of labor, including managerial responsibility and authority. Also, the personal fortunes and borrowing abilities of the participants may be pooled.
Because there are no clear lines of authority (unless expressly provided for in the partnership agreement), conflicts may emerge among the partners concerning overall goals and the strategies for pursuing them. And while the owner's liability is unlimited in the proprietorship, the problem is compounded in the partnership because any liability incurred by a partner or employee may extend through to the personal fortunes of all other partners. Also, the life of the partnership is severely restricted in duration to the shortest life of any of the partners. When one partner dies or withdraws, the partnership legally must be dissolved, although it may be immediately reconstituted by an agreement of the surviving partners who may choose whether or not to accept as new partner(s) the heirs of the deceased partner.
Given the weight of these negatives, fewer than ten percent of the business enterprises in the U.S. economy are organized as partnerships. Even large partnerships rarely have more than a few dozen partners, and few have as many as a hundred. In recent years some partnerships (particularly of accountants and attorneys) have effected transitions to the corporate form of organization in order to limit the liability of the principals.
The corporate form of commercial organization has been known for centuries; the British East India Company was chartered by the English crown in the 17th century to explore and exploit the resources of the New World. However, the corporation began to achieve popularity as a form of commercial organization only during the 19th century. By the late 19th century, it had attained such notoriety as to induce the Congress of the United States to enact "antitrust" legislation to deal with what were widely perceived to be unacceptable industrial structures and firm behaviors. Similar enactments followed in other countries that also favored competitive market environments. We shall delve further into the relationships between the enterprise and the government in Chapter 20.
Because of its hierarchical form of managerial organization, the corporation is especially well suited to specialization and the division of managerial responsibilities and authority. Indeed, there may be numerous tiers of management structure in a corporation. Also, the corporation may acquire financial resources far more extensive than those available to proprietorships or partnerships by selling equity shares (common or preferred stocks) in itself, or by issuing liabilities (bonds) against itself. Although such shares and bonds may be sold locally on an "over-the-counter" basis, the development of "open markets" for stocks and bonds has enabled listed corporations to sell shares or issue bonds to literally millions of investors, enabling the accumulation of billions of dollars to be invested or used as working capital.
Another significant feature of the corporation is the limitation of the exposure to liability that an owner (i.e., a shareholder) of the corporation must suffer. The maximum amount that the shareholder can lose if the corporation is sued or otherwise fails is the amount invested in shares in the company. The personal fortunes of the investors are otherwise insulated from further liability that may descend upon the corporation. This feature is a result of the legal personhood of the corporation. As a legal person (a "corporate person"), the corporation has a life that is independent of the lives of any owners, directors, managers, employees, suppliers, customers, or any other parties associated with the corporation in any way. The corporate person may be sued in a court of law, and may initiate lawsuits in its own behalf. However, such suits against the corporation can hope to capture only the assets of the corporate person, and not the personal fortunes of the shareholders.
There are some negatives associated with the corporate form of business organization. Given the privileges conferred by a corporate charter, the corporation is required to report to governments for tax and other legal purposes far more often than are proprietorships and partnerships. Such legal "red tape" is enough to convince many entrepreneurs to stay with proprietorship or partnership organizational forms. Also, in the United States and many other countries the income of the corporation is subject to double taxation. It is taxed first as income to the corporate person; then if the income is distributed (as dividends) to the shareholders of the corporation, it is taxed again as personal income of the shareholders.
Even with these negatives, the popularity of the corporate form of business organization is on the ascendancy throughout the world. Although only slightly more than ten percent of U.S. business firms are organized as corporations, they include the largest firms in the economy, and they are often situated in highly concentrated industries (i.e., a small number of firms accounting for a large proportion of industry output). Some corporations in North America and Western Europe have hundreds of thousands of employees, own billions of dollars worth of assets, and achieve sales in the billions of dollars each year. Such large scale commercial enterprises necessarily entail high levels of managerial complexity.
CHAPTER 2. THE GOALS OF THE ENTERPRISE
The Role of Modeling in Economic Analysis
Models in all of their possible formats (tabular, functional notation, graphic, equation, computer statement) constitute the primary instructional vehicles employed in economics texts to convey to students understandings of the functioning of economic mechanisms. Modeling is the chief analytical vehicle employed by those economists who are pushing the frontiers of economic knowledge. Models, ranging from the highly simplified to the extremely complex, are designed in both the private and the public sectors to forecast the future courses of economic phenomena.Perhaps the most productive use of modeling for managerial decision making is to structure a model of the manager's decision making context (the firm as a whole, or parts of it such as demand functions, production functions, and cost functions). If the structured model is a good enough depiction of the real mechanism, it may allow the manager the luxury of trying-out policies before having to implement real decisions that affect stock-holders, employees, suppliers, or customers. What are the consequences of making a bad decision in a policy simulation model? The benefit may be the realization of the likely detrimental effects of the decision so that it can be corrected before its "real-time" implementation.
The approach of this book is that of model methodology. The economic criteria for rational managerial decision making are elaborated with models; managerial behavior patterns and consequences are depicted with models; and the procedures for policy simulation and economic forecasting modeling are presented. Appendix 2A to this chapter outlines the procedures that economists typically employ in attempting to model some economic phenomenon.
One of the first steps that the economic analyst must take in modeling an economic phenomenon is to select an appropriate behavioral premise to serve as a foundation upon which the model may be built. Economists usually presume that rational decision makers attempt to maximize some positive quantity or minimize something that has negative connotations for the decision maker. In modeling the commercial enterprise referred to as the business firm, economists have traditionally assumed that managers attempt to maximize profits. It is because this behavioral premise has been called into question that we devote this chapter to a critical consideration of it before proceeding to an elaboration of the mathematical analysis of model construction.
Eras of Managerial Behavior Patterns
Survival is perhaps the single behavioral goal that has dominated individual productive effort across the span of human existence. It was the organization of human effort into enterprises enabling collective and cooperative effort that necessitated the exercise of management as it is known today. Until such time, however, we may perceive the survival behavior pattern as the effort to minimize hunger and privation, or, if the producer had risen above the biological necessity threshold, to try to maximize the possession of creature comforts. With the emergence of the concept of "income" in money using societies, we can perceive of the individual craftsman, trader, or agriculturalist as simple income maximizers.By the late nineteenth century, economists such as Alfred Marshall theorized about proprietors and partnerships as autonomous owner-entrepreneurs who could attempt to maximize profit, the net difference between their incomes and their costs. Such entrepreneurs were simultaneously owners and managers of their productive enterprises. Little impinged upon their firms from outside to constrain them except for the pressures of competition from other, similar owner-managed enterprises. Their activities and scales of operation had yet to attract social concern, and government was hardly a force to impose curbs on their operations.
Even before Marshall and his contemporaries were contriving descriptions of such competitive conditions, the corporate form of commercial organization was becoming popular as a means of marshalling greater capital resources and enabling specialization and division of labor in management. As the scale of the corporations grew, it was inevitable that the owners would hire managers to run their enterprises for them. As long as owners of enterprises remained relatively close to their operations, they could impose their wills upon their managerial employees. While the managers may have had interests that diverged from those of their owner-employers, their decisions were still constrained by the wills of the owners imposed upon them, and they could still be perceived to be effective profit maximizers.
With the progressive growth of scale of operations, the ownership interests became ever more remote from the managers, whose personal interests could become at least as important as the profit interests of the owners. Such personal interests include, in the words of William Baldwin, "personal financial rewards, security, power and prestige within the organization, desire to be liked, human sympathy, the urge to create, and perhaps occasionally the desire for an easy life."[1] While some of these interests may be compatible with the interests of owners, others are likely to be in conflict with them. The problem for the owners was to keep the emerging interests of their managers subsidiary to their own interests.
Two additional twentieth-century developments have affected the goals of managers and the patterns of their decision making: the dispersion of ownership of corporate shares, and a rising tide of social concern about the operations of the business community, together with managerial recognition of its social responsibilities. The first of these two phenomena emerged during the first half of the twentieth century. Its impact is aptly described by Kanji Haitani:
The consequence of the control conferred by dispersion of stock ownership is that the personal interests of managers may ascend to dominance over the interests of owners. The essential conclusion is that profit-maximization may not be the behavior assumption that is relevant to modeling the modern commercial enterprise; rather, it could be the maximization of any of the personal interests of managers.
The rising tide of social concern about the operations of the commercial enterprise is largely a product of the latter half of the twentieth century. Business-related social concerns have ranged from the level of concentration in industry to environmental pollution and the distribution of income between profits and wages. Whatever the impetus to such social concerns, the important point is that business managers have widely acknowledged a level of social responsibility unprecedented in human experience. William Baldwin indicates the emerging managerial attitude as follows:
In those firms for which this is the prevailing perspective, the interests of the owners is but one among a wide variety of competing interests among which the managers must mediate. Although their decisions are certainly constrained by a variety of both internal and external factors, such managers cannot be perceived to be attempting to maximize or minimize any single identifiable quantity.
Thus, it is apparent that four historical developments have unfolded to lead us to question whether indeed managerial decision makers attempt to maximize profits: the advent and growing popularity of the corporate form of business organization; the increasing scale of operations resulting in the employment of managers who have little or no ownership interests; the progressive dispersion of ownership of the corporation leading to ever greater managerial control; and the emergence of social concerns acknowledged by the managers of large corporations. As these developments have unfolded, the goal of profit has moved from center stage to become but one of the background characters in the drama. And constraints upon managerial decision making, at one time limited only to competitive pressures, seem to have attained the level of obsession with managers of at least some large enterprises.
Alternative Premises
The stage is now set for an examination of a variety of alternative theses about the goals pursued by managerial decision makers and the behavioral patterns exhibited by them in pursuit of those goals. We could identify a large number of plausible behavioral premises and still not exhaust the possibilities. We shall specify five, and invite the reader to explore yet others.(1) The original, classic behavioral premise for the manager of a commercial enterprise is that of simple, absolute, unconstrained profit maximization. Models of the enterprise erected upon this premise are elaborated in Chapter 12-15. It is this behavioral premise that has served for a century as foundation for the so-called "theory of the firm."
While profit is usually taken to be the goal of the manager of the enterprise, recognition of other possible managerial goals requires us to admit that any of those enumerated by William Baldwin in the quotation cited above may be pursued instead of profit. We should then stipulate that the mathematical modeling procedures are the same irrespective of the identity of the dependent variable, i.e., the presumed goal being pursued by the manager.
More than one of Baldwin's enumerated managerial goals may be handled in a model in which it is presumed that the objective of the manager is to maximize personal utility that is affected by multiple goals.[1] While this may be an intellectually satisfying approach to dealing with a multiplicity of possible goals that the manager may pursue, we must note the general impracticality of specification of utility functions. Also, even if a manager's utility function could be adequately specified, this approach provides no single managerial decision criterion upon which the manager can key decisions.
(2) The manager of the enterprise may attempt to optimize the profits of the enterprise, i.e., to maximize profits subject to one or more constraints. The constraints may be limitations on the operations of the enterprise imposed from exogenous sources that are not under the control of the management. Such forces may include physical conditions such as climate, weather, geography, and demography. Social, cultural, religious, and political realities may also constrain the operations of the enterprise.
Kenneth Boulding has suggested that the multiple goals pursued by managers must be regarded in a hierarchy so that the manager can choose one of them for primary pursuit.[4] The problem for the manager in regard to the other, or subordinate, goals is to keep them subordinated to the primary goal that the manager pursues. This is a problem because exigencies of the moment often lead to the "insubordination of subordinate goals." As we shall note in Chapter 6, the subordinate goals can also be incorporated into the decision-making model by treating them as constraints upon the maximization of the primary goal. This treatment then is also a form of optimization.
(3) As noted in (1) above, profit may not be the primary goal of the enterprise's management. William Baumol has theorized on the basis of extensive consulting experience that the primary goal of many enterprise managers is some growth-related variable such as unit sales, sales revenue, or share of market.[5] Particularly, Baumol suggests that the goal of many enterprise managers is to maximize unit sales subject to a constraint in the form of a minimum acceptable amount of profit or rate of profit. If the goal is a so-called "target rate of return" (TROR) on invested capital, the necessary amount of profit can be computed if the investment in capital is known. For example, if a million dollars has been invested in plant and equipment, and an 8 percent return on investment is desired, then the manager must operate the enterprise to yield $80 thousand per annum. Once this target has been met, the manager may be free to pursue another objective, e.g., the volume of sales. An elaboration of a model of the firm incorporating the Baumol thesis is presented in Chapter 16.
(4) Herbert Simon approaches the behavior of the enterprise manager from the perspective of behavioral psychology:
From this starting point, Simon deduces that firm managers often attempt to achieve a satisfactory rate of profit rather than the maximum amount possible. Simon in effect created a new verb, "to satisfice", to describe the behavior pattern. Business managers often indicate in surveys and interviews that they work toward meeting a target rate of return on invested capital. Such responses are taken by Simon to support his satisficing thesis.
Intuitive support for the satisficing thesis may also be found in the fictional story about the tailor who had dropped his last of several needles on his shop floor that was covered with straw (in earlier centuries it was not uncommon for animals to be brought into the shop or dwelling at night, hence the straw on the floor). Before he could continue his work the tailor had to find one of the needles, so he swept the straw up into the proverbial haystack. We may now pose the crucial question: what is it rational for the tailor to do, find the sharpest needle in the haystack (which, incidentally, will require him to find all of them), or to find only one that is sharp enough to get the job done? We must admit that the latter is the more economic approach, and one that also supports the satisficing thesis.
Simon also prefers the satisficing approach to managerial decision behavior because of its adaptability:
We may agree with Simon that satisficing models have great appeal because of their ability to handle adaptive behavior. But while the adjustment principles could be easily expressed above in verbal terms, we must also acknowledge the extreme difficulty of structuring and specifying a decision model in mathematical terms that accommodates both satisficing and adaptive behavior.
(5) Enterprise managers who perceive themselves to be responsible to a variety of constituencies can probably not be construed as attempting to maximize or minimize any quantity. In fact, their behavior may be in response only to constraints, with no clearly definable objective of pursuit other than "survival". The response pattern has been described as that of mediation among the competing constituencies, an essentially political process. Enterprise managers who give lip service to "social responsibility" may only be attempting to achieve legitimacy for the power that they wield. William Baldwin further hypothesizes that if successive generations of corporate executives repeat often enough their company's litany of social responsibility, they may come to actually believe it and begin to live by it.[8]
The problem for modeling the behavior of the enterprise is that economists have not ventured far enough into the wilderness of political processes to allow us to offer a clearly defined model of constituent mediation for the reader's consideration. We may envision the possibility that some of the management's constituencies may at any time become the primary object of the manager's concern, given the exigencies of the moment. In either case, optimization models may be appropriate for analysis of situations wherein one of the constituencies has, at least temporarily, become the focus of the manager's attention.
However, the manager may attempt only to minimize the value of some negative connotation associated with the constituency, subject to constraints imposed by the perceived need for deference to the other constituencies. Here the manager may be in the avoid-avoid dilemma illustrated by Kenneth Boulding in his example of the donkey between two skunks (this is in contrast to the donkey's approach-approach dilemma when it finds itself between two bales of hay). If optimization modeling can indeed be applied to the situation of constituent mediation, the manager must anticipate that the identities of the behavioral goal and its constraints will be exchanged from time to time as the concerns of one and then another constituency rise to the surface (the squeaky wheel gets the grease).
Choosing a Behavioral Premise
In the previous section we outlined five possible behavioral premises and variations upon them that might be taken to serve as foundations upon which might be erected a theory of managerial decision making. Other behavioral premises could be considered, and perhaps in the future yet other possibilities will surface to prominence in the literature. We now come to the task of making a selection from among them to serve us through the remainder of this book.By virtue of the fact that there is great diversity among the more than twenty million identifiable business firms in the American economy, it might be defensible to argue that all five of the possible premises outlined above ought to be retained in view of the fact that there are without doubt numerous firms whose managers exhibit the behavioral characteristics of each premise. This would require the development of at least five different models of managerial behavior, and such may indeed be appropriate. In order to economize on our effort (and the volume of matter that the reader must absorb), we shall pursue a strategy of adopting one premise for primary elaboration, but make reference to variations and alternatives where appropriate.
William Baldwin suggests the tack that virtually all writers in the field of managerial economics have followed during the past two decades:
Baldwin, concerned primarily with the "typical large corporation," concludes the profit maximization premise to be satisfactory; yet the corporate form of business organization accounts for only about eighteen percent of all business firms in the American economy. The simple, unconstrained profit maximization premise should be acceptable with even less question for the 74 percent of the American firms organized as proprietorships. It may even serve adequately for the remaining nine percent organized as partnerships in those firms within which the partners have reached some consensus of direction for the firm.
Milton Friedman argues that the realism of the assumptions (a behavioral premise is an assumption) underlying a theory are less important than the ability of the theory to explain or predict.[10] In Friedman's parlance, what is important is that people behave as if the assumptions about their behavior are true, whether or not the assumptions are factually descriptive. Applying this concept to the present issue, we may argue that a model based upon the premise of profit maximization may be useful if managers behave as if they are attempting to maximize profits, irrespective of what they actually are attempting to do. So, it does not matter whether it is profit or some other behavioral objective, or whether the decision maker is attempting to maximize, satisfice, or only mediate, the relevant consideration is whether a model erected upon a profit maximization assumption can explain or predict well enough. Baldwin concluded in the quote cited above that the opportunity loss resulting from adopting the profit maximizing assumption would be small.
There may even be reason to believe that the simple profit maximization assumption will be adequate to the modeling of satisficing behavior. Herbert Simon, the inventor of the satisficing idea, even though he judges satisficing models to be richer than maximizing models, acknowledges that "the psychological evidence on individual behavior shows that aspirations tend to adjust to the attainable. Hence in the long run...the level of aspiration and the attainable maximum will be very close together."[11] If this can be taken as a justification for employing a maximizing assumption where a satisficing assumption might be preferable, it is due to the richness of the satisficing approach that accommodates adaptation, rather than the adaptability of the maximization model.
Whatever it is that business decision makers are pursuing, and whatever their behavioral pattern with respect to the objective, our conclusion is that profit maximization can serve as a satisfactory proxy in developing the theory of managerial decision making. In Chapter 5 we shall elaborate a modeling approach to both maximization and optimization (i.e., maximization subject to one or more constraints), and in subsequent chapters we shall employ the maximization or optimization behavioral premises as appears appropriate, but we shall be prepared to refer to alternative objectives or other behavioral patterns as needed.
Profit in the Short and Long Runs
The student of managerial economics should recognize from the outset that the unbridled pursuit of profit in any short-run setting could be detrimental to the earning of profit in any subsequent period (each future setting is of course its own short run), or even to the survival of the enterprise in the long run. A wise manager, one whose time horizon stretches beyond the immediate circumstances, upon occasion will see the need to sub-maximize with respect to a profit objective in the short run in the interest of both survival into the long run and the possibility of maximizing profits in future short runs. We thus acknowledge the rationality of deliberate non-maximizing behavior during any particular short-term time frame if justified by long run considerations.One approach to analyzing profit in the long-run time frame is that the manager of the firm attempts to maximize the value of the firm in the long run. This idea can accommodate both profit maximization and deliberate non-maximization behavior in the sequence of short-runs that comprise the long-run.[12]
An Object of Pursuit or an Indicator of Success
A word of caution in regard to profit may be in order for the prospective business manager. Profit, after the fact an easily measurable quantity, may be much like the more nebulous and hard-to-measure state of happiness. Personal happiness is a condition that virtually all human beings (exceptions being masochists) aspire to attain. But it often appears that if happiness per se is taken to be the object of personal pursuit, the harder one tries to achieve happiness, the more elusive it becomes. Particularly, members of a materialistic society often appear to pursue happiness by acquiring things such as bigger and nicer homes, cars, boats, condos at the beach or chalets in the mountains, etc., only to discover that once the object of desire has finally been acquired, they are in fact no happier than they were before. We philosophize to suggest that the more effective way to attain happiness is to pursue and achieve some other personally satisfying or socially beneficial end. Happiness thus would be the by-product rather than the object of pursuit, and may be achievable in greater abundance by not pursuing it than by pursuing it.The application of this consideration to the context of managerial decision making is the possibility that if profit is the object of pursuit, it may turn out to be highly elusive. On the other hand, if the enterprise management takes some other more socially redeeming goal, e.g., to provide well-designed, functional, high-quality merchandise or service at the lowest possible price, a larger volume of profit may result as a by-product and a reward for successful entrepreneurship then could have been achieved had profit been the primary object of pursuit. Here, the role of profit is to serve as an indicator of success in pursuing some other goal, rather than as the object of pursuit itself. Indeed, it has been suggested that if profit is the only object of pursuit, profit will be the main product, with poor-quality and high-priced merchandise the by-product. We can only conjecture that the seeming obsession of American corporate enterprise (and the academia that attempts to explain its behavior) with short-run profit is one of the factors in the declining competitiveness of American products on world markets.
Kanji Haitani offers the following indictment of an obsession with profit maximization:
Chapter 2 Endnotes:
[1] William Baldwin, "The Motives of Managers, Environmental Restraints, and the Theory of Managerial Enterprise," in The Quarterly Journal of Economics, May 1964, p. 241.[2] Kanji Haitani, Comparative Economic Systems, Prentice Hall, 1986, p. 228-229.
[3] Baldwin.
[4] Kenneth Boulding, "The Ethics of Rational Decision," Management Science, February, 1966.
[5] William Baumol, Business Behavior, Value and Growth, New York: Harcourt Brace Javanovich, 1967.
[6] Herbert Simon, "Theories of Decision Making in Economics and Behavioral Science," American Economic Review, June, 1959, pp. 253-280.
[7] Simon.
[8] Baldwin, 1964, p. 249.
[9] Baldwin.
[10] Milton Friedman, "The Methodology of Positive Economics" in Essays in Positive Economics, University of Chicago Press, 1953.
[11] Simon.
[12] This decision perspective can be represented by the present value model introduced in equation (1) of Endnote [1] in Chapter 4:
The return, R, in each of the n short runs is the profit of the period that the manager may have attempted to maximize, but may have deliberately chosen not to maximize in the interest of outcomes in other short runs and the long run. The i in each of the denominator terms is the discount rate that reflects the remoteness of outcomes expected in the future time settings. The number, n, of future short runs that comprise the long run depends on the length of the manager's time horizon. The essential long run behavioral premise is that the manager attempts to maximize the present value of the enterprise, PV, even if non-maximizing behavior is indulged in with respect to any of the short-run profits indicated by the R symbols.
[13] Haitani, p. 240.
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CHAPTER 3. ECONOMIC METHOD AND MODELING
Understanding Economic Behavior
Over the past couple of centuries economists have developed an effective approach to understanding "the way the world works." This approach, known as theoretical, deductive, or a priori method, may also be described as model methodology. The objective of economic modeling is to produce an abstract representation of a real economic context. Such a representation can be used to explain how the context works, to instruct about it, to forecast its behavior, and to simulate policy in regard to its function.Economists regard modeling as a form of scientific method. When the term "scientific method" is mentioned, people often think of experimentation within a laboratory setting. Such experimentation generates data that can serve as the basis for an inference about the validity of a scientific theory or hypothesis. Economists have only upon occasion undertaken experiments as a means of discerning the economic nature of the world.
Several good reasons have been offered for the paucity of experimentation in economic inquiries. Social systems, economic mechanisms in particular, usually are regarded as too large and complex to be fitted into the confines of a laboratory. Indeed, young economists often are told that the world itself is their laboratory. More importantly, in any social system it is usually too difficult (which for the economist means too costly) to exercise laboratory control over all of the matters that are extraneous or peripheral to the social system. Also, there typically are moral implications to efforts by social scientists at experimenting on human subjects. The moral implications follow from the likelihood that any social experiment will leave the subjects of the experiment either better or worse off than before the experiment.
The most significant practical objection that can be raised with respect to experimentation on human subjects is the Hawthorne effect, i.e., that intelligent human beings, once they perceive that they are the subjects of experimentation, tend to engage in affected behavior. This affected behavior may be to try to present themselves in best light in the eyes of the experimenter or those who will analyze the experimental data. Such behavior has the effect of contaminating the experimental results so that they cannot be taken as indicative of normal behavior. The only way to avoid the possibility of such affected behavior is for the experimenter to try to keep the subjects from perceiving that they are subjects of experimentation, but there may be moral implications to this approach as well. For any of the reasons expressed above, economists have tended to avoid an experimental approach.
Model Method
The approach favored by economists was pioneered by David Ricardo, who in his 1817 book, Principles of Political Economy and Taxation, described a hypothetical opportunity of England to exchange cloth with Portugal for wine. The purpose of this example was to elaborate the virtues of international specialization according to comparative advantage. The example was an abstraction because it was both imaginary and highly simplified. Although Ricardo's tabular information was not by him given graphic or equation format, it can still be considered an early model in the modern vein.From Ricardo's time until about the middle of the twentieth century, economists employed roughly the same approach. They further developed the method to employ mathematics in order to give their models both graphic and equation representations. Their models enabled them to deduce conclusions (hence the name, "deductive method"), but they rarely attempted to subject their deduced conclusions to empirical verification. Indeed, those holding more extreme views in this regard declared that there was no need for empirical testing. Such tests would be a waste of time since the deduced conclusions were true in an a priori sense (hence the name, "a priori method"). The basis for such an extreme position was their belief that since they started from accurate observations, made appropriate assumptions, and obeyed the laws of logic (both inductive and deductive), the conclusions that they derived had to be true (in the a priori sense). But, perhaps a more practical reason for a general reluctance to attempt verification of the a priori deductions was the extreme difficulty of computation in an era that lacked both mechanical and electronic calculators and computers.
The deductive or a priori approach started to "come apart" early in the twentieth century as economists began to realized that some of their most fervently held conclusions about the economic nature of the world could not explain current happenings and conditions. In particular, the "classical economists" (as John Maynard Keynes called them) presumed that their understanding of markets at the microeconomic level (deduced using good a priori procedures) would be applicable to the whole macroeconomy. Accordingly, their theories failed either to predict or explain the "Great Depression" of the 1930s decade. Nor could they recommend adequate policy prescriptions for dealing with the great contraction. Nonetheless, the early twentieth century economists were no more ready to give up their time-honored method of analysis than they were to give up the theories derived from it.
Although the procedures and tools of modern statistical analysis were well developed by the 1920s, the tremendous computational effort required for statistical testing with empirical data continued to prevent many economists from undertaking the effort. It took a technological and information revolution after the middle of the twentieth century to bring about a significant change in the economist's model method. With the advent first of the calculator and subsequently the computer, economists began to modify their methodology. They would still employ a theoretical approach for developing a model; they would continue to employ deductive logic to derive model conclusions; but the deduced conclusions would no longer be regarded as a priori truths. Rather, the deduced conclusions would be treated only as tentative hypotheses to be subjected to efforts at empirical verification.
Although few of the "principles of economics" elaborated in the economic texts of the 1940s had been verified with empirical data, today virtually all of them have been tested many times over. That they had not earlier been verified does not mean that they were untrue, only that their validities had not been determined. Upon occasion, empirical testing has led to the rejection of some long and firmly held economic beliefs, but in most cases the efforts at empirical testing have served to validate the conclusions deduced earlier by a priori methods.
Modern Modeling Procedures
Although economists have not agreed upon a formalized list of procedures for modeling an economic phenomenon, we shall offer the following outline as a guide to the prospective economic model builder. We shall also note parallels and differences between the modeling approach and an experimental approach.(1) Any scientist, whether natural or social, is first attracted to a new topic by observation of some phenomenon. The observation may be perfectly casual, as when walking down the street one notices a peculiar pattern of leaves on a bush, or the behavior of a child selecting an ice cream cone from a vendor. Alternately, the observation may be made in conjunction with some other formal inquiry, as for example when a chemist, in experimenting with a reaction between certain elements, notices another element (present as a contaminant) also entering into the reaction. Or an economist, intent upon analyzing the real growth of a region, coincidentally notices a pattern in the price data that have been removed from the regional product data by process of deflation. In any of these cases, the first observation serves as a platform from which to depart into further analysis.
(2) Given knowledge and experiences in the discipline, the scientist then hypothesizes a relationship between the object of interest (treated as dependent variable) and some number of determinants (treated as independent variables). The economist selects a fundamental behavioral premise to serve as a principle that governs behavior. A behavioral premise is usually an assumption that someone is trying to minimize or maximize some quantity.[1]
(3) The economist as well as the natural scientist must now find some means of simplifying or abstracting from the complexity of the phenomenon under examination. Here the natural scientist often has an advantage over the economist in being able to accomplish the abstraction by means of laboratory control. The slash in the functional notation statement above separates the independent variables to be included explicitly in the analysis (those to the left of the slash) from those to be isolated from the analysis (those to the right of the slash represented by the ellipsis symbols). The natural scientist then designs an experiment so that the facilities of laboratory control may hold constant (or eliminate) the extraneous variables. The experiment is in effect isolated from the surrounding environment by means of the laboratory control. But, as we have noted above, economists find it to be extremely costly or physically impossible to effect laboratory control over the extraneous variables in an economic system. Their alternative approach, admittedly a second best to actually being able to hold the environment constant, is to assume all of the extraneous influences as given or constant for purposes of the analysis. The economist's method of abstracting from complexity of the phenomenon under study is assumption of constancies.
(4) While the natural scientist proceeds to conduct an experiment in order to generate data, the economist employs inductive logic (i.e., reasoning from first observation and behavioral premise to a generalization about them) to structure a model. The model, including only those independent variables that are not assumed constant, may be represented in the form of verbal assertions of relationships, mathematical equations, or graphs of the equations. Once the structure of the model is in place, the economist may employ deductive logic (i.e., reasoning from a generalization to a particular conclusion) to derive conclusions about the model.
(5) An economist who is a strict apriorist will be inclined to regard a deduced conclusion as an a priori truth to be accepted without further consideration. But the more usual present day approach is to treat the deduced conclusion as a tentative hypothesis to be subjected to empirical verification.
(6) Assuming that the deduced conclusion is an hypothesis to be tested, the economist is confronted with the need for appropriate empirical data. In contrast, the natural scientist is provided with data generated in conducting the experiment (a stochastic process). The experiment is probably conducted numerous times, generating enough data for a statistical inference about the validity of the hypothesis. But what data should the economist use? Since experimentally generated data cannot be relied upon, the economist must turn to the world itself as a stochastic process. The on-going processes of the phenomenon that the economist has determined to study produce continuing experience that can yield data as soon as they are observed and recorded. The world itself is surely the most prolific of all stochastic processes. The analyst must simply watch what is going on and record observations about it. The economist's job is to find appropriate data already captured and published by others, or to engage in original field research to record the needed data from observations of natural processes. Once adequate data are in hand, the economist may employ the tools of statistical analysis to test the hypothesis, thereby accepting or rejecting it on grounds of statistical inference. The statistical procedures are usually conducted by computerized statistical software.
The economist still has a problem to resolve. The model was structured only after appropriate simplifying assumptions were made, but the data available for testing the model conclusions reflect natural processes for which nothing was or could be held constant. The economist must recognize the dynamic (changing over time) nature of the real world; it holds no aspect of itself constant for the convenience of the analyst. The dynamic natural process data are unlikely to match very closely the conclusions that were deduced from a model structured under various constancy assumptions.
One approach to dealing with this problem is to add to the model more of the determinants that were assumed constant in structuring the model, but this approach may ultimately defeat the purpose of modeling the phenomenon. An alternate approach, illustrated in Chapter 7, is to adjust the data for the dependent variable to get rid of the influence of the determinants that were assumed constant. Once the influences of the extraneous determinants have been purged from the dependent variable data, the independent variable data are more likely to validate the model conclusions.
(7) A final step in model method is one that often has been omitted, and occasionally by some very prominent economists. This final step is to relate the model conclusions (which were deduced under a variety of constancy assumptions) back to the real world phenomenon that the economist is investigating. The means for accomplishing this step is an intellectual exercise to reconsider the deduced conclusions in light of the assumed constancies, modifying them to take into account those factors which, though assumed constant, in fact do change.
John Maynard Keynes, widely regarded as the intellectual father of modern macroeconomic analysis, was guilty of a failure to take the last step in the modeling process. In constructing his concept of a consumption function, Keynes assumed constant many factors, among them the stocks of liquid assets (e.g., the quantity of money) and real wealth. Keynes proceeded to structure his model of the macroeconomy, deduce conclusions about how it worked, and recommend policy prescriptions to deal with the ensuing "Great Depression." But he failed to return to his model conclusions to reconsider the impacts of changes in liquid assets and real wealth. In so doing, Keynes himself set the stage for a resurgence of classical economics in the guise of Monetarism.
Review
A brief review of these modeling procedures is in order. The economic analyst observes some phenomenon that attracts attention for further examination. The analyst hypothesizes a relationship and selects an appropriate behavioral premise upon which the model may be structured. The next step is to simplify from the complexity of the phenomenon under investigation by assuming constant all extraneous matters. The analyst then employs inductive logic to structure a model relating the dependent variable to the independent variables that have been chosen for treatment in the model, and deductive logic to derive conclusions about the functioning of the model. In the modern approach, the deduced conclusions are regarded as tentative hypotheses to be validated by statistical tests on data taken from real-world circumstances. Finally, if the model conclusions are supported by the data, they should be reconsidered in light of changes in factors that were assumed constant in structuring the model.Appendix 3A describes regression analysis, the most common approach to modeling economic relationships.
Simulation Modeling
As we noted at the end of Chapter 2, economic models have a variety of possible uses, including instruction of economic relationships, analysis of economic phenomena, forecasting of future economic circumstances, and policy simulation prior to making managerial decisions. Algebraic forms of economic models are introduced and techniques of estimation of model parameters are elaborated in Chapter 4.
Chapter 3 Endnotes:
[1]The hypothesized relationship can be expressed in mathematical, functional notation as
where y, the object of analysis, is the dependent variable, and x is an independent variable, i.e., a determinant of the behavior of y. More than one independent variable may be included in the model. All independent variables to the right of the slash (...) are assumed constant. The selected behavioral premise is implicit in the presumed functional relationship, f.
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CHAPTER 4. MODELING THE DECISION CONTEXT
Models constitute the primary vehicles for conducting economic analysis. Economic theorists, attempting to push the frontiers of economic knowledge, employ models to discern the economic nature of the world. Models constitute the nearly universally employed instructional vehicles of the economics classroom. Government as well as private-sector decision makers use models to forecast important environmental conditions. They also use specially tailored models for policy simulation purposes, i.e., to examine "what if" circumstances before actually having to make real-world decisions.
Models may be represented in any of several possible formats. The most rudimentary form is that of a verbal assertion of a relationship between a dependent and one or more independent variables. An example of such a verbal assertion is the law of demand, i.e., that people will tend to buy items in larger quantities at lower prices, and vice-versa. Mathematical functional notation may be employed to represent the model, as, for example, y = f(x1, x2, ...), where y is understood to be a dependent variable, the behavior of which is determined in some sense by one or more independent variables, x1, x2, etc.
The specific structure of the model cannot be shown in functional notation format. The model can be made specific by putting it into an equation format, such as the so-called slope-intercept form of a linear relationship, y = a + bx. Here, a is the y-axis intercept, and b is the slope of the line representing the relationship between x and y. Other equation formats are also possible, as will be discussed below. And from the equation format, it is but a short step to the computer language statement to represent the model. Indeed, most economic models designed for forecasting and policy simulation purposes eventually find their ways into computerized implementations.
The process of specifying a model can be described in several identifiable steps. The first step is to model relationships between the dependent variable and one or more independent variables. The modeling process, following the procedures outlined in Chapter 3, involves selection of independent variables thought most likely to affect the behavior of the dependent variable, and guesses at the nature of the relationships (i.e., whether direct or inverse, linear or curved, and if curved relationships, the direction of curvature). Such guesses lead to expectations of signs (+ or -) of the coefficients of the variables, positive for direct relationships, negative for inverse relationships. Prospective independent variables not expressly included in a model are treated as if they are constant (even if in actuality they are not).
The next step is to acquire data for all of the variables expressly included in the model. The data may be captured cross-sectionally (i.e, at a point in time but across a number of subjects) or as a time series (i.e., for a single subject, but over a period of time). The process of data capture can be expected to be costly in terms of time, effort, and various explicit expenses.
The third step in the model specification process is to estimate the values of the parameters (or constants) of the hypothesized relationships. In the slope-intercept equation model format, the values of the constants a and b must be estimated. Although these values may be estimated by informal means (use of the imagination, "eye-balling"), the remainder of this chapter will be devoted to elaboration of the formal statistical procedures that have been adopted nearly universally by economic analysts for the specification process. After the model has been specified, the final step in the process is to attempt to verify the model, or ascertain its adequacy to the end for which it was constructed. The tools of statistical inference are applied to this objective, but the ultimate test of a model is its ability to explain, predict, simulate, or instruct.
Estimating a Model by Regression Analysis
Regression analysis is the most widely used, formalized method of estimating the demand (or any other type of) functional relationship in economics and business administration settings.
Simple Regression Models
The simplest form of regression model relates two variables, of which one is described as dependent, and the other as independent. The format for this simplest regression model may be described in functional-notation form as
The simple linear regression analysis may be extended to multiple regression with the addition of terms for other independent variables, or to higher-order relationships with the addition of terms for values of the single independent variable raised (or transformed by self-multiplication) to successively higher powers. The general form of the linear multiple regression model is
Figure 3A-1. Scatter diagram for variables y (vertical axis) and x (horizontal axis).
Regression analysis functions to accomplish mathematically what the analyst may have drawn as a free-hand curve of average relationship using an "eye-ball" fitting technique. Although there are several possible regression principles, the most commonly-used approach is to "fit" the average relationship curve to the plotted points so as to minimize the squared deviations of the curve from the points. Assuming this so-called "least-squares" technique is properly applied, there is no other mathematical function that can be "fitted" to the plotted points with any smaller average error relative to the location of the plotted points. The regression analysis produces estimates of the parameters (intercept, slope) of the best-fit average relationship curve.
Depending upon the amount of variation in the dependent variable, the resulting regression equation may be able to estimate, with some error, values of existing observations within the data set, and to predict values of hypothetical observations not included in the data set. This latter possibility constitutes the potential of regression analysis to serve as a modeling technique. Given a regression equation such as that developed from a "least-squares" regression procedure on a set of data, unknown values of the dependent variable, y, may be estimated by inserting a known value of the independent variable, x, into the regression equation and solving for the dependent variable value. The error involved in estimating or predicting such values constitutes a potentially serious problem that will be discussed subsequently.
Multiple Regression Models
Some dependent variables can be adequately modeled with reference to a single independent variable, but other independent variables can be modeled only inadequately in this manner. As we shall note later in this chapter, there are two possibilities for these variables: either they are characterized so extensively by random noise that they cannot be modeled, or there are one or more other phenomena that govern or influence the behavior of the variables. If comparable data for these other phenomena can be acquired, then conventional simple and multiple regression procedures may be invoked to model the relationships. The conventional formats for the simple and multiple regression models are given by equations (2) and (3) above.Once a multiple regression model has been specified and the parameter values estimated, the analyst may discern the predictive ability of each of the included independent variables by examining the inference statistics for each of them as discussed later in this chapter. Any independent variable that in the judgment of the analyst does not make a satisfactory contribution to the explanation of the behavior of the dependent variable data may then be deleted from the model when the model is respecified. Many statistical software packages include options for stepwise deletion of inadequately contributing independent variables from the model according to some criterion specified by the programmer or the analyst. In the stepwise regression procedure, the full model including all variables selected by the analyst is first estimated, then the model is automatically respecified in subsequent steps, omitting one variable in each step, until only one independent variable remains in the model. The analyst may then inspect the sequence of model specifications, looking for a significant drop in the overall level of explanation of the behavior of the dependent variable. Once this loss is identified, the model specified prior to the deletion of the independent variable resulting in the significant loss is the optimal model.
Non-linear Regression Models
The multiple regression equation, linear in its equation (3) format, can be made to fit curvilinear data paths by converting it to a polynomial format. The polynomial equation includes one independent variable raised to successively higher powers. For example, a quadratic polynomial equation includes linear and second-order (or squared) terms in the format:
Figure 3A-2. A hypothetical scatter diagram illustrating a second-order relationship.
Figure 3A-3. A hypothetical scatter diagram illustrating a third-order relationship.
Finally, we should note that the multiple regression format can accommodate a mixture of all of the formats described to this point, and further incorporate moving averages as well as components of a decomposed time series. For example, suppose the analyst finds that variable x1 is a significant predictor of the behavior of the object series, but that the explanation needs to be supplemented by the presence of two other independent variables, x2 and x3, the first linear and the other in a second-order relationship. Such a regression model might have the following appearance:
Multiplicative Models
All of the models that we have illustrated to this point have been additive in the sense that the effects of all of the separate independent variables are simply added together to compose the total effect on the dependent variable. Each independent variable is assumed to have its impact on the dependent variable independently of any other independent variable. There may be reason to believe that two or more independent variables have joint or interactive impact on the dependent variable. An example might be found in utility analysis where the total utility realized from consumption of a particular good, e.g., beer, can be expected to depend not only on the quantity of beer consumed, but also the quantity of pretzels available for consumption along with the beer. In cases like this, a multiplicative functional relationship such as that in equation (7) may be more appropriate:
Here, the total effect on y is the product of x1 raised to the power b and x2 raised to the power c, multiplied by a scale factor a. Equition (7) can be converted to a form that can be handled by (additive) multiple linear regression by taking the logarithms of all terms in the equation:
Regression analysis purports to provide answers to a very specific question: "What is the nature of the relationship between the dependent variable and an independent variable?" The question is answered by estimating values of the parameters in a best-fit equation. But regression analysis begs two other very important questions: "Is there a significant relationship between the selected variables?" and, if so, "How strong (or close, or reliable) is the relationship?" If there is no significant relationship, or even if the existing relationship is only trivial, a regression analysis will dumbly estimate the values of the parameters. The appendix to this chapter delves into the significance of the relationship estimated by regression analysis.
APPENDIX 4A. INFERENCES ABOUT REGRESSION MODELS
Regression analysis purports to provide answers to a very specific question: "What is the nature of the relationship between the dependent variable and an independent variable?" The question is answered by estimating values of the parameters in a best-fit equation. But regression analysis begs two other very important questions: "Is there a significant relationship between the selected variables?" and, if so, "How strong (or close, or reliable) is the relationship?" If there is no significant relationship, or even if the existing relationship is only trivial, a regression analysis will dumbly estimate the values of the parameters. It is therefore necessary to delve into the significance of the estimated relationships. The existence and significance of an hypothesized relationship should perhaps be brought into question even before the regression analysis is conducted.
The statistical complement to regression analysis that attempts to address the questions begged by it is correlation analysis, a special application of the tools of statistical inference. Although the user of statistics is typically concerned with the results of both the correlation and the regression analyses, it is possible to conduct either analysis without making computations for the other.
The Existence and Strength of the Relationship
For our purposes, the evaluation criteria developed by the inference analysis will be divided into two groups. The first, usually described as "analysis of variance," yields four evaluation criteria that may serve as bases for inferences about the existence, strength, and validity of a regression model:
(b) The coefficient of determination, r2, is interpreted as the proportion of the variation in the dependent variable data that can be statistically explained by data for the independent variable for which the r2 is computed. In a multivariate regression model, a coefficient of multiple determination, R2, may be computed; if there is only one independent variable in the model, the computed R2 will be equal to the only simple r2. Since r2 is computed as the squared value of the correlation coefficient, r2 is unsigned, and falls within the range of zero to +1. Although computed values of r and r2 contain essentially the same information (except for differences in sign), and each implies a value of the other, many analysts prefer to focus attention on r2 because of its determination interpretation.
The interpretation of any computed r2 statistic is subjective, and hence open to dispute. For example, how high (toward unity) does the r2 have to be in order for the analyst to infer the existence and strength of a relationship? How low (toward zero) can an r2 statistic be before the analyst may draw the inference that no statistically identifiable relationship exists between the dependent and an independent variable? Analysts in the natural sciences often expect r2 values in excess of 0.9 (or even higher) to indicate the existence of a useable relationship.
Because of the degree of randomness, capriciousness, and ignorance that may characterize human decision making and behavior in the aggregate, a social scientist may defensibly judge an r2 that is in excess of 0.7 (or perhaps even somewhat lower) to be indicative of a statistically meaningful relationship. But most analysts are skeptical of the existence of a statistically meaningful relationship if the r2 between the dependent and independent variables is below 0.3 (in statistical jargon, the null hypothesis, i.e., that there is no relationship, is supported). For our purposes, the r2 values of 0.3 and 0.7 will be taken as evaluation benchmarks: values of r2 in excess of 0.7 are sufficient to reject the null hypothesis; values below 0.3 support the null hypothesis. But the reader should be aware that both of these values are rather arbitrarily selected and are subject to challenge.
Assuming that these values will serve satisfactorily as evaluation criteria, what of the r2 range between 0.3 and 0.7? This constitutes a statistical "no-man's land" wherein no strong inferences can be drawn about either the existence or the non-existence of a statistically meaningful relationship between two variables. The interpretation of r2 values below 0.3 or in excess of 0.7 may be further refined with reference to the statistical significance of the regression model and particular variables within it.
(c) The computed F-statistic may be used as a basis for drawing an inference about the statistical significance of a regression model. Once the F-value is computed, the analyst must consult an F-distribution table (which may be found in any statistical source book or college-level statistics text). For the particular regression model under consideration, its computed F-value may be compared with F-distribution table values in the column for "1 degree of freedom in the numerator," and on the row corresponding to the number of degrees of freedom (DF) of the regression model. The DF of a regression model is the number of observations less the number of variables (dependent and independent) in the model. For a regression analysis including a dependent variable and two independent variable conducted with 60 observations, the DF is 57. If the regression model's computed F-value exceeds the F-distribution value read from the appropriate column and row in the table, the analyst may infer that the model is statistically significant at the level indicated in the heading of the table for the F-distribution (usually .05, i.e., only 5 chances in 100 that the model is spurious).
Suppose that the computed F-value for a regression model is 4.73, with 60 degrees of freedom. An F-distribution table reveals that the F-value required for significance at the .05 level is 4.00; the F-value required for the .01 significance level is 7.08. These findings support the inference that the regression model is statistically significant at the .05 level, but not at the .01 level.
For many less-consequential forecasting purposes, most analysts probably would be willing to accept (though with hesitancy) a regression model with r2 of 0.7 and statistical significance at the .05 level. If truly consequential decisions are to be based upon the regression model forecasts, the analyst may not be willing to use any model for which r2 is less than some very high value (like 0.9 or 0.95), with statistical significance below some very low level (like 0.01 or 0.001).
(d) The standard error of the estimate (SEE) may be used to specify various confidence intervals for forecasts made with the regression model. Realistically speaking, the likelihood that the actual value at some forecast-target date will fall precisely on the value estimated in a regression model is nearly zero. In other words, the forecasted value is a "point estimate" that the analyst hopes will be close to the actual value when it finally occurs. The computed SEE specifies a numeric range on either side of the point estimate within which there is an approximate 66 percent chance that the actual value will fall. Two other confidence intervals are also conventionally prescribed. There is a 95 percent probability that actual value will lie within a range of two standard errors of the forecasted point estimate, and a 99 percent probability that the actual value will lie within three SEEs of the forecasted value. For example, suppose that a regression model forecasts a point estimate of 732 for the target date, with an SEE of 27. The 66 percent confidence interval may thus be computed as the range from 705 to 759 (i.e., 732 +/- 27); the 95 percent confidence interval is from 678 to 786; and the 99 percent confidence interval is from 651 to 813. It should be apparent that the higher the required confidence in the forecasts made with a regression model, the wider will be the range within which the actual value likely will fall. As a general rule, the SEE will be smaller the higher the r2 and the lower the statistical significance of the regression model. Other things remaining the same, a regression model with a smaller SEE is preferable to one with a larger SEE. In any case, the analyst would be better off in reporting the results of a regression model forecast to specify confidence intervals rather than the single-valued point estimate that will almost certainly not happen.
The Significance of the Coefficients of the Independent Variables
Certain inference statistics are also computed for purposes of assessing the statistical significance of the regression coefficient (b, the estimated slope parameter) of each included independent variable.
All such regression coefficient estimates are presumed to constitute a normally-distributed population for which a standard deviation (a measure of average dispersion about the mean) may be computed. This particular standard deviation is called the standard error of the regression coefficient. It may be used to specify the 66, 95, and 99 percent confidence intervals within which the true coefficient value is likely to lie. As a general rule, the smaller the value of the SEC relative to its regression coefficient, the more reliable is the estimate of the regression coefficient.
(b) The t-value may be computed for each regression coefficient. In generalized inferential analysis, the "student's t-test" may be used to test for the significance of the difference between two sample means. Applied to regression analysis, the t-value may be used to test for the significance of the difference between the estimated regression coefficient and the mean of all such regression coefficients that could be estimated. Since the latter is unknowable, the t-value is usually computed for the difference between the estimated regression coefficient and zero. As such, it can only be used to ascertain the likelihood that the estimated regression coefficient is non-zero.
Once the t-value for a regression coefficient is computed, the analyst may consult a student's t-distribution table on the appropriate DF row to see where the computed t-value would lie. The t-table value just below the computed t-value identifies the column in the t-distribution table that specifies the significance level of the test. Suppose that the absolute value (unsigned) of the computed t-value for an estimated slope parameter is 1.73, with 60 degrees of freedom. A t-distribution table would show 1.73 lying between the values 1.671 and 2.000 on the 60 degree-of-freedom row. The column heading of the row containing the value 1.671 is the 0.1 significance level, implying that there is only one chance in ten that the estimated regression coefficient is not different from zero.
Problems with the Multiple Regression Context
There are several possible problems that may emerge in the multiple regression model context. All are consequences of violation of one or another of the assumptions or premises that underlie the multiple regression environment. Adjustments may be made to the data or the analysis to deal with some of the problems, but in cases of others the analysis should simply be aware of the likely effects.Multicollinearity. The most fundamental of the multiple regression assumptions is that the independent variables are truly independent of one another. Multicollinearity may be identified by the presence of non-trivial correlation between pairs of the independent variables included within the model. Multicollinearity may be detected by examining the correlation matrix for all of the variables contained in the model.
Multicollinearity is almost certain to be present in any autoregressive or polynomial regression model of order higher than 1st. Because the successive terms in a kth-order autoregressive model use essentially the same data as the first term, except shifted by some number of rows, the assumption of independence among the "independent" variables is clearly violated. Likewise, because the successive terms in a kth-order polynomial model employ the same data as the first term, except as raised to successively higher powers, the assumption of independence again is clearly violated.
Multicollinearity may also be present among the different independent variables included in the model, even if they are not autoregressive with the dependent variable, and even if they are each only 1st order. If two independent variables are linearly similar, i.e., very correlated with each other, it is as if the same variable were included two times in the model, thereby contributing its explanatory power twice, and thus amounting to so much "deck stacking." The usual effect of the presence of non-trivial multicollinearity is to inflate the standard errors of the coefficients of the collinear independent variables, rendering their computed t-values too low, implying excessively high levels of statistical significance (bad, since the lower the significance level the better).
Some statisticians prefer to remedy the presence of any non-trivial multicollinearity by removal of one or the other of the two collinear variables from the model. Others suggest that if there are good conceptual reasons for including both independent variables, they should both be retained in the model unless the multicollinearity is extreme (i.e., the correlation between the collinear independent variables approaches 1.00 in absolute value), or unless the analyst is particularly concerned about the statistical significance of either of the collinear independent variables. In this latter case, if the independent variables are time series, the analyst might try differencing the collinear independent variables and respecifying the model with the differenced series in place of the raw data series to see if significant information is contained in either of the collinear independent variables that is not also contained in the other.
Autocorrelation. Another of the premises underlying multiple regression modeling is that the forecast errors constitute an independent random variable, i.e., a random noise series. If there is a discernible pattern in the forecast error series, then autocorrelation is present in the dependent variable series. Autocorrelation may be detected by computing autocorrelation coefficients to some level of specified order of autocorrelation. Alternately, the analyst may construct a sequence plot of the forecast error series. The statistical software system may facilitate this procedure by allowing the user to have the forecast error series written to the next available empty column in the data matrix so that the sequence plot of that column may be constructed. If the forecast error series exhibits alternation of points above and below its mean, then the object series is negatively autocorrelated. Positive autocorrelation is present if the error series exhibits "runs" of points above the mean alternating with runs of points below the mean in a cyclical (or seasonal) fashion. The expected number of runs if the series is truly random noise may be estimated for comparison with the actual (by count) number of runs exhibited by the series. If the actual number of runs is smaller than the expected number, then autocorrelation almost surely is present in the dependent variable series.
The effect of the presence of autocorrelation within the dependent variable series is to render the r, F, and t statistics unreliable. In particular, the presence of autocorrelation will likely result in understated standard errors of the regression coefficients, thus causing overstatement of the t-values, implying better (i.e., lower) significance levels for the estimated regression coefficients than warranted. Although the estimated regression coefficients themselves are unbiased (i.e., not unduly specific to the particular data set), autocorrelation results in computed confidence intervals that are narrower than they should be.
Some degree of autocorrelation is likely present in every economic or business time series, and the analyst should probably ignore it unless it is extreme. As noted earlier in the chapter, one or more auto-regressive terms may constitute or be included in the regression model as the primary explanatory independent variables. If the analyst discovers the presence of non-trivial autocorrelation in a regression model that was specified without autoregressive terms, he might consider respecifying it to include one or more such terms as the means of handling the autocorrelation. The approach in this case is to try to use the autocorrelated information rather than purge it from the model.
Heteroskedasticity. The problem of hetero-skedasticity occurs if there is a systematic pattern between the forecast error series and any of the independent variable series. Homoskedasticity is the absence of such a pattern. Whether the model exhibits the property of heteroskedasticity may be discerned by having the forecast errors plotted against data for each of the independent variables in scatter diagrams. If the scatter of the plotted points exhibits any discernible path, then heteroskedasticity is present within the model.
If the regression model is non-trivially heteroskedastistic, the mean squared error and the standard error of the estimate will be specific to the particular data set; another data set may yield inference statistics that diverge widely from those computed from the first data set. Likewise, the inference statistics associated with the particular independent variables (SEC, t, and significance level) will also be specific to the data set. We shall leave the matter of heteroskedasticity with the warning to the analyst of the likely consequences for his model, i.e., that its usefulness for modeling may be strictly limited to the range of data included in the object series.
An Application
We conclude this chapter by applying the various models discussed here to data series presented in Tables 3A-1 and 3A-2. Figures 3A-4, 3A-5, and 3A-6 display results of specifying simple linear, polynomial, and multiple regression models.
Table 3A-1. Monthly data for series Y1. MONTH YEAR1 YEAR2 YEAR3 YEAR4 YEAR5 YEAR6 1 233.4 249.4 234.1 240.7 245.6 252.1 2 236.6 229.2 234.1 231.3 244.9 253.1 3 239.8 229.5 229.7 245.3 248.3 254.3 4 242.7 231.3 233.6 244.5 251.9 255.3 5 245.2 233.7 234.1 249.1 253.9 256.4 6 252.2 238.6 238.4 249.7 260.3 259.4 7 252.3 239.7 237.0 248.1 255.1 257.5 8 252.2 241.1 236.2 248.6 255.8 9 251.1 238.0 237.1 249.1 255.8 10 251.1 240.8 235.5 247.4 255.5 11 252.2 240.2 236.0 248.2 255.1 12 251.7 242.3 232.8 246.6 254.3Table 3A-2. Monthly data for series Y2 MONTH YEAR 1 YEAR 2 YEAR 3 YEAR 4 YEAR 5 YEAR 6 1 15.7 14.5 13.1 11.9 14.9 12.8 2 14.3 13.7 14.6 11.8 15.6 18.6 3 13.8 14.1 13.1 12.6 15.8 15.9 4 13.6 14.8 13.6 13.3 14.9 14.1 5 12.4 14.1 11.6 13.1 16.6 14.8 6 13.9 14.2 11.1 14.1 15.9 15.6 7 15.4 14.1 11.7 12.9 15.6 15.4 8 13.8 14.1 11.1 13.5 15.4 9 14.1 14.1 11.9 15.0 15.6 10 13.5 13.4 11.6 14.6 14.9 11 14.1 14.2 11.3 13.9 15.9 12 15.0 13.1 12.8 14.0 14.2
Figure 3A-4. Simple linear regression analysis of dependent variable Y1 against independent variable Y2.
Figure 3A-5. Polynomial regression analysis of dependent variable Y1 against independent variable Y2.
Figure 3A-6. Multiple linear regression analysis of dependent variable Y1 against Y2 and two other independent variables.
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CHAPTER 5. THE ANALYSIS OF VALUE AND RISK
Much of the substance of managerial economics is about marginal decision making affecting operations in the short-run time frame. Most of the rest of this text elaborates the marginal criteria for short-run decision making; this chapter is devoted to long-run decision considerations and the analysis of risk.
The Remoteness of the Long Run
In addition to the differences noted in Chapter 1 between long and short runs, a major distinction remains to set the long-run decision problem apart from short-run decision making. Since the effects of the long-run decision can be expected to impact the enterprise in the future, some recognition must be made of the remoteness of those effects. The sense of the problem is that the expectation of a benefit to be realized in the future is worth less to the decision maker than an equivalent benefit received immediately. Specialists in finance often refer to this phenomenon as the "time value of money," but the phenomenon would exist even in a barter economy (one that does not use money). The phenomenon is described by the ancient adage that "a bird in the hand is worth two in the bush." The problem pertains to costs as well as to benefits. In addition, costs that must be paid at some future time are also less meaningful to the decision maker than those that must be paid today, although the wise decision maker should plan and make careful arrangements to cover expected future costs.Since future possibilities are worth less than present realities, economists have acknowledged this phenomenon by discounting the expected future values at an appropriate rate. This rate is usually taken to be the best market rate of interest for which the enterprise can qualify. The interest rate is used as a discount rate on the premise that the equivalent of the expected future value, less the cost of interest, can be had at present by borrowing the future sum. This relationship should be true whether the borrowed principle and the interest to be repaid are expressed in barter or monetary terms.[1]
If we abstract from the possibility of a scrap value of the capital at the end of its useful life, the discount rate must be just sufficient to make the sum of the net income flows (i.e., revenues in excess of operating costs) over the life of the investment opportunity just equal to its capital outlay. The discount rate is interpreted as a rate of return because if all of the net amounts of the net income flows were invested at the interest rate, they and their interest earnings would add up to the capital outlay. The investment criterion that justifies undertaking the investment opportunity is that its rate of return is at least as great as the best market interest rate for which the enterprise can qualify.[2]
A Marginal Decision Criterion for the Long Run
The so-called "internal rate of return" (IRR) is the discount rate that equates the sum of the net income flows to the capital outlay. The IRR can be computed for each prospective investment opportunity currently under consideration by the enterprise's management. For example, suppose that the management of an enterprise is considering five prospective investment opportunities, designated A through E, that require the capital outlays and promise the internal rates of return reported in Table 5-1. These opportunities have already been arrayed in descending order of internal rates of return. When the capital outlays are "stacked" from left to right on a set of coordinate axes with capital expenditures on the horizontal axis and IRRs on the vertical axis as in Figure 5-1, the plotted points A through E constitute a downward sloping path that John Maynard Keynes called the "marginal efficiency of capital" (The General Theory of Employment, Interest, and Money, Harcourt, Brace & World, Inc., 1964, p. 135). Suppose that the enterprise can borrow funds from the capital markets at an interest rate i = 8 percent, represented by the horizontal dashed line. The marginal investment criterion then is to undertake additional investment opportunities in descending order of IRRs as long as the IRRs are at least as high as the interest rate. In the illustrated example, investment opportunities A, B, and C ought to be undertaken; opportunities D and E ought to be rejected because their rates of return would not be sufficient to pay the interest on borrowing to finance them.
Table 5-1. Hypothetical investment opportunities and internal rates of return.
Figure 5-1. IRRs and the interest rate.
We should note that the IRR as a long-run investment decision criterion is appropriate even if the enterprise can finance its capital outlays from internal sources. The rationale is that funds accumulated internally by depreciation allowances and retaining earnings have been (or could have been) "invested" on financial capital markets earning interest rate, i, that must now be foregone if the funds are used to finance the prospective investment opportunities instead.
Attitudes Toward Risk
Decision makers' attitudes toward risk may vary widely. People who have strong preferences for risk assumption may turn out to be chronic gamblers. Such people get their "kicks" from accepting adverse-odds bets (long shots) with negative expected values. Even though the odds are against them, it is more intellectually satisfying to them to win "big" on rare occasions than to gain small sums more frequently on favorable-odds bets. Risk preferers are likely to lose (on net balance) over the long run. Luckily for society (and themselves), they are in the minority. It is theoretically possible for a decision maker to be essentially risk-neutral, having neither preference for nor aversion toward risk. However, this is such a "razor's edge" state that few people find themselves there.The vast majority of all people who regard themselves as rational thinkers are risk-averse, and the more extreme of them are risk avoiders (they expect bad things to happen to them each morning as soon as they get out of bed). A normally risk-averse decision maker likely would not accept an even-odds bet on a two-possibility event (50 percent chance each way) because the loss of the sum at risk would mean more to them (negatively) than would the gain of an identical sum would mean to them (positively). It is likely that most business decision makers, who tend to be a conservative lot, are risk averse. This does not mean that they seek to avoid risk altogether (if so they would not behave as entrepreneurs); rather, they attempt to manage risk by seeking more information in order to diminish it, by attempting to take offsetting positions, or by attempting to insure against the risk.
If it were practical to specify personal utility functions for decision makers, it would be possible to include the decision maker's attitude toward risk as an argument (i.e., one of the independent variables) in the function. We might find the risk preferer to "consume" risky items under conditions of increasing marginal utility, the risk-indifferent decision maker to exhibit a linear risk utility function, and one who is averse to risk to experience diminishing marginal utility with respect to risk.
Means of Dealing with Risk
A first approach to dealing with risk is to seek more information about the decision alternative. Additional information often reveals that the range of outcome variability is narrower than at first thought, and that the decision alternative is thus less risky than earlier imagined. But information itself is a scarce resource that is costly to acquire. The determination to acquire additional information is a managerial decision that is based on a comparison of the benefits of the additional information relative to the cost of acquiring it. At some point, the benefits of acquiring additional information must be judged as not outweighing the costs, and the decision must be made under conditions of uncertainty or risk. The decision maker must then find some way to deal with (i.e., manage) the remaining risk, possibly by insuring against it, offsetting it (possibly by hedging), or by simply accepting it. One of the essential functions of an entrepreneur is to assume risk in undertaking new ventures or in changing the operation of the enterprise.Since it has not been found practical to specify utility functions, we shall take a more intuitive approach to how decision makers might deal with risk. A potentially useful concept for short-run decision analysis is that of the certainty equivalent. In this approach, the decision maker must ask himself what certain sum he would be willing to accept in lieu of the risky outcome at issue. The risk-averse decision maker can be expected to indicate a lesser certain sum than the risky possibility ("a bird in the hand is worth two in the bush"), whereas the risk preferer would have to have a larger certain sum as a compensation for the insult of removing the gamble from his consideration.[3]
Another approach is possible in the analysis of risk in the long run. A subjectively determined risk premium may be added to the interest rate that serves as a discount rate. The risk premium serves as a risk adjustment to the discount rate in computing the value of the investment opportunity. The risk-adjusted value will be smaller than before risk adjustment in reflection of the larger discount factor. The risk-adjustment factors will differ from one decision opportunity to another, but their values, adjusted for risk, will be more realistic selection criteria.
Allowing for Anticipated Inflation
Finally, we should note that neither discounting to allow for the time value of money nor risk-adjustment of the discount rate constitutes an allowance for the risk of inflation. If over the life of a decision opportunity inflation is expected to ensue, a deflation factor (i.e., an inflation risk adjustment factor) may be added to the interest rate and other risk adjustment factors that serve as discount rate to the value of the investment opportunity.[4] Each deflation factor is a decimal equivalent, e.g., .04, of an anticipated rate of inflation, e.g., 4 percent. The deflation factors may differ from term to term if inflation is thought likely to accelerate or decelerate over the life of the decision opportunity.
Decision Making Under Uncertainty
Suppose that a decision maker simply cannot in any meaningful way assess the probabilities of the possible outcomes of an investment opportunity. How can the decision maker decide whether or not to invest in the venture described in the Regret Matrix of Table 5-2? Under the "maximin" decision rule, the decision maker would examine the worst-case scenarios, $0 for not investing and -$1 million if the investment is undertaken and fails; the choice under this rule would be not to invest because it yields the least of the worst scenarios.
Table 5-2. Regret Matrix for Investment Decision.
The minimax regret rule, however, yields a different conclusion. A so-called "payoff matrix" may help to illustrate the computations. In Table 5-2, columns (1) and (2) show the outcomes of the invest and do-not-invest alternatives if successful or failures. Columns (3) and (4) show the "regrets" associated with each outcome if selected relative to the best possible outcomes of success and failure. The regrets in column (3) are computed by subtracting each entry in column (1) from the highest-valued entry in column (1). Likewise, the regrets in column (4) are computed as the differences between each entry in column (2) and the highest-valued entry in column (2). The zeros in columns (3) and (4) result from subtracting the highest-valued entries from themselves. According to the minimax regret rule, the alternative with the least regret of not selecting the best outcome should be chosen. In the example above, a much larger regret ($4 million) would be suffered from not investing if the investment turns out to be successful than would be realized ($1 million) from investing that is not successful. Therefore, under this rule the decision maker should choose to invest.
What's Ahead
The decision problem is a complex phenomenon with many dimensions. The next two chapters are devoted to an examination of the means for analyzing patterns of behavior and the procedures for modeling behavioral relationships.
Chapter 5 Endnotes:
[1] If we let the symbol i stand for the interest rate that will serve as discount rate, the present value of the expected future outcome can be expressed as
[2] In the present value formula (1), values for V and i are known or estimated, and the value of PV is computed.
An alternative version of the present value formula permits computing the so-called internal rate of return,
[3] The certainty equivalent, CE, of the risky outcome, V, is substituted in the numerators of the ratios in the expected value (1) and present value (2) formulas:
For a risk averse decision maker, CE < V; where the decision maker is risk indifferent, CE = V; and in the case of a risk preferer, CE > V.
[4]In the present value formula (2), a subjectively determined risk premium, a, is added to the interest rate discount in the denominator,
The premium constitutes a risk adjustment to the discount rate, i.
[5] A deflation factor, d, may be included in the denominators of the terms of the present value equation,
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PART B. TOOLS OF ANALYSIS
APPENDIX 5A. MARGINAL UTILITY AND RISK
Marginal Utility and Risk
The conditions under which a decision maker realizes satisfaction (i.e., utility) with respect to income (whether monetary or "in kind") are thought to influence his attitude toward risk. Three possible shapes of total utility functions are illustrated in Figure 5A-1. For decision maker A, utility increases at a constant rate as income increases. Decision maker B's utility increases at a decreasing rate (the utility function, though positively sloped, is concave downward). This illustrates the principle of diminishing marginal utility, and is thought to be descriptive of typical human behavior with respect to the receipt of income. Decision maker C realizes additional utility at an increasing rate as income increases (i.e., the curve is concave upward). Although this utility pattern is thought to be atypical of human behavior except in the very early stages of consumption, it would illustrate a phenomenon of increasing marginal utility. In all three cases, the utility function is extended into graphic quadrant III (negative values for both income and utility) for purpose of illustration. Although utility is hardly measurable, and certainly not comparable from one decision maker to another, we shall indulge in the heroic assumption of the same numeric scale on the vertical axis of all three graphs.
Figure 5A-1. Possible shapes of total utility functions.
Suppose that these three decision makers are all presented with an investment opportunity that requires a capital outlay of $1 million, and which can be expected to result in only two possible outcomes, success yielding a $5 million return, or failure yielding a zero return. Although the three decision makers might estimate widely divergent probabilities of success and failure, for purposes of argument let us for the moment suppose that all three accept a conventional wisdom that 80 percent of such ventures are doomed to failure, but 20 percent succeed. The expected value of such an investment opportunity may be computed as follows:
EV = $4 million x .2 - $1 million x .8
EV = $800 thousand - $800 thousand = $0.
The expected value of the decision alternative not to invest (which will require no capital outlay and yield no return) is also $0. On the basis of expected value of the returns, it would appear that all three decision makers should be indifferent between the decision to invest and not to invest (indeed, since the expected value of the opportunity is $0, why bother?).
However, an examination of their expected utilities (a probability weighted average of the utilities that they would realize) reveals a different story. The expected utility for decision maker A may be computed as
which is the same utility realized from not investing. In this case, the conclusion is identical to that reached by examining the expected value of the opportunity.
Decision maker B realizes additional utility under conditions of diminishing marginal utility. The expected utility may be computed as
Decision maker B would suffer an absolute loss of utility if the investment were undertaken, and would therefore prefer to realize a utility of zero from not investing.
The expected utility for decision maker C, who realizes additional income under conditions of increasing marginal utility, may be computed as
Decision maker C would enjoy a net of 74 units of utility from undertaking the investment compared with zero units from not investing, and therefore can be expected to proceed with this "long shot."
Although there is no direct linkage here between marginal utility and risk, there is a rather strong presumption that decision maker B's diminishing marginal utility implies that he is risk averse, while decision maker C's increasing marginal utility leads to a preference for risk. Decision maker A's constant marginal utility function results in indifference with respect to risk.
Several important managerial implications follow from this analysis. One is that the expected value of a decision alternative is a good selection criterion only in the case of a decision maker who realizes increased satisfaction at an approximately constant rate. Alternately, if the marginal utility for a decision maker is approximately constant in the neighborhood of the EVs of the available decision alternatives, the EVs may serve as adequate selection criteria. For other decision makers who realize increased satisfaction at decreasing or increasing rates, it is necessary to consider the expected utilities of the decision alternatives.
Even slightly different assessed probabilities may change the decision picture significantly. Suppose that the probability of success decreases to 15 percent, while the probability of failure rises to 85 percent. The recomputed expected value and expected utilities are as follows:
EUA = 400 x .15 - 100 x .85 = -25 units of utility
EUB = 270 x .15 - 150 x .85 = -87 units of utility
EUC = 650 x .15 - 70 x .85 = 38 units of utility
In this case, the expected value is negative and decision makers A and B would rationally choose not to invest. But decision maker C would realize positive utility from the investment, even though the expected value of the venture is negative! Such a decision maker who experiences increasing marginal utility of income strongly enough to induce him to accept an adverse-odds venture with a negative expected value is surely a gambler.
If the probability of success rises to 25 percent while the probability of failure of the venture falls to 75 percent, the computed expected values become:
EUA = 400 x .25 - 100 x .75 = 25 units of utility
EUB = 270 x .25 - 150 x .75 = -65 units of utility
EUC = 650 x .25 - 70 x .75 = 110 units of utility
Under these probability circumstances, the expected value of the venture is positive, but decision maker B is still so risk averse due to diminishing marginal utility as to be unwilling to undertake it. This is because the prospect of losing $1 million in case of failure means so much more than the prospect of gaining $4 million in case of success of the venture. Decision maker B would hate losing $1 million more than the enjoyment of gaining $4 million. The reader should confirm that in order for risk-averse decision maker B to realize a positive expected utility from the venture, the probability of success would have to rise to 36 percent.
In the real world, three decision makers would likely experience not only different utility conditions, but may also come up with different assessments of the probabilities of success and failure of the decision alternatives before them. This means that two or more decision makers examining exactly the same decision opportunities may reach widely divergent conclusions about them. For example, suppose risk averse decision maker B assesses the probability of success of the venture at 36 percent, which would yield a positive expected utility, while risk preferring decision maker C assesses the probability of success at only 9 percent, which would yield a negative expected utility. Under these circumstances we might witness the irony of the risk averse decision maker undertaking the venture while the risk preferer rejects it.
A Return-Risk Preference Function
Theoretically, a preference function relating satisfaction (or utility) to risk and return may be constructed for a decision maker. Practically, the specification of such a preference function is difficult if not impossible to achieve. A functional notation representation of such a preference function might appear as
where U is the amount of utility realized by the decision maker, V is the value of the return from a decision alternative, and s indicates the risk associated with the opportunity. The argument (1-s) is the complement of the amount of risk incurred, or the "degree of certainty" that a particular outcome within the range of all such possible outcomes will occur. We ignore the characterization of "certainty" as an absolute so that we can understand it as exhibiting varying degrees.
Graphically, such a preference function for a normal decision maker might appear as depicted in Figure 5A-2. Risk (degree of uncertainty) and return occupy the floor axes of the three-dimensional graph; utility is measured in the vertical dimension. The right-hand side of the utility surface can be identified because the degree of certainty reaches a maximum, i.e., the degree of risk approaches zero. But the left-hand end of the risk-certainty axis cannot be specified since risk may increase without bound. The utility surface may be "sliced" parallel to the floor and at any altitude of utility. Four such slices are illustrated in Figure 5A-1, and their vertical projections down into the floor of the surface have been drawn. These projections constitute so-called "indifference curves" for the two phenomena represented on the floor axes, i.e., return and degree of certainty. Any number of such indifference curves may be constructed by slicing the utility surface at any chosen utility altitudes.
Figure 5A-2. A utility surface for certainty and return.
Figure 5A-3 depicts a map of selected indifference curves generated from the utility surface illustrated in Figure 5A-2. In effect, the map depicted in Figure 5A-3 is the sliced surface of Figure 5A-2 viewed "from above." In Figure 5A-3, a movement from left to right along the horizontal axis represents an increase of certainty about which outcome within the range of all possible outcomes will occur (and implicitly a narrowing of the range of possible outcomes). At the right end of the horizontal axis, the decision maker may be certain that there is only one possible outcome, and thus that risk is minimal (or zero). Risk therefore increases from right to left along the horizontal axis, but the left end of the axis may not be specified in the sense that risk may increase with-out bound. Any point in the coordinate space of the map represents some combination of risk and return, and each point lies on some indifference curve, such as I2, for a certain level of utility. Any movement along I2 would leave the decision maker in a state of indifference. For example, the movement from point A to point B would result in an increase of risk (a "decrease of certainty"), for which the decision maker would have to be compensated by an increase of return in order to remain at the same level of utility. Or, at the higher return associated with point B, the decision maker would tolerate more risk (less certainty). The indifference curves for a more risk-averse decision maker would be more steeply upward sloped (right to left) because such a decision maker would require even greater return for each level of risk.
Figure 5A-3. A risk-return indifference map.
The determination of a risk adjustment factor may be illustrated by an indifference map that is a variation upon that illustrated in Figure 5A-3. Figure 5A-4 depicts a decision maker's indifference map with risk on the horizontal axis and percentage rates of return on the vertical axis. In this case, the procedure is first to find on the right-hand vertical axis the current riskless return on something like a government bond, say 8 percent. This identifies the relevant indifference curve, I4, which may be followed. Then, when the risk factor, v1, for the decision opportunity is computed, a vertical may be erected at v1 on the horizontal axis to intersect indifference curve I4 at point D. At point D the decision maker is indifferent between the low return on the riskless government bond and the higher return on the risky decision opportunity. A horizontal may be drawn from D to the right-hand vertical axis to find the higher return, 10 percent as illustrated. In the denominator of the present value formula, the value of i is taken to be 8 percent, and the risk premium a is 2 percent (i.e., 10 percent minus 8 percent). If the market interest rate on government bonds changes, then some other indifference curve would become relevant and a new risk premium found in similar fashion.
Figure 5A-4. Risk adjustment factor in a risk-return indifference map.
The illustrated procedure for determining the risk adjustment factor is operational only if the decision maker's preference function can be specified (heroic at best), but this model does illustrate the thought process that must be used by a rational decision maker in selecting a risk adjustment factor. There is no scientific way to specify a schedule of either certainty-equivalent or discount rate adjustment factors. These are such highly subjective matters that they must be left to the personal judgment of each decision maker. This is one reason that different decision makers, confronted with the same scenarios and information, can reach such different investment conclusions. The naive or inexperienced decision maker may have no ability at all to determine either certainty equivalents or discount adjustment factors. The ability to determine either will come only with time and the accumulation of a stock of experience in considering risky alternatives.
Although it may not be practical to specify preference functions, the certainty equivalent approach may be illustrated by the risk-return indifference map in Figure 5A-4. The map is reproduced in Figure 5A-5 with dollar amounts (rather than rates of return) on the vertical axis. The preference function illustrated in this map is for a normally risk-averse decision maker. Suppose that a decision opportunity promises a return of $6000, but entails a risk of v1. This particular combination of risk and return lies at point C on indifference curve I3. If we now follow indifference curve I3 downward to the right until the vertical axis is reached, we find that it intersects the vertical axis (where risk is zero) at $3000. The sum of $3000 is thus the certainty equivalent of the $6000 return that entails risk v1. The certainty equivalent of any other risky sum may be found in similar fashion. The reader may imagine the appearance of an indifference curve map for a decision maker who prefers risk.
Figure 5A-5. Certainty equivalent and the risk-return indifference map.
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CHAPTER 6. THE MARGINAL IN DECISION ANALYSIS
A veritable revolution in economic thought ensued in the 1870s. This revolution brought into economic analysis the use of calculus, the branch of mathematics that analyzes small changes in mathematical functions. The tools of the calculus were first developed by Isaac Newton and Gottfried Leibniz (working independently of each other) in the latter half of the 17th century. Although there were numerous forerunners of the use of calculus in economics, one name stands out in the development of the analysis of marginal change in economics: William Stanley Jevons (1836-82). Jevons, an English economist of the Classical School, first described a "final degree of utility" in a paper read in 1862. But it was not until the publication of his Theory of Political Economy in 1871 that the world at large was made privy to his description of the effects of consuming successive units of food. Jevons referred to the analysis of such effects as "a Calculus of Pleasure and Pain." Indeed, it was this introduction of the principles of derivative calculus into economic analysis that fomented the marginalism revolution and initiated the Neoclassical Era of economic thought.
The ensuing development of the analysis of change at the margin in the theories of consumer behavior, production, and costs has yielded a powerful analytical tool to theoretical economists. Its impact in applied economics lies in the provision of decision criteria for marketing, production, and financial decision makers.
The Applicability of Marginal Analysis
As noted in Chapter 2, the types of managerial decisions range from selecting one among several alternative courses of action to deciding to accelerate or retard some activity already under way. If the choice involves a discrete change or discontinuity of operations, as for example in most entrepreneurial decisions, then marginal analysis may not be applicable. Examples of decision contexts that are not particularly amenable to marginal analysis are the initiation or termination of business, the selection of items to produce or carry in inventory, the construction of a new plant or the disposition of an old one, and executive hires or fires. Such discrete changes in operations are usually associated with the long run, a period of time that is long enough to allow changes in all matters within the decision maker's realm of responsibility.Marginal analysis comes into its own when a process under way changes in a relatively smooth, continuous fashion. Such changes occur within a short-run time frame when at least some matters are not amenable to alteration by the decision maker, for example, the size or capacity of the productive facility. Where a process may change smoothly and continuously, the decision maker needs a criterion for deciding to do more or less of what is already being done. An example might be to produce a larger or smaller quantity of an item in the enterprise's product line.
Even if the process does change in a smooth and continuous fashion, marginal analysis is "information hungry" in the sense that it presumes that the decision maker already possesses a substantial amount of information about the likely consequences of advancing or retarding the rate at which the process is occurring. Such prior information can only be based upon an accumulation of historical experience, either the decision maker's own or someone else's. Marginal analysis cannot provide a useful decision criterion for how much of a newly invented item to produce in the first production run.
There is a broad range of decision contexts to which marginal analysis may be applied, even when the restrictions noted above are recognized. These include whether to increase or decrease the rate of production (or to keep on doing so), whether to use more or less of a particular productive input, and whether to raise or lower the price of an item. Marginal analysis has been extended to bridge the distinction between the short and long runs by providing criteria for adding or deleting items from the product line, and increasing or decreasing the enterprise's capital investment.
The Marginal in the Decision Process
We shall assume that the decision maker is responsible for some process that changes in a relatively smooth and continuous fashion, and that the decision maker has access to a stock of accumulated experience with the behavior of the process. The decision maker's concern then is whether to expand or contract the process, and in either case to keep on doing so.Any productive process is affected by a number of deterministic forces. It is usual to refer to the result or outcome of a productive process as the "dependent variable", while the deterministic forces are referred to as "independent variables". The independent variables are the potential means by which control is exerted over the productive process by a decision maker. Many of these independent variables are simply environmental constraints or conditions that affect the dependent variable but are not amenable to control by the decision maker. As a simplification, we shall assume that the decision maker has direct control over only one of the independent variables, and that all other independent variables are environmental matters not amenable to control by the decision maker, at least in the short-run decision framework. These other independent variables then may be assumed to be constant (or given, or accounted for). This assumption allows us to focus attention upon the relationship between the dependent variable and the one independent variable that the decision maker can control.
To illustrate the benefit of knowing marginal relationships, let us first suppose that in the process under decision making control, currently the amount of the dependent variable (y) is 7 when the value of the decision variable (x1) is 13. (We keep in mind that there are other independent variables, x2, x3, etc.) This may be graphed as point A, located at (x,y) coordinates (13, 7) in Figure 6-1. We may also suppose that it is the objective of the decision maker to increase the amount of the dependent variable (although there are circumstances in managerial control where a smaller amount of the dependent variable might be deemed desirable). On the basis of this so-called "total" information (i.e., the total amount of the dependent variable when the decision variable value is 13), should the decision maker increase the amount of the decision variable to 14 (or some higher value), or decrease it to 12 (or some lower value)? The simple fact is that there is no way to tell from the information considered thus far.
Figure 6-1. Initial values of dependent and independent variables.
Suppose that the decision maker can estimate from his accumulation of past experience that point B at coordinates (14, 8) in Figure 6-2 will likely be achieved when the decision variable is increased by one unit (by assumption the smallest amount by which the decision variable can be changed). In this simple example, the ratio of the Dy/Dx1 when Dx1 = 1 is referred to by economists as the marginal y, or the marginal increase of the dependent variable consequent upon a one-unit change of the decision variable. The value of the marginal in this example is a positive number. (In subsequent discussion we will note circumstances in which the magnitude as well as the sign of the marginal is significant). The decision maker can now use this information as a decision criterion. He may be confident that when the marginal value of y is positive, an increase of decision variable x1 will increase the value of y, the object of his control. We note in passing that the ratio Dy/Dx1 measures the slope of a line passing through points A and B, and that the line slopes upward.
Figure 6-2. A second estimated point.
But suppose, as illustrated in Figure 6-3, that when the decision variable value is increased from 13 to 14, the amount of the dependent variable decreases to 6, reaching point C at coordinates (14, 6). In this case the positive one-unit change of the decision variable resulted in a one-unit decrease of the dependent variable. Thus, the value of the marginal y, Dy/Dx1, is now a negative number and the line passing through points A and C slopes downward. The negative marginal y can serve as a decision criterion. When the marginal y is negative, the decision maker should expect an increase of his decision variable x1 to result in a decrease of the amount of y, the object of his decision making. If his objective is to increase the value of y, he should then decrease the value of the decision variable x1 when the marginal y is negative. (The reader is encouraged to consider how information about positive or negative marginal y values should serve as decision criteria when the objective is to decrease the value of y, as for example when production costs are the concern of managerial decision making.)
Figure 6-3. A decrease of the dependent variable.
The examples considered thus far have been ideal in the sense that Dx1 was one unit (assumed to be the smallest amount by which x1 can be changed) in both cases. This enables us to refer to the ratio of Dy/Dx1 as the marginal y. However, the real world rarely allows a one-unit change of a decision variable like x1. We should therefore note that when the change of the decision variable Dx1 is not one-unit, the ratio Dy/Dx1 does not accurately measure the marginal y, although it may be an approximation to the marginal y with some error depending upon how large is the change of x1. In subsequent discussion, we shall refer to the ratio Dy/Dx1 where Dx1 is larger than one unit as the incremental y.
The significance of the incremental y is that while the marginal y is the appropriate decision criterion, it is rarely observable; the incremental y, though commonly observable, is only an approximation to the marginal y, and thus may serve only imperfectly as a decision criterion. The wise managerial decision maker should be cautious in employing an observable incremental y as a decision criterion. The incremental y will almost certainly be of a different magnitude than that of the marginal y, and it may be of different sign as well if the Dx is relatively large.
The Marginal to Find a Maximum Value
We have now established the usefulness of the y marginal in deciding whether to increase or decrease the value of a decision variable like x1. The value of the slope of the graph of a mathematical function of a dependent variable at some value of a decision variable like x1 measures the y marginal. The y marginal at various points along a function can be measured by the slopes of tangents to those points, e.g., R, S, and T in Panel (a) of Figure 6-4. Panel (b) illustrates the graph of the marginal y function (the so-called first derivative of the function), where y might be revenue, cost, or product. The slope of a tangent to the parabola at point R in Panel (a) is positive, so the y marginal in Panel (b) is positive at point r. The slope of a parabolic function becomes ever shallower as the peak of the parabola is approached. At the peak itself, the slope of a tangent to the function is zero, i.e., the tangent is horizontal as at point S in Panel (a). The zero value of the slope at point A in Panel (a) corrersponds to the value zero at point s in Panel (b). At any point past the peak, like point T in Panel (a), the slope of the tangent is negative, so the y marginal is negative at point t in Panel (b). It is the behavior of the marginal that permits us to find the maximum (or minimum) value of a function, but the slope of the tangent to the function (i.e., the marginal y) is zero at the peak or trough. The use of the calculus to find the peak or trough of a function is described in Appendix 6A.
Figure 6-4. The graph of the marginal to a parabolic function.
Multiple Independent Variables
To this point we have assumed that all independent variables but one are constant, and that there is only one dependent variable. As noted in Chapter 2 in discussing the dimensions of the decision problem, it is possible (and probably not uncommon) for a decision maker to have to deal with two or more decision variables (x2, x3, etc.). Appendix 6A explores the facilities of the calculus to address decision contexts with multiple independent variables that cannot be assumed constant.
Multiple Dependent Variables
It is also possible for a decision maker to be confronted with multiple goals for simultaneous pursuit, i.e., multiple dependent variables. The decision maker is lucky if two or more of the goals are compatible with a common strategy. An analogy from ballistics is where two or more targets can be lined up and hit by the same projectile. Otherwise the decision maker may be torn among several conflicting objects of pursuit. A principle drawn from the algebraic theory of simultaneous equations (n unknowns require n equations for their solution) and that is often applied in macropolicy is that as many policy tools (or weapons) are required as there are incompatible problems to be dealt with (or targets to be hit simultaneously).If the decision maker cannot bring to bear as many means as there are conflicting goals to pursue, it will be necessary to select one goal for primary pursuit, and then regard all other goals as subordinate to the selected primary goal. Kenneth Boulding has noted the manager's difficulty in keeping these goals subordinated to the one selected for primary pursuit ("The Ethics of Rational Decision," Management Science, February, 1966). Although the manager may simply give up pursuit of the subordinate goals in favor of the primary goal, in some circumstances it may be possible to incorporate them into the decision making process so as to regard them as constraints upon the pursuit of the primary goal. The term applied to this process is optimization, which we shall take to mean maximization (or minimization) subject to constraint(s). Two mathematical tools for optimization, the calculus and linear programming, are examined in Appendix 6A and Appendix 6B , respectively.
APPENDIX 6A. CALCULUS AND THE MARGINAL
Calculus and the Marginal
As an analytical convenience, suppose that a productive process can be represented in mathematical functional notation,
where y, the dependent variable, is the object of the decision maker's control. The independent variables, x1, x2, ..., xn, are the potential means by which control is exerted. The slash inserted in functional notation statement (2) indicates that all variables listed to the right of it are assumed constant:
In order to illustrate how the calculus can be brought to bear upon marginal analysis, let us suppose that the relationship given in functional notation statement (2) can be specified (or estimated employing appropriate statistical procedures) by an equation of some order, say 2. The highest power of a term in such an equation is the squared term. The format of a second order (or quadratic) equation is
The terms a, b, and c are constants that specify the way in which the dependent variable y relates to (or is affected by) the independent variable x1. We note that independent variables x2,...,xn do not appear in equation (3) because they were assumed constant in functional notation (2). Suppose that in a particular specification of the equation, the constants a, b, and c take on the values 288, 64, and -2, respectively (the estimation of these values is discussed in Appendix 3A),
This equation, which plots as a parabola oriented about a vertical axis and opening downward (i.e., vertex pointing upward) as depicted in Fig 4-4, might well represent a total revenue function for a business firm.
The marginal y can be computed for any one-unit change of x1, say from x1= 4 to x1= 5 as the slope of a chord connecting points A and B in Figure 6A-1. The value of y increases from 512 to 558 (found by solving equation (4) for x1 values of 4 and 5) an increase of 46 units. Hence, the marginal y over the 4 to 5 range of x1 is 46. Thus when Dx1 = +1, Dy = +46, and the ratio of Dy/Dx1 = 46/1 = 46.
In the calculus, the derivative of a function that measures the rate of change of the function is conventionally represented as dy/dx, read "the derivative of y with respect to x." The value of the derivative may be computed by the formula
Figure 6A-1. The graphic plot of a second-order equation.
This limit measures the slope of the function at a point on the function. The slope can be represented graphically as a tangent to the function at the point. This concept differs from the economist's concept of the marginal only in that in the denominator of the marginal ratio, Dx, takes on the value 1, which is assumed to be the smallest possible change of x, whereas the denominator of the derivative is presumed to approach, but not reach, zero. Thus, the mathematician's concept of the derivative approximates the economist's concept of the marginal. The practical value of this coincidence is that if the economist knows the equation of a function, (the subject of Chapter 4) he or she may compute the derivative of a function at a particular value of x to serve as a measure of the marginal y value.
Employing conventional differentiation formulas (described below), the derivative of equation (4) is
Thus, when x1 is 4, the value of the derivative is 64 - 4(4) = 48. When x1 is 5, the value of the derivative is 64 - 4(5) = 44. These two values lie on either side of the value previously computed using the marginal ratio over the range of x1 from 4 to 5.
The important consideration then is that the process of differentiation estimates the slope of the function at a point on it (i.e., when x1 = 4 or when x1 = 5), but the marginal is computed over the range between two points that are separated by only one unit of x1 (in this case between 4 and 5). The differential of the function y estimates the slope of the function at either end of the range; the marginal computes the slope over the one-unit range. The differential is thus a close approximation to the marginal (and vice versa). It is for this reason that economists feel confident in employing differential calculus to estimate the values of marginals.
We can employ an application of differential calculus to compute the value of the independent variable x1 that yields a maximum value of the dependent variable y. Since the slope of a function is known to be zero at its peak (or its trough), the method is simply to set the derivative from equation (5) equal to zero and solve for the value of x1:
The conclusion of this operation is that the function reaches a maximum y value when x1 = 16. The maximum may be computed by entering 16 for x1 in the original equation (4),
Thus, when x1 = 16, y attains its maximum value of 800. The reader is invited to confirm this conclusion by trying x1 values on either side of 16, e.g., x1 = 15 and x1 = 17, to confirm that y is less than 800 in both cases.
The same methodology may be employed in the case of a function that reaches a trough rather than a peak, but without actually plotting points on a function it may not be obvious that a particular equation reaches a peak or a trough. Here the mathematician's concept of the second derivative may help to discern which, peak or trough, has been reached. The second derivative is the derivative of the first derivative; it measures the rate of change of the rate of change of the original function, i.e., the rate of acceleration of the original function. Economists regard the second derivative function as the marginal to marginal function, or the rate at which the marginal function changes.
Figure 6A-2 illustrates in its panel (a) the graphic plot of an idealized third order (cubic) function of form
The cubic function has two directions of curvature separated by an inflection point at A. Panel (b) illustrates the associated first derivative or marginal function, of form
Figure 6A-2. Graphs of an original third-order function and its first and second derivatives.
The first derivative function is of one order lower than the original function, and has one fewer directions of curvature than does the original function. We note that the peak of the first derivative function occurs at the same x1 quantity at which the inflection point of the y function occurs. The second derivative function also attains zero y values at the levels of x1 at which the original y function reached both minimum and maximum.
Panel (c) illustrates the associated second derivative function of form
The second derivative function is one order lower than the first derivative function, and two orders lower than the original function. It has one fewer directions of curvature, in this case being linear, than does the first derivative function.
It is important to note that since the first derivative function reaches a value of zero when the original function is at either minimum or maximum, it is not possible without plotting the graphs of the functions to know from computing the first derivative alone whether the original function has reached a maximum or a minimum. However, the second derivative provides a solution to this problem. Since, in Figure 4-6, the first derivative cuts the horizontal from below and is thus positively sloped at the x1 value for which the original function is at a minimum, the value of the second derivative function is positive at this level of x1. It is also true that the first derivative cuts its horizontal from above, and is thus negatively sloped at the x1 level at which the original function is at maximum. Hence, the second derivative exhibits a negative value when the original function is at a maximum.
It is knowledge of these relationships that allows us to reverse the process and identify whether the original function has reached a maximum or a minimum without plotting its graph. The procedure is to:
b) Set the first derivative equal to zero and solve for the value(s) of x1. At these values of x1, the function reaches either a maximum or a minimum value of y, a fact that cannot yet be discerned.
c) Compute the second derivative of the function and evaluate the second derivative at the x1 values for which the first derivative is zero. The criterion is that if the value of the second derivative is positive, an original function minimum has been identified; and if the value of the second derivative is negative, an original-function maximum has been found.
This application of the calculus has served economists and managerial decision makers well in the cases of a number of economic situations, including those of both production functions and revenue functions. However, there is an important class of economic functions for which these procedures will fail, and we should thus note that they are not applicable to these functions. Specifically, total cost functions, whose estimated equations typically plot as illustrated in Figure 6A-3, never reach either maximum or minimum values for y.
Figure 6A-3. A total cost function that does not reach maximum or minimum.
While the marginal to a cost function can be computed by derivative calculus, when the derivative is set equal to zero, the y value solved for will be infinite. There is thus no point in asking where total costs reach minimum or maximum values (they never do); economists, however, do analyze the average or per-unit functions that can be derived from the total function (e.g., average total cost), and find that the average function can be expected to attain a minimum value. Thus, the derivative calculus can be used to discover the value of x1 for which the average function reaches minimum even though the total cost function reaches neither minimum nor maximum. Functions of this type are examined in Chapter 10.
Multiple Independent Variables
An extension of the derivative calculus enables treatment of two or more independent variables. Functional notation statement (2) may be rewritten to accommodate two explicit independent variables, all others assumed constant:
An example of an equation containing two independent variables is
This particular equation is of second order in both x1 and x2, but an equation could be specified to any order in as many independent variables as the analyst wishes to include.
When two or more independent variables are present, the calculus enables the differentiation of the function with respect to each independent variable. In computing each derivative, all other independent variables are treated as if they are constants, and the derivatives, called partial derivatives, are signified by the lower case of the Greek letter, d. In computing the partial derivative of y with respect to x1, the variable x2 is taken to be a constant (the derivative of which is zero):
In computing the partial of y with respect to x2, the variable x1 is taken to be a constant:
Each of these partial derivatives then represents the rate of change of the y function when one variable changes but the other does not change. The graph of a function like (10) and equation (11) would be three dimensional with a parabolic appearance such as that in Figure 6A-4. Here u and v are the x1 and x2 coordinates of the point directly below the peak of the surface. Supposing for the moment that u and v are known coordinates, if we were to move a point such as r along the path from v toward t, we could observe that the slope of the surface, as measured by a tangent to the surface at r, becomes ever shallower until it is zero at the peak. Likewise, if a point such as s is moved along the path from u toward t, the slope of the surface as measured by a tangent at s would also become ever shallower, and also reach zero at the peak. It is knowledge of this behavior that allows us to find the values of u and v when they are unknown.
Figure 6A-4. The graph of a second-order function with two independent variables.
The unknown values of u and v may be found by setting the partial derivatives (12) and (13) equal to zero,
and solving the pair of equations simultaneously for x1 and x2 to find that x1 = u and x2 = v. Once these values are known, they may be substituted for x1 and x2 in the original function equation (11) to find that
Thus the maximum value of y is t, which occurs when x1 = u and x2 = v.
An example of this application of partial differentiation occurs in the case of a production relationship where the amount of output, y, is determined by two inputs, x1 and x2. Such a function graphs as a three dimensional surface similar to that depicted in Figure 6A-4. Suppose that the productive process may be simulated by the equation
The objective is to find the maximum value of y that it is possible to produce when there are no limits on the availability of the x1 and x2 inputs. The first step is to compute the partial derivatives of output with respect to each of the inputs:
Next, these partial derivatives are each set equal to zero to form differential equations that may be taken together as a system of simultaneous equations to be solved for the values of x1 and x2:
The second equation may be multiplied through by 2,
and added to the first equation in order to eliminate the x1 variable and solve for the value of the x2 variable,
Then, 8 may be substituted for x2 in one of the differential equations in order to solve for x1,
We note that the second derivatives, i.e., the derivatives of the first derivatives, are both negative,
This confirms that the output reaches a maximum value when x1 = 9 and x2 = 8. We may find the maximized value of output by substituting these numbers in the original equation,
The conclusion is that 155 units of output is the most that can be produced from this production process.
While the examples illustrated here include only two independent variables in the equation of the function, more than two may be dealt with by computing the partial derivatives of the function with respect to each of the independent variables in their turns. If there are n independent variables in the equation, then n partial derivatives may be computed. Each may be set equal to zero, and the resulting set of equations solved simultaneously to find the values of the independent variables that maximize (or minimize) the value of the dependent variable. It is not possible to render a graphic representation of a function with more than two independent variables.
Multiple Goals
Multiple decision goals may be expressed as dependent variables in model equations. The differential calculus as a means of optimizing a set of goals is a powerful but limited procedure. Its power lies in its ability to treat nonlinear functions and constraints. Its limitation is the fact that the constraints can be only equalities that must be met precisely. If any of the subordinate goals must be taken as inequalities (i.e., greater or lesser than stipulated quantities), then the differential calculus may be applied to the decision problem only with qualification. In a case of maximization subject to inequality constraints, the calculus can be used to find only the outer bounds of the inequality constraints as if they were equalities; but the optimal input values may be less than the outer bounds. Unfortunately, in the vast majority of real-world decision problems that require an optimization approach, at least some of the constraints are inequalities. Appendix 5B describes the ability of a linear programming approach to deal with inequality constraints.The calculus employs the mathematical tool of partial differentiation to address the multiple goal problem. The procedure of partial differentiation serves as a tool of analysis in a decision setting best dealt with by attempting to optimize the value of the selected decision goal subject to various constraints that are in fact alternate, but subordinate goals. Suppose that all of the goals may be expressed in functional notational forms:
y2 = g(x1, x2, x3, ..., xn),
.
.
yn = k(x1, x2, x3, ..., xn).
We should note that while some of the goal functions may share independent variables in their argument listings, not all independent variables will appear in each argument listing. Also, some argument listings may be mutually exclusive with other argument listings. To be amenable to treatment by differential calculus, three conditions must be met:
(2) it must be possible to select one of the goals, say y1, for primary pursuit (i.e., to be maximized or minimized); and
(3) it must be possible to specify the subordinate goals, y2,...,yn, as equality constraints such that the value of each y is a constant that must be met precisely. If the constraint goals are inequalities (i.e., greater or lesser than some value), then the differential calculus cannot be applied.
Although we shall illustrate the calculus procedure for dealing with multiple goals with only two goal functions, we stress that the procedure can encompass any number. We assume that the goal functions have been specified as behavioral equations. The steps in the procedure are to:
1. select the single goal for primary pursuit;
2. express the subordinate goal(s) as constraint(s) by moving all terms to the left side of the equality, with only 0 on the right side;
3. specify a new function, called the Lagrange (after the mathematician who first proposed the procedure) function, which is a combination of the primary and subordinate goals in the sense that it has the constraints built into the primary function; the constraint terms introduce new, artificial independent variables signified by the Greek letter lambda, l1, l2,...,ln, one such artificial variable for each of the constraints;
4. compute the partial differentials of the Lagrange function with respect to each of the independent variables;
5. set each of the partial differentials equal to zero and regard the differential equations as a set of simultaneous equations; and
6. solve the set of simultaneous equations for the values of the independent variables, including the artificial ones.
The resulting values of the original independent variables are those that maximize (or minimize) the value of the primary goal function subject to the constraint(s) imposed by the subordinate goal function(s). The value of the artificial variable may be interpreted as the marginal contribution to the value of the primary goal when the respective constraint is relieved by one unit.
To illustrate these procedures, let us suppose that the goal is still to maximize the output function (16). However, there are now only 15 productive units that can be set up as either x1 or x2 inputs. A second goal, then, is to keep the sum of the inputs within a maximum of 15 units. The two goal equations may be given as
and
In the second goal equation, the value of the dependent variable is taken to be a constant, i.e., an absolute goal that must be fulfilled. The independent variables x1 and x2 are common to both goal equations. The procedural steps are as follows:
2. The subordinate goal is expressed in constraint format as
3. The Lagrange function is formed as
Note: Had there been other constraints, they would have been designated l2 through ln; then each of the constraints would have been added to the Lagrange function.
4. The partial differentials are computed as
dly/dx2 = 3x1 - 4x2 + 5 - l1
dly/ dl1 = 15 - x1 - x2
3x1 - 4x2 + 5 - l1 = 0
-x1 - x2 + 15 = 0
(b) solving the third equation for x1 and substituting:
-9(15 - x2) + 7x2 + 25 = 0
-135 + 9x2 + 7x2 + 25 = 0
16x2 = 110
x2 = 6.875
x1 = 8.125
Thus, the maximum value of y occurs when x1 = 8.125 units and x2 = 6.875 units. Since x1 and x2 are indivisible units, we round them to x1 = 8 units and x2 = 7 units. When the 15 available inputs are set up as 8 x1 and 7 x2 units, the maximum output that may be produced is computed from the original production function equation,
= 240 - 192 + 168 + 35 - 98 = 153.
Differentiation Rules
There are numerous rules for differentiating functions of various types. We shall identify only six for use in the economic decision context:1. The simple derivative (d) of a function which is a constant is zero, i.e.,
then dy/dx = 0.
then dy/dx = k.
then dy/dx = 1.
then dy/dx = akxa-1.
4. The simple derivative of a function containing multiple, additive terms is the sum of the derivatives of the separate terms, i.e.,
then dy/dx = akxa-1 + bjxb-1.
where u = f (x) and v = g (x),
then dy/dx = v(du/dx) + u(dv/dx).
then dy/dx = akxa-1 + 1,
and dy/dz = 1 + bjzb-1.
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APPENDIX 6B. OPTIMIZATION BY LINEAR PROGRAMMING
A possible solution to the inequality constraint problem noted in Appendix 6A is to employ the procedures of mathematical programming, the most widely used variant of which is linear programming. Linear programming is an optimization technique that can accommodate inequality constraints. However, it suffers the limitation that the equations of the primary goal function and all of the constraint functions must be linear, i.e., first order equations. This too is a serious problem for real-world decision analysis because many relationships in the real world simply are not linear. This objection can be relieved only by shifting to versions of mathematical programming that are so complex as to require substantial mathematical expertise and computational power to implement them. Such nonlinear mathematical programming techniques are generally inaccessible to most business decision makers, and thus are beyond the scope of this book.
However, a compromise is in order. We recognize that the nonlinear relationships found in the real world can often be approximated by linear functions for small changes in the near neighborhoods of current values of the independent variables. It is for this reason that linear programming has found extensive use in various military, commercial, and industrial applications. The danger in the use of linear programming is in attempting to push it too far, i.e., beyond the neighborhoods of current values where the nonlinearities of real-world relationships become significant. But changes of such magnitude require us to depart the realm of marginal decision analysis.
The Simplex Method
In most general terms, the "simplex method" of solving a linear programming problem involves:1) the specification of the primary objective function and all relevant constraints as linear equations or inequalities;
2) the solution of the set of such simultaneous equations to find the coordinates of points of intersection of pairs of constraints if the functions were plotted in coordinate space; and
3) the determination of the intercepts of the primary objective function equations that pass through the intersection points.
The intersection coordinate set that yields the highest value (if maximization is the object of decision making) or lowest value (if minimization is the object) of the dependent variable computed from the objective function equation that passes through the intersection point is taken to be the solution to the decision problem.
Variables, Equitions, and Inequalities
The total number of variables, including all independent variables (x1, x2, etc.) and the dependent variable (y, the maximum or minimum value of which is to be found) may not exceed the number of equations and inequalities in the system, including the objective function and the constraints. In a simultaneous equations context, if there are more variables than equations and inequalities, the system is "underdetermined" because values may not be found for all of the unknowns (i.e., variables) in the system. A problem involving too few equations and inequalities (or too many variables) is not amenable to linear programming treatment.It is possible for a problem to involve fewer variables than equations and inequalities. Indeed, it may be typical of situations that are amenable to linear programming solutions that there are more constraints than variables. In a simultaneous equations context, such a system would be "overdetermined" because multiple solutions are possible. The linear programming problem then is to identify the one among the multiple solutions that yields the highest (in case of maximization) or lowest (in case of minimization) value of the dependent variable.
Linear Programming by Computer Application
The algebraic solution of a linear programming problem is usually accomplished by entering the necessary parameters into a linear programming computer application. In order to enter data into the computer program, each constraint equation or inequality should be arranged with variables (x1, x2, etc.) on the left of the equality or inequality sign, and the constant (k) on the right. The constraint equations and inequalities are then entered in the sequence required by the computer program:
b1x1 + b2x2 + ... + bnxn < kB
.
.
.
g1x1 + g2x2 + ... + gnxn = kG
h1x1 + h2x2 + ... + hnxn = kH
.
.
.
r1x1 + r2x2 + ... + rnxn > kR
s1x1 + s2x2 + ... + snxn > kS
.
.
.
The program user must indicate whether to perform a maximization or minimization linear programming solution, then enter the number of constraints and the number of variables so that the program may prompt for entry of the coefficients of the equations of the constraints and the objective function.
Once all of the coefficients of the constraints and the objective function have been entered, the system is solved by simplex method to find the coordinates of intersections of the constraint functions. Then the intercepts of the objective function equations that pass through the intersections are computed. Finally, the values of the dependent variables are computed from the objective function equations at the intersection points. The solution to the problem is the highest (in the case of maximization) or least (in the case of minimization) value of the dependent variable, y, computed from an objective function equation that passes through a constraint intersection point.
Graphic Illustration
With more than two independent variables, it becomes impossible to illustrate a solution graphically because too many graphic dimensions are required. Simple linear programming problems with only two independent variables, say xa and xb, may be illustrated by drawing the paths of the constraint and objective functions in two-dimensional coordinate space.Suppose that the problem is to maximize y in the objective function,
subject to three explicit constraints,
b1x1 + b2x2 <= kB, and
c1x1 + c2x2 <= kC,
The non-negativity constraints impose a solution only in graphic quadrant I. It is possible that constraints might intersect in quadrants II (for negative values of x2) or IV (for negative values of x1). As we shall note below, if there are no constraint intersections in quadrant I, there will be no feasible solution to the linear programming problem.
In a maximization problem, the constraints are usually equalities or less-than inequalities. The three constraints when taken as equalities can be plotted in x1-x2 coordinate space as illustrated in Figure 6B-1. Since each constraint is a "less-than or equal-to" relationship, the constraint path constitutes a boundary or frontier, points on or below which are possible solutions, but points above which are not. The region bounded by 0JKLM then is referred to as the "feasible solution space." Since this is a maximization problem, the solution will lie somewhere along the outer boundary JKLM.
Figure 6B-1. Three constraints for a maximization problem.
The objective function may be solved for x1,
Figure 6B-2 illustrates the graphic solution with the objective function path passing through point L at the intersection of constraints B and C. The x1 axis intercept of the objective function is at point N. Since it is now known that y/w1 = N, the value of y may be solved for as y = N/w1, which is the maximum value of y that may be obtained from the objective function, given the constraints upon it.
Figure 6B-2. Graphic solution given the objective function.
Had this been a minimization problem, the constraints would likely have all been either equalities or greater-than inequalities, which might be plotted as illustrated in Figure 6B-3. Here the feasible solution space lies to the northeast of the constraint path J'K'L'M'. The graphic solution is similar to that of the maximization problem illustrated above, but with the objective function equation passing through the point of intersection of a pair of constraint paths that yields the minimum value of y.
Figure 6B-3. Three constraints for a minimization problem.
Qualifications
Three qualifications must be noted. If the slope of the objective function happens to coincide with the slope of one of the constraints, e.g., constraint B in Figure 6B-2, a unique maximum value of y does not exist. Rather, multiple solutions are possible since y can be maximized at any point along constraint B between points K and L.If there happens to be another constraint, D, whose path lies wholly above the JKLM path as illustrated in Figure 6B-3, it is redundant or non-binding. It may be said that only constraints A, B, and C are binding. In Figure 6B-3, since the solution lies at the intersection of constraints B and C, but lies below constraint A, it may be said that constraint A is not binding as well.
Finally, it may also be possible that none of the constraints intersect each other and any path that the objective function may follow in quadrant I, i.e., for positive values of all of the independent variables; in this case there is no feasible solution to the linear programming problem.
We should reiterate that these graphic illustrations are possible only for the simplest case of a problem involving only two independent variables. They serve only to illustrate the fundamental principles underlying linear programming analysis. Problems involving more than two independent variables are simply not amenable to graphic solution, and may be treated only algebraically.
The Dual Linear Programming Problem
A dual linear programming problem is implied by any so-called primal linear programming problem. If the primal linear programming problem is to find the maximum value of an objective function subject to constraints upon it, the dual problem is to find the minimum value of an associated dual objective function that may be derived from the primal objective function and its constraints.The interpretation of the value of a dual independent variable is the opportunity cost of one unit of the capacity lost from a process, given its constraint. The opportunity cost of a process capacity unit foregone would be positive only if the constraint with respect to it is binding. As illustrated in Figure 6B-4, the opportunity cost of a unit loss of capacity in a process for which the constraint is non-binding is zero.
Figure 6B-4. A non-binding constraint.
The dual linear programming problem may be structured from the primal linear programming problem by employing as many artificial variables as there are constraints in the primal problem. Each artificial variable, v, represents the opportunity cost of the loss of capacity from the process for which the constraint was relevant. There will be as many constraints in the dual problem as there are variables in the primal problem.
Given the primal problem introduced earlier, i.e., to maximize the function,
b1x1 + b2x2 <= kB, and
c1x1 + c2x2 <= kC,
a2vA + b2vB + c2vC = w2,
We note that the coefficients of the variables in the dual objective function are the constants of the primal constraints. The coefficients in the first dual constraint are the coefficients from the column of x1 primal constraint coefficients. The coefficients in the second dual constraint are the coefficients from the column of x2 primal constraint coefficients.
Once the dual problem is structured, its solution follows the same procedures employed in solving the primal problem. However, the solution to the dual problem follows from the solution to the primal problem, and the solutions are usually found simultaneously.
An Example
The most critical aspect of a linear programming problem is to set it up properly for manual or automated solution. This involves properly interpreting the natures of the objective function and constraints so that their equations and inequalities may be properly structured and arranged. To illustrate this point, suppose that the problem is to maximize the profit, y, from two products, x1 and x2, that are produced by three processes, A, B, and C, each with limited capacities.Experience indicates that the firm can expect $21 of profit per unit of x1, and $85 per unit of x2. The equation of the objective function is thus,
In process A, a unit of product x1 requires 7 capacity units (e.g., hours of processing time) while a unit of product x2 requires 11 capacity units. But there are only 385 units of processing capacity available in the relevant time frame. The constraint for process A may therefore be expressed as,
By similar reasoning, the requirements of products x1 and x2 in processes B and C with their respective capacities result in the following constraints:
constraint C: 19x1 + 90x2 <= 1710.
The user specifies that the primal problem is one of maximization, that there are 2 primal independent variables and three explicit primal constraints, and that all of the explicit primal constraints are less-than inequalities. Non-negativity constraints are implicitly assumed. The user enteres the coefficients and constants of each of the primal constraints, and the coefficients of the primal objective function. The computed results are that 24.1379 units of x1 and 14.4138 units of x2 should be produced to yield a maximum profit of $1732.07.
The structure of the dual problem is automatically derived from the primal problem, and the dual values are computed. The dual value of a capacity unit in process A is $1.5747, which is the amount of profit that must be foregone if a capacity unit in process A is lost. Since the dual values of capacity units in processes B and C are both zero, it may be inferred that the constraint of process A is binding, while those of processes B and C are not.
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PART C. THEORETICAL FOUNDATIONS
CHAPTER 7. CONSUMER BEHAVIOR AND DEMAND
Chapter 9 begins with the assertion that production is the central function of the organized business enterprise. Production is undertaken in the hope of relieving the economic problem of scarcity. But a rational decision to produce any particular good or service is predicated upon the existence of a social phenomenon: an adequate demand by other members of society for the fruits of the productive effort. This chapter focuses upon the managerial problem of identifying the characteristics of the demand that may be tapped by the productive enterprise, and the possibility of manipulating (creating, increasing, altering) that demand in the interest of the enterprise. We begin with a consideration of the principles of consumer behavior.
Consumer Behavior
In Chapter 2 we noted the possibility that people may act without engaging in any prior, deliberate decision making. Indeed, there is reason to believe that human beings often engage in such conditioned responses. Such responses often occur in circumstances where the decision maker has compiled a great deal of past experience with similar conditions, and where the consequences of choosing among alternative courses of action are essentially trivial. We must also admit the existence of capricious actions taken by people who give little or no consideration to the consequences, even when the alternative outcomes are likely to be non-trivial. Each of us probably engages in conditioned response behavior much of the time, and everyone occasionally indulges in the capricious action. While capricious behavior cannot be modeled, conditioned-response behavior may be treated with a default forecasting model, i.e., that tomorrow will be like today because today is like yesterday.We now turn attention to the phenomenon of deliberate, rational decision making on the part of the consumer. We must acknowledge two possibilities with respect to the information upon which the consumer must predicate the decision: the consumer either has perfect information about the possible alternatives to be purchased, or the consumer has some information but lacks knowledge of much that is relevant to the decision context. The task of analyzing consumer behavior would be greatly facilitated if consumers always have all needed information, but, unfortunately, the world is much different from this ideal situation. We must therefore employ the concept of the expected value of the possible outcomes from the consumer's choice as introduced in Chapter 2. The expected value of a particular consumer choice is the probability-weighted average of all of the possible outcomes resulting from the choice. In the event that the probability of occurrence of one of the possible outcomes is 100 percent, then the expected value becomes the certain value of the choice. Treating certain value as a special case of expected value, we shall make all subsequent references in this regard to expected value.
The time-honored term that economists have used to refer to the expected value of the outcome of a consumer choice is "utility." Utility, or satisfaction, is an amalgam of a wide range of the consumer's attitudes with respect to the results of the choice. Its dimensions include the extent to which the choice is perceived to meet a particular need, and may extend to such nebulous concepts as the pleasure or enjoyment derived from the outcome of the choice. We must also acknowledge the possibility that the outcome of a consumer choice may be negative in the sense that the perceived need was not met by the choice, or that the choice resulted in displeasure or pain (emotional as well as physical).
In the cases of so-called "big ticket" items that are typically purchased in discrete quantities of ones (e.g., houses, cars, boats, cameras, stereo systems, mink coats, etc.), the consumer's choice usually is of the all-or-nothing variety, i.e., whether or not to make the acquisition. Before the acquisition, the consumer can only estimate the expected value of the choice to acquire the item. Only after the fact of the acquisition (often, long after the fact) can a comparison of the actual outcome be made to the estimate of the expected value made before the acquisition. The rational decision criterion is whether the expected value of the choice to acquire is greater than the cost of the acquisition. The consumer's decision can be judged to be good or bad only in the retrospective comparison of the actual value of the outcome to the acquisition cost. Intelligent consumers will compile a stock of experience concerning preacquisition estimates of expected values compared to post-acquisition realized values. Sellers wishing to manipulate the prospective consumer's demands for their products may attempt to pursue strategies to get the consumers to over-estimate their expected values of the outcomes, or to ignore their accumulated experiences with ex-post realized values relative to ex-ante estimated values.
An even larger proportion of the consumer's choices is not all-or-nothing, but rather more-or-less choices. In these cases, the consumer, after deciding that some of the good or service is needed, must also decide how much to acquire. All of the principles described above apply to the fundamental decision to acquire any of the good or service. But the quantity question requires recognition of an additional decision criterion. Economists have deduced from a great deal of personal and collective experience that consumers, in acquiring successive additional units of most goods or services, tend to realize declining amounts of additional value (i.e., utility or satisfaction). This phenomenon is referred to the in the economics literature as the "principle of diminishing marginal utility."
Economists recognize that the consumer may experience an initial surge of realized value from consuming the first few units of the good or service, but they have also become convinced of the certainty of eventual diminishing marginal utility for most goods. The qualification is in regard to goods (alcohol, drugs) or activities (hobbies, sex) that may be addictive or compulsive. Although there is much that is yet unknown in regard to addictive behavior, it may be hypothesized that the consumer realizes increasing marginal utility when consuming successive units of goods that are objects of addiction.
Figure 7-1.
Figure 7-1 illustrates what economists think that a so-called total utility (TU) function and its derived marginal utility (MU) function might look like for a normal good, assuming all other factors constant. The underlying functional relationship can be given by
i.e., the total utility realized in consuming good x is determined by the quantity of x consumed, given all other factors. The graph of the TU function can be perceived to be a two-dimensional section through a three-dimensional utility surface (illustrated in the Appendix to this Chapter). As it is illustrated in panel (a) of Figure 7-1, the TU curve is concave upward initially, over the range from the origin to Q1. This is the initial consumption range over which the consumer may experience the surge of utility rising at an increasing rate. But beyond Q1, and up to quantity Q2, total utility increases at a decreasing rate. The key concept here is the decreasing rate of increase of total utility. This is the phenomenon that economists refer to as “diminishing marginal utility”. It is apparent that the total amount of utility realized in the consumption of commodity x reaches a maximum at quantity Q2. Successive units consumed beyond Q2 actually yield negative satisfactions, so the total amount of utility decreases.
The MU curve is derived from the TU curve according to the principles outlined in Chapter 6. We can observe that over the quantity range for which TU is increasing at an increasing rate, from the origin to Q1, MU rises, reaching a peak at Q1. Over the quantity range for which TU is increasing at a decreasing rate, MU falls, reaching a value of zero at Q2 the quantity at which TU is maximum. The quantity range between Q1 and Q2 is described as the range of diminishing marginal utility. And it is this range that economists think represents the usual circumstances under which consumers make most of their choices. The reader is now invited to speculate on the likely appearances of the TU and MU curves for a commodity that is an object of addiction or compulsive consumption.
In the case of a non-addictive good or activity, the rational decision criterion is to continue to consume more of the good, even while realizing declining additional utility, until the marginal value realized in consumption is no longer greater than the marginal cost of the acquisition. In order to make such a comparison, the marginal cost of acquisition must be perceived in units comparable to those in which satisfactions are measured. One way to do this is to regard the acquisition cost in terms of dissatisfaction or disutility at having to part with purchasing power to make the acquisition. If the marginal utility does indeed decline, a point at which additional consumption should cease will be reached. In Figure 7-1, curve MD (marginal disutility) represents the marginal cost of acquiring additional units of the commodity (constant as illustrated). The consumer should push consumption only to Q3, beyond which the marginal utility falls below the marginal disutility realized in acquisition.
In the case of a good or activity that is an object of addiction, since the marginal utility always increases as successive units are consumed, no consumption-limiting criterion is ever reached unless the marginal disutility rises to exceed the increasing marginal utility. Even then, it cannot be assumed that the addictive subject can engage in rational choice. An enterprise wishing to promote the sale of its product or service may pursue a strategy designed to induce the consumer to suffer the illusion that marginal utility declines at a slower rate than it does in reality, or to believe that marginal utility only increases as with an addictive good or activity. In either case, the naive or unwary consumer may be induced to consume larger quantities than he might with more rational consideration. Intelligent consumers can be expected to add to their stocks of experience such comparisons between ex-ante estimates of expected values of satisfactions and ex-post realizations of actual satisfactions. The manager should be aware that intelligent, experienced, and mature consumers are likely to be more resistant to efforts at manipulation of their preferences. The obverse of this principle is that less-experienced consumers (especially children and adolescents) or less-capable adult consumers may be more amenable to preference manipulation. This possibility should raise ethical "red flags" in the minds of conscientious managers.
Perhaps a less controversial approach to promoting sales of the product is for the enterprise to try to change one or more of the non-quantity determinants of utility, which to this point have remained unspecified and assumed constant. One of those surely is the consumer's taste for the good or service. An effective promotional strategy may improve the image of the good or service, thereby making it more desirable to the consumer. This will cause the TU curve, and with it the MU curve, to shift upward and to the right. The reader is invited to envision a modification to Figure 7-1 to illustrate this phenomenon. The shifted MU curve should intersect the MD curve at a quantity larger than Q3, thus achieving the seller's objective.
The Theory Of Demand
Demand is the desire for a good or service, together with the purchasing power to make the desire effective, both backed by the willingness of the consumer to part with the purchasing power. The demand curve is a graphic representation of the path along which the consumer would rationally choose to purchase quantities of the good or service at various prices. The so-called Law of Demand is the hypothesis that consumers will buy ever greater quantities of the good or service at progressively lower prices, i.e., acquisition costs. The fundamental behavioral principle underlying the concept of the demand curve is the shape of the marginal utility curve over the range of diminishing marginal utility. The connection between demand and utility is that the seller must offer the consumer some inducement to purchase more of the good once his marginal utility has fallen to the level of the disutility realized in acquiring the last unit. The obvious inducement is a lower price or acquisition cost. Consumers can be expected to purchase more at lower prices. The inverse is also expected: consumers will purchase smaller quantities at higher prices.In addition to the marginal utility principle, economists offer two other explanations for the law of demand, the income and substitution effects. The substitution effect occurs when an increase in its price leads consumers to shift their purchases away from the good or service and to its substitutes--hence the inverse relationship between the own-price of the good or service and its quantity demanded. A downward change in the price of an item leads to an increase in quantity demanded as consumers shift their purchases away from substitutes and toward the item.
The income effect of a price change results from recognition that the consumer is faced with a range of choices. For example, when the price of an item falls, the consumer can purchase more of the item itself, or more of other items that he consumes, or retain unspent purchasing power. The decrease in the price of the item then results in an implicit increase of his income. Conversely, an increase in the price of the item means that the consumer must purchase less of item, less of other items that he normally purchases, or spend more than he has spent in the past. In either case, an inverse relationship between the price of the item and the quantity consumed of it is a consequence.
Demand Curves and Demand Surfaces. To this point we have spoken of demand in regard to the quantities of an item that might be purchased by a single consumer. But demand can also be regarded as a collective concept, i.e., as the summation of the quantities of an item that would be purchased by a collection of consumers over the range of possible prices. The collection of consumers may include all who are "in the market" for the particular item, but it may be more narrowly construed to those who are likely to purchase the item from a particular seller. In the former case we can speak of market demand, and in the latter case the demand faced by the particular seller, i.e., the firm's demand. Whether that for an individual consumer or some collection of consumers, the functional notation representation of the demand relationship may be given by
i.e., the quantity demanded of a good or service is determined by the price of the good or service, given all other determinants. The functional relationship, f, is presumed to be inverse for the relationship between quantity and price. This inverse relationship, i.e., the Law of Demand, can be illustrated by drawing a demand curve on a set of coordinate axes for price and quantity as in Figure 7-2. The downward (left to right) slope of the demand curve is a manifestation of the principle of diminishing marginal utility.
Figure 7-2.
We have drawn the demand curve in Figure 7-2 as a straight line with a negative slope. The equation for such a linear demand curve can be given in slope-intercept form as
where c is the quantity-axis intercept, and d is the (assumed negative) slope of the demand curve. The linearity of this demand curve is assumed only for purposes of simplicity. In reality, a demand curve may exhibit any degree of curvature, and it may be concave upward or downward. Even if a straight line can approximate the price-quantity relationship, the linear demand curve may exhibit a range of slopes, from nearly horizontal at one extreme, to almost vertical at the other. And even these extremes are not effective limits on the possible slopes that demand curves may take. If the income effect of a price change of an inferior good were great enough to outweigh the substitution effect, the demand curve would slope upward from left to right in apparent contradiction to the law of demand.
If the demand curve illustrated in Figure 7-2 can be presumed to be a realistic representation of a real demand relationship for good x, then a decrease of the price from P1 to P2 can be expected to lead to an increase in the consumer's purchases of x from Q1 to Q2. Economists refer to such a movement from one point to another along a fixed-locus demand curve as a "change of quantity demanded." Such a change of quantity demanded is attributable exclusively to a change in the price of the good, given all other determinants.
The demand for any good or service is actually determined by many factors in addition to the price of the good or service. In fact, for some items the price may be one of the lesser-significant determinants of its demand. A more general specification of a demand curve may be given by
where I is the income of the consumer, T stands for "tastes and preferences" (the same tastes and preferences referred to above as determinants of utility), B is the consumer's current level of indebtedness, Py is the price of a relevant substitute good, and Pz is the price of a related complement good. The ellipsis symbols ( ... ) between B and Py suggest that there are other non-price demand determinants that have not yet been specified (or even identified). Those following Pz allow for prices of yet other substitute and complement goods.
There is nothing particularly significant about the order in which the determinants of demand are listed on the right side of the equation. The order of the listing can be changed at will, and any one of them can be moved to the head of the queue as required. The price of the good itself (i.e., the good's "own price") is typically listed in the first position because, historically, the attention of economists turned to this determinant first. Also, in the cases of most goods and services, the own price may indeed be the most important or significant (in a statistical sense) determinant of the quantity demanded. Yet any such hierarchy of determinants is something to be discovered by analysis, rather than assumed at the outset.
In order to draw the two-dimensional representation of the demand curve illustrated in Figure 7-2, it was necessary to treat all of the non-own price demand determinants as if they were constant, even if they in fact were not constant (more about this below). A revision of equation (3) to represent this specification is given by
where the slash (/) is used to separate the single demand determinant that is presumed to be variable (P) from all the rest, that are assumed not to change. Indeed, if any of the other determinants are variable, it is technically not even possible to draw a discrete locus for the demand curve in the two-dimensional space of the P-Q coordinate axes.
Economists employ the term "change of demand" to refer to the circumstance where some determinant of demand other than the item's "own price" has changed. The effect of such a change is to shift the own-price demand curve from its former locus to some position, as illustrated in Figure 7-3. Here, D1 is the original locus of the demand curve, and D2 is the new locus after something other than the price of the good has changed. For example, improving tastes and preferences for the good or service, or a decrease in consumer indebtedness, could possibly explain the illustrated right-ward shift of the demand curve.
Figure 7-3.
Another perspective on the demand-shift phenomenon is provided by a three-dimensional graphic representation of the demand relationship. In this representation, the slash of equation (5) is moved one item to the right,
In this relationship, two demand determinants, P and I, are presumed variable, while all other possible determinants are treated as if they were constant. A graphic representation of this relationship is given in Figure 7-4, where the third dimension (depth) is occupied by the income determinant. A number of "slices" (or vertical sections) have been made through the three-dimensional demand surface at different income levels. If the three-dimensional surface were viewed from a perspective opposite the price-quantity plane, in effect collapsing the surface into two dimensions, the viewer would see something like that represented in Figure 7-5. Here, the several vertical slices through the three-dimensional surface appear as a demand curve that shifts in two dimensions.
Figure 7-4.
A 3-D view of a demand surface can be explored if a VRML plugin has been installed in the browser. (A Plugin Detector can examine the browser and give access to several plugins that will work if one has not already been installed.)
Figure 7-5.
The three-dimensional perspective enables another important observation. In Figure 7-4, the intersection of the demand surface with the floor (the income-quantity plane) traces out path RSTUV, which when viewed from above yields the two dimensional graph illustrated in Figure 7-6. In this figure, income is measured on the vertical axis, and is thus taken to be the demand determinant relative to quantity demanded on the horizontal axis. The path, RSTUV, thus traces out an income-demand curve (or Engel Curve, as it is referred to in the literature), for which the functional notation relationship would be given as
In equation (7), the only variable determinant of demand is presumed to be income, while all other demand determinants, including price, are taken to be constant. As we noted above, price may not be the most significant demand determinant, and it is legitimate to move any of the demand determinants to the head of the list of determinants so that it may be analyzed, assuming all other determinants as givens.
Figure 7-6.
The three-dimensional surface represented in Figure 7-4 is for two demand determinants, own-price and income, relative to quantity demanded. It is unfortunate that we can have access to no more than three graphic dimensions, because this necessarily limits our analysis to no more than two demand determinants at one time as long as we wish to stay with the graphic analysis. (We can treat more than two determinants at one time only by exiting the graphics and entering the realm of multivariate algebra.) However, within the realm of three-dimensional graphics, we can move any two determinants to the head of the determinant queue in order to construct a three-dimensional surface showing the relationship between quantity demanded and the two selected determinants. And by judiciously slicing the three-dimensional surface, we can extract two-dimensional demand curves showing the relationship between quantity demanded and any single demand determinant.
Normal and Inferior Goods. The income-demand curve illustrated in Figures 7-4 and 7-5 happens to slope upward from left to right (i.e., to exhibit a direct relationship between quantity demanded and income), and is therefore illustrative of the phenomenon of a "normal" good. A normal good is one for which quantity demanded increases when income rises, or decreases when income falls. An "inferior" good is one for which quantity demanded decreases when income rises, and increases when income falls. The two-dimensional income-demand curve for an inferior good would slope downward from left to right, with appearance similar to that of an own-price demand curve drawn on a set of price-quantity axes.
Most of the goods and services consumed by human beings are likely normal in the sense that people will consume more of them when their incomes rise. But there are also many examples of inferior goods to examine, although the items with respect to which they are inferior should be identified. For example, in the late twentieth century American culture, ground beef is probably inferior to most solid beef cuts; margarine is probably inferior to real butter, and Ford Escorts are probably inferior to Lincoln Town Cars. The word "probably" is included in the foregoing sentence because of the highly personal nature of preferences. Even if most of the members of American society would prefer a New York strip to a hamburger, there are some members of American society (teenagers come readily to mind) who might prefer a hamburger to the New York strip.
We should also stress that the characteristics of normalcy and inferiority are time and culture bound. For example, potatoes were probably regarded as inferior substitutes for mutton by eighteenth century Irish peasants, whereas twentieth century Americans tend to regard potatoes as complement to both steaks and hamburgers. The inferiority of potatoes relative to meat has ceased to be an issue for Americans, although the issue may be reopened in a choice between potatoes and rice.
The normalcy or inferiority of a good may be revealed in the income effect consequent upon a price change, as well as with an explicit change of income. We earlier identified the income and substitution effects of a price change as further (in addition to the principle of diminishing marginal utility) explanations of the law of demand. In the case of a normal good, the income effect may be expected to reinforce the substitution effect: when the price of a normal good falls, people will tend to increase their purchases of it, not only because it is now less expensive relative to substitutes, but also because they have realized an implicit increase of income due to the price change. In the case of an inferior good, however, the income effect will offset the substitution effect: when the price of the good falls, people will tend to consume more of it than more expensive substitutes, but the realization of its inferiority retards the increased consumption. Although economists have found little evidence of its existence, it is hypothesized that the income effect in the case of an inferior good may be so great as to more than offset the substitution effect. If such a phenomenon should occur, the own-price demand curve would appear to slope upward from left to right, and would thus be an apparent violation of the law of demand.
What are the managerial decision implications of inferiority and normalcy? In a growing economy, or during a period of cyclical expansion, the enterprise should attempt to produce normal goods or services since their demands will increase at the same or a faster rate than incomes are rising. The enterprise should avoid production of inferior goods since their demands will increase at a slower rate (or may even decrease) as incomes rise. However, during a period of cyclical decline, the enterprise would be better off in producing inferior goods because their demands will tend to decrease more slowly (or possibly even increase) as incomes fall. But, suppose that the main product lines of the enterprise are inferior goods that must continue in production through periods of expansion as well as contraction. In this case, the design strategy of the enterprise might be to alter the real nature of the product so that it becomes perceived to be a normal good relative to substitutes. Alternately, the enterprise's promotional strategy might be directed toward improving the clientele's tastes and preferences for the good, or altering the image of the good so that it is perceived to be normal rather than inferior.
Substitutes and Complements. Two other demand determinants that deserve the attention of the manager are the prices of substitutes (Py) and complements (Pz). Each of these determinants may of course be moved to the head of the determinant queue for analysis while assuming all other determinants (including the own-price of the item) constant. The functional notation equation of a substitute good demand relationship would appear as
for which a so-called cross-price demand curve can be constructed. In the case of a substitute good, the cross-price demand curve slopes upward from left to right because when the price of the substitute Py is raised, although its quantity demanded Qy will decrease, the quantity demanded of the good Qx will increase. This increase can be illustrated as a movement upward along the cross-price demand curve, but would be a cause of a rightward shift of the own-price demand curve illustrated in Figure 7-3. We leave it to the reader to imagine the shape of the cross-price demand curve for a complement good, and the own-price demand shift implications of a change in the price of the complement.
The enterprise rarely has ability to directly influence the prices of goods that are substitutes or complements for those produced by the enterprise. But the management of the enterprise should be aware that competitors do produce substitutes for those produced by the enterprise, and that the pricing decisions of competitors can be expected to cause shifts of the own-price demand curves for the enterprise's products. Likewise, the management of the enterprise should be aware that its own pricing decisions will likely result in shifts of competitor's own-price demand curves, and may induce strategic responses from them.
Demand and Revenue
The price of the product can be understood to be its average revenue (AR), or the revenue per unit of the product sold by the enterprise. Thus, the total revenue (TR) that the enterprise will realize on the sale of Q units of its product can be computed by the formula(8) TR = P x Q,
or if total revenue is known, the average revenue, or price, can be computed by solving equation (8) for P, or
Knowledge of these relationships enables us to derive an equation for a total revenue function from the equation for the demand function, or an equation for the demand function if that for the total revenue function is known. Either such equation can be specified employing the procedures discussed in the last section of this chapter. Suppose that demand equation (3) above has been specified with parameter values c=20 and d = -4, resulting in equation (10),
(10) Q = 20 + (-4)P.
We have omitted the subscript "d" in equation (3) for clarity of exposition. In order to derive the total revenue equation, we must first solve equation (10) for P,
(11) P = 5 - .25Q.
Since from equation (8) we know that TR = PxQ, we may derive the total revenue equation (12) by multiplying equation (11) through by Q,
(12) TR = 5Q - .25Q2.
Alternately, had TR equation (12) been specified first, since AR = TR/Q, the AR equation could be derived by dividing the TR equation through by Q,
(13) AR = 5 - .25Q,
which is the same as equation (11) when it is recognized that P is the same as AR.
The derivation of these equations by simple algebraic manipulation enables us to illustrate in two dimensions the graphic relationship between AR and TR. The TR curve is shown in panel (a) of Figure 7-7; its associated demand curve (AR) is shown in panel (b). Corresponding average and total revenue curves for a linear demand relationship. Because the demand curve is linear with a negative slope, its associated total revenue curve is a second-order (or quadratic) equation that graphs as a parabola that opens downward and spans the positive-price range of the demand curve on the quantity axis. In Figure 7-7 we have also drawn a box in panel (a) below the demand curve formed by a horizontal at price P1 and a vertical at quantity Q1, the quantity that will be sold at price P1. We have also drawn a vertical in panel (b) below the TR curve a quantity Q1. By the formula for the area of a rectangle (area = length x width), we can assert that the area of the box in panel (a) measures the total revenue resulting from selling quantity Q1 at price P1. This same area is also represented by the altitude of the vertical at Q1 up to the TR curve in panel (b).
Figure 7-7.
Figure 7-8 is a reproduction of Figure 7-7, but with several additional price-quantity boxes drawn below the AR curve, and corresponding verticals drawn below the TR curve. The reader should verify by inspection of the boxes that as price falls toward P3 and quantity increases accordingly, the boxed areas increase to a maximum corresponding to the tallest vertical below the vertex of the TR parabola. If the demand curve is indeed linear, the maximum total revenue will occur at a quantity that is half the horizontal axis intercept of the demand curve. In Figure 7-8, prices successively lower than P3 yield revenue rectangles of progressively smaller area. The graphic approach illustrated in Figure 7-8 provides one means of identifying the price-quantity combination that yields the maximum total revenue, but it is not a means that yields an effective decision criterion. However, an alternate approach that employs concepts from the calculus can provide a useful revenue-maximization decision criterion.
Figure 7-8.
The value of Q for which TR is at its maximum value can be found by differentiating the TR function with respect to Q, setting the differential equal to zero, and solving the resulting differential equation for Q. Thus, for TR equation (10),
(14) dTR/dQ = 5 - .5Q.
Setting dTR/dQ = 0,
and solving for Q,
Thus, if the demand curve in panel (b) of Figure 7-8 is a graph of equation (3), the value of Q at Q3 is 10 units. Further, by substituting 10 for Q in the TR function, the maximized total revenue is found to be
The revenue maximizing price can be found by substituting Q=10 into the average revenue equation,
Thus, if the price denomination is the U.S. dollar and the unit denomination is 1000 each, a maximum total revenue of $25,000 can be realized by selling 10,000 of the item at a price of $2.50 each.
Economists refer to the differential of TR with respect to Q as the "marginal revenue" (MR). Conceptually, marginal revenue is the addition to total revenue consequent upon selling one more unit of the item, or
where DQ is 1 unit of the item. This is the approximate equivalent of the definition of the derivative,
as DQ approaches zero. MR can be reconciled to dTR/dQ if it is recognized that the closest that DQ can approach to zero is one unit of the item.
Equition (14), the differential of the TR function with respect to Q, can be rewritten as
(15) MR = 5 - .5Q.
A comparison of the MR equation (15) to the AR equation (13) leads to the inference that the two curves must share a common price-axis intercept (in this case 5), but that the slope of the MR function (.5) is twice that of the AR function (.25), and both are negative. This means that the MR curve must slope downward more steeply than does the AR curve. Figure 7-9 is a reproduction of Figure 7-7, but
Figure 7-9.
with the MR curve drawn in. The most important observation to make in regard to Figure 7-9 is that the MR curve reaches zero at the quantity level for which the TR parabola attains its maximum value. This corresponds to the calculus procedure of setting the differential of TR equal to zero in order to find the Q for which TR is maximum.
The relationships described above provide a most useful managerial decision criterion. If the objective of the enterprise is to produce a quantity of an item and sell it at a price that yields the maximum possible revenue, it can do so by finding the quantity for which marginal revenue is zero. We qualify this conclusion immediately by noting that simple revenue maximization may not to be the behavioral objective of the management of the enterprise. Rather, the management may be oriented toward profit maximization (which, as we shall see in Chapters 12 through 15, is not likely to coincide with revenue maximization). Even so, we shall discover subsequently that marginal revenue is one of the two decision criteria that are relevant to profit maximization.
Looking Ahead
Chapter 8 extends the concepts developed in Chapter 7 into the realm of the statistical estimation of the demand function. A decision criterion, elasticity of demand, is first elaborated in Chapter 8, then the implications for elasticity of demand of various specification problems are considered.
EXPENDITURE OPTIMIZATION PROBLEM
The data presented on the following page are for a hypothetical consumer who has $40 to spend on four categories of consumer goods: Food, Clothing, Housing, and Entertainment. The data contained in columns (2), (4), (6), and (8) are for the amounts of utility (or satisfaction, usefulness) that the consumer would gain from consuming each successive unit of each item, proceeding from the top of the page to the bottom. The data in column (10) are for the amounts of utility that would be lost by spending successive dollars from the consumer's bank account, proceeding from the top of the page toward the bottom. The problem is to allocate the limited budget so as to maximize utility. The consumer may acquire units of the consumable goods only by spending money and giving up utility according to the conditions specified in column (10).1. Characterize the patterns of utility realization by the consumer in regard to each of the items purchased; ...in regard to the money spent.
2. What is the purpose of columns (3), (5), (7), (9), and (11)? Compute and fill in the numbers for these columns as needed.
3. What is the economic criterion for continuing to purchase each of the items? How many units of each should the consumer purchase? What total utility will the consumer realize if he/she purchases these quantities?
4. What criterion should the consumer use in deciding whether to spend successive additional dollars from the bank account? When the consumer stops spending money on the items, how many dollars will be left in the bank account? How much total utility will the remaining bank balance provide?
5. Is there any alternative collection of the four items and money, or any other purchase sequence by which the consumer could realize a greater mass of utility (total) than that achieved using those criteria specified in numbers (3) and (4) above?
BACK TO CONTENTS
APPENDIX 7A. PREFERENCE AND INDIFFERENCE
Copyright 2011 by Richard A. Stanford
In this appendix we pursue the alternative approach to that elaborated in Chapter 7 for analyzing consumer behavior. In the following discussions we shall not attempt an exhaustive exploration of the approach, but shall develop only those concepts necessary to requirements in subsequent chapters.
The Horizontal Slice
Figure 7A-1 illustrates a consumer's three-dimensional utility surface with utility measured vertically against the quantities of two goods, X and Y, represented on the floor axes. The functional notation representation of the utility surface is
Figure 7A-1.
The Indifference Curve Map
Figure 7A-2 shows a two-dimensional view from a perspective above the surface illustrated in Figure 7A-1. In effect, the three-dimensional surface appears to be collapsed into the floor when viewed from above, but the path e'f'g'h' represents the slice through the surface at utility altitude I4. Economists refer to the e'f'g'h' path as an isoutility curve (meaning same utility) because it represents a sequence of points, the (K,L) coordinates of which are the combinations of the two goods that can yield the I4 level of utility. For example, utility I4 can be realized with the X1 quantity of good X combined with the Y1 quantity of good Y. Utility I4 can also be realized with Y2 if a larger, X2, is consumed. This suggests that good X and good Y are to some extent substitutable for one another in the consumer's preferences. Since path e'f'g'h' is drawn as a continuous curve, the implication is that there are an infinite number (or as many as there are points along the path) of combinations of X and Y that can yield the I4 utility level.
Figure 7A-2.
Economists also refer to path e'f'g'h' as an "indifference curve". The reason is that the consumer should be indifferent between the combinations of goods represented by different points along the same isoutility curve because they all yield the same level of utility. Combination (X1, Y1) at point f' yields the I4 level of utility, but so also does combination (X2, Y2) at point g'. However, the consumer would prefer combinations of X and Y at utility level I4 to any combination of X and Y that yields a lower level of utility. But the consumer would give preference to any combination of X and Y that yields a higher level of utility than I4. We will refer to such curves as indifference curves rather than isoutility curves in subsequent discussion.
Suppose that instead of selecting an (X,Y) combination represented by a point along the indifference curve, the consumer chooses the Y2 quantity of good Y with the smaller X2 quantity of good X, reaching point j on the utility surface in Figure 7A-1, and j' in Figure 7A-2. It should be apparent that the smaller quantity of good x combined with less of good y will yield some utility level lower than I4.
Figure 7A-3 is an elaboration of Figure 7A-2 to show the paths of several other "representative" indifference curves that could be generated by horizontally slicing the surface at altitudes other than I4. It is now apparent that the X1 quantity of good X along with the Y2 amount of good Y can yield only the I3 level of utility, which is less than I4 level. Theoretically, any number of such indifference curves could be generated by slicing the utility surface at different altitudes so that the floor of the surface might appear "dense" with concentric indifference curves. The collection of representative indifference curves may be referred to as an indifference curve map. The indifference curve map may be likened to the collection of isotemp or isobar lines on a weather map, or to the contour lines on a geological or military map.
Figure 7A-3.
Suppose that the horizontal slices taken through the surface to generate the indifference curve map illustrated in Figure 7A-2 were taken at successively higher utility altitudes that are equal utility increments apart. In this case, (I2- I1) would be equal to (I3- I2), and so on. When viewed from above the surface in Figure 7A-1, the indifference curve map illustrated in Figure 7A-2 betrays the likely shape of the surface that cannot be seen explicitly in Figure 7A-2. From indifference curve I1 up to indifference curve I4 the indifference curves appear to be getting closer together, implying that the surface is increasing at an increasing rate in the utility dimension. This corresponds to the range from the origin to Q1 along the total utility curve illustrated in panel (a) of Figure 6-1. From indifference curve I4 through indifference curve I7 the indifference curves appear to become farther apart, suggesting that utility is increasing at a decreasing rate. This corresponds to the range from the origin to Q1 along the total utility curve illustrated in panel (a) of Figure 6-1. The reader is invited to analyze the likely shapes of the indifference curve maps that could be generated from the surfaces linear and second-order (quadratic) shapes.
The Marginal Rate of Substitution
The slope of an indifference curve at any point may be measured by the slope of a tangent drawn to the curve at the point, or it may be approximated by the slope of a chord connecting two points near to each other along the indifference. For example, the slope of the I4 indifference curve over the f' to g' range in Figure 7A-3 can be approximated by the slope of the chord from f' to g', or
The technical name for this slope is the "marginal rate of substitution" (MRS). The MRS is interpreted as the rate at which the consumer can substitute good X for good Y while remaining at the same level of utility. Over the f'g' arc of the I4 indifference curve, the consumer can maintain utility at the I4 level as the good Y amount is reduced from Y1 to Y2 only by increasing the quantity of good X consumed from X1 to X2. It should be obvious that between f' and g' the MRS is negative since Y2 is less than Y1. The MRS will normally be negative over the economic range of consumption.
It will be instructive to examine the right triangle formed by the points f', g', and j'. As we have just noted, the ratio of the sides of this triangle, f'j'/j'g', measures the slope of the third side (or hypotenuse), which forms the f'g' chord. The diagonal movement from f' to g' may be regarded as two separate adjustments represented by the vertical and horizontal sides of the triangle. Specifically, the movement from f' to j' is a decrease in the consumption of the Y good (-DY) which, other things remaining the same, would decrease the consumer's utility from I4 to I3, or -DI1. The movement from j' to g' is an increase in the consumption of X (DX), which by itself would cause output to increase from I3 to I4, or DI2. DI2 is of the same magnitude, but opposite sign, as DI1, so we shall use DI without sign or subscript to refer to both quantities. Identification of the utility changes allows us to specify the marginal utilities of good X and good Y as
Further, we may note that the ratio of the marginal utility of good X to the marginal utility of good Y also measures the MRS:
This point will prove of value in subsequent discussion.
The Consumer's Budget
The indifference curve map provides information about consumption possibilities, but by itself cannot provide the consumer with a criterion for selecting an optimal combination of two goods. Additional information is needed in the consumer's budget (or that portion which is reserved for the two goods) and the prices of the two goods, X and Y. Suppose that the prices of good X and good Y are PX and PY, and the consumer has determined that the budgeted outlay must be limited to the dollar sum B. This information can be brought together in the following equation:
The sense of this equation is that the product of the number of units of good X consumed (X) times its price (PX) plus the number of units of good Y consumed (Y) times its price (PY) cannot exceed the budgeted outlay (B). The consumer could underexpend the budget, but suppose that the consumer typically commits the entire budget to the purchase of quantities of good X and good Y so that the inequality symbol may be ignored. What quantities of each good should the consumer purchase in order to maximize the consumer's utility?
Equition (4) can be usefully rearranged in the following format:
Equition (5) is linear and in the so-called "slope-intercept" format, y = a + bx, where the slope of the line that represents the equation is the ratio of the price of labor (PX) to the price of capital (PY). It should be noted that this ratio is negative. The conceptual interpretation of this slope is the rate at which the consumer can substitute good X for good Y while remaining within the budget The vertical axis intercept is the ratio of the budgeted outlay (B) to the price of good Y (PY), which determines the maximum amount of good Y that could be purchased by the consumer if he or she purchased none of good X. Equition (5), henceforth referred to as the budget line, can be plotted on the same set of coordinate axes containing the indifference curve map. We may suppose that the values of B, PX, and PY are such that the budget line is plotted as in Figure 7A-4.
Figure 7A-4.
The Optimal Combination of Goods
At what point along the budget line should the consumer select a combination of good X and good Y? As the reader has likely already guessed, the relevant decision criterion is a comparison of the slopes of the indifference curve and the budget line, i.e., whether
Point m' is one option involving a large amount of good Y with a small amount of good X. At point m' the slope of the indifference curve, though negative, is very steep, implying that if the consumer were to give up the (Y3- Y4) quantity of good Y, he or she could purchase the (X4- X3) quantity of good X while remaining within the budget. This additional quantity of good X is a great deal more than the consumer would have to have to remain at the I2 level of utility. In fact, to exchange the (Y3- Y4) quantity of good Y for the (X4- X3) quantity of good X would enable the consumer to move to a higher level of utility on indifference curve I3 at point n'. This is obviously a good move that the consumer should undertake. The reader is now invited to repeat this analysis using point n' as the departure point.
Suppose that the consumer maker had first determined to try the input combination represented by point s'. At this point the consumer purchases a relatively large quantity of good X along with substantially less of good Y. The MRS at point s' is negative, but quite small (i.e., the slope of the indifference curve is shallow). The consumer is considering replacing the (X5 - X6) quantity of good X with additional good Y. Only a small amount of additional good Y will be needed to allow the consumer to remain at the same level of utility, I3. However, by giving up the (X5- X4) quantity of good X the consumer can still remain within the budget by purchasing the (Y6- Y5) quantity of good Y, which will enable the consumer to increase utility almost to the I4 level. This is a good move that the consumer should undertake.
As may be readily deduced, the consumer will find a utility-increasing incentive to substitute good X and good Y by moving downward along the budget line from points such as m' and n' until the incentive disappears. Likewise, a similar incentive will be found to move upward along the budget line from points such as r' and s' until the incentive is eliminated.
When does the substitution incentive expire? This occurs when a point is reached along the budget line where the slope of the budget line is just equal to the slope of the indifference curve. At such a point, e.g., f' in Figure 7A-4, the conceptual interpretation is that the rate at which the consumer can substitute good X for good Y while remaining at the same level of utility (the MRS) is just equal to the rate at which the consumer can substitute good X for good Y while remaining within its outlay budget (PX/PY). This is the point of tangency of the budget line with an indifference curve. It is also the highest-utility indifference curve that the budget line can reach. At this point the consumer will have found the utility-maximizing combination of good X and good Y, given the limitation of the budgeted outlay.
Substitution and Income Effects
In Figure 7A-5, budget line B1 represents the initial conditions under which the consumer can purchase quantities of X and Y, given their respective prices, while not exceeding the budget. The slope of the budget line is measured by the ratio, PX/PY. The consumer thus can maximize utility at point J, the tangency of the budget line with indifference curve I4, purchasing the quantities X1 and Y1.
Figure 7A-5.
Suppose that the price of one of the items, say X, falls. In order to illustrate the point with a graphic change that can be easily examined, we shall make the heroic assumption that the price falls by half, thus allowing the consumer to purchase twice as much X relative to each quantity of Y as before the price change. The new budget line is illustrated as B2 in Figure 7A-5. Now the consumer can realize a higher maximum utility at point K, the tangency of the B2 budget line with indifference curve I5, purchasing quantities X2 and Y2.
However, this increase of utility consequent upon the price change is composed of two effects, a substitution effect as the consumer shifts purchases away from other goods to X, and an income effect due to the fact that with a lower price of something in the consumer's budget, the consumer can now purchase more of all goods. These two effects may be illustrated by hypothetically removing enough from the consumer's budget at the new PX/PY price ratio to return the consumer to the former level of utility, I4. This would be represented by the budget line B3, which reaches tangency with indifference curve I4 at point L where the consumer would purchase quantities X3 and Y3.
The substitution effect now can be illustrated in Figure 7A-5 as the movement along the original indifference curve, I4, from point J to point L. In order to remain at the same level of utility as the price of X falls, the consumer would purchase a larger quantity, X3, but a smaller quantity, Y3. However, with the implicit increase in purchasing power of the consumer's income consequent upon the fall in the price of X, the budget line implicitly shifts from B3 to B2, allowing the consumer to purchase the larger quantities, X2 and Y2.
We may note that in the case of a normal good as illustrated, the income effect is in the same direction as the substitution effect, and thereby reinforces the substitution effect. With the fall in the price of X the consumer purchases more of X due to the substitution effect, any yet more of X due to the income effect. In the case of a normal good, the demand curve slopes downward from left to right for two reasons, the substitution effect and the income effect. The reader is invited to construct a graphic analysis to illustrate the substitution and income effects consequent upon a price increase.
In the case of an inferior good, the income effect is in the opposite direction to that of the substitution effect, and therefore offsets (at least partially) the substitution effect. In such a case, with a fall in the price of X, more of good X is purchased due to the substitution effect, but not as much more as might have been purchased had there been no offsetting income effect. In the case of an inferior good, the demand curve still slopes downward from left to right, but only because the substitution effect is strong enough to be only partially offset by the income effect, but not overwhelmed by it. The reader is invited to imagine the shape of the indifference curve map for two goods, X and Y, to illustrate the case of an inferior good consequent upon price changes in either direction.
Alfred Marshall, in his 1890 Principles of Economics, made anecdotal reference to a phenomenon reputed to have been observed by Sir Robert Giffen during the 19th century potato famine in Ireland. With the decrease in the availability of potatoes, a staple of the Irish peasants' diets, the price of potatoes increased substantially. Because the peasants' incomes were so meager, they could not get enough calories by substituting more expensive sources, such as mutton, for the higher-priced potatoes. So according to Giffen they attempted to buy more potatoes at the higher prices to replace even the small amounts of mutton they had formerly consumed in their diets. Economists have subsequently looked far and wide for empirical evidence of the existence of so-called "Giffen goods". However, the search has to date been fruitless since no verifiable empirical evidence has yet been found to substantiate the actual existence of a Giffen good.
Giffen goods if they could be identified, would be inferior goods with such strong and offsetting income effects as to completely over-power their substitution effects when their prices change. In the case of a Giffen good, the demand curve would be sloped upward. Again, the reader is invited to imagine the likely shapes of the indifference curves in an indifference curve map of a good that has such a strong offsetting income effect that it would be a Giffen good.
The managerial implications of income and substitution effects lie in determining the degree of price elasticity of the demand curve, a topic explored in Chapter 8.
BACK TO CONTENTS
CHAPTER 8. ELASTICITY AND DEMAND SPECIFICATION
In this chapter we extend the concepts developed in Chapter 7 into the realm of the statistical estimation of the demand function. First, we consider the concept of elasticity of demand as a decision criterion. Then, after we have discussed the procedures for the specification of a demand function, we consider the implications of various specification problems for the elasticity of demand.
Revenue and Elasticity
The slope of the own-price demand curve, DQ/DP, contains some information that may be useful to the management of the enterprise. It may be interpreted as the number of units by which quantity sold can be expected to change in response to a change in the price of the item, given all other determinants of demand. If the management is interested in nothing more than predicting the number of additional units that can be sold by changing price, the slope of the own-price demand curve is an entirely adequate decision criterion. However, if the management is concerned about profitability or one of its components, the revenue generated in selling the item, the simple slope of the own-price demand curve is an inadequate decision criterion. The reason for its inadequacy is that the slope of a linear own-price demand curve never changes over its entire positive-price range, but, as became apparent in the previous chapter, total revenue does differ from one point to another along the demand curve.Even if the slope of the demand curve does change because it is not linear, the simple slope still fails to convey information about how the revenue of the firm changes consequent upon a price change. A more useful revenue-oriented decision criterion can be constructed by computing the ratio of the percentage change of quantity demanded to the percentage change in the price that resulted in the quantity change, or
Figure 8-1. Demand, Revenue, and Elasticity for Qx = 80 - 4Px.
curve, from price of $20 down to $10, is labeled the elastic range. It is characterized by positive marginal revenues and elasticity ratios (absolute values) greater than unity. The lower portion of the demand curve, from price $10 down to $0, is labeled the inelastic range. It is characterized by negative marginal revenues and fractional elasticity ratios (again, absolute values). The midpoint of the linear demand curve (at price $10) is labeled the unitarily elastic point because the absolute value of the demand elasticity ratio is precisely 1.0 at this point. Demand at the unitarily elastic point is also characterized by zero marginal revenue.
In the elastic range of the demand curve, any particular percentage decrease of price will result in a larger percentage increase of quantity demanded. Thus, what is lost to revenue by cutting price is more than made up for in increased quantity sold, so total revenue increases. For example, if price is lowered from $18 to $16, quantity demanded will increase from 8 units to 16 units, and total revenue will increase from $144 to $256. Price fell by 11 percent, but this was more than made up for by a 100 percent increase in quantity sold.
However, in the elastic range of the demand curve, any particular percentage increase of price will result in a larger-percentage decrease of quantity demanded, thus causing a decrease of total revenue. In this case, what is gained in raising the price is more than offset by the loss in quantity sold. Thus, if the manager can verify that the enterprise is presently selling the item at a point in the elastic range of the demand curve, the appropriate direction in which to change price in order to increase revenue is down.
The opposite conclusions emerge for the inelastic range of the demand curve. A price cut in the inelastic range will result in an increase of quantity demanded, albeit one of a smaller percentage magnitude, so that total revenue can be expected to decrease. If the objective is to increase revenue, price should be raised because a smaller-percentage decrease in quantity demanded will result. In the example illustrated in Figure 8-1, a price cut from $9 to $8 will result in an increase of quantity sold from 44 to 48 units, but a decrease of total revenue from $396 to $384.
Small percentage changes of price in the near neighborhood of the unitarily elastic point of the demand curve will be offset by the same percentage changes of quantity demanded (but in the opposite direction), thereby leaving revenue unchanged. In our example, if price is raised from $9 to $11, quantity demanded will fall from 44 to 36 units, leaving total revenue unchanged at $396.
If the enterprise were to progressively lower price, moving down the demand curve from its intercept with the price axis toward its intercept with the quantity axis, total revenue would increase to a maximum (at the unitarily elastic point), and then decrease; concurrently, marginal revenue would decrease from positive values, through zero (at the unitarily elastic point), to negative values. And, elasticity would fall from (absolute) values greater than unity to (absolute) values less than unity.
The significance of own-price elasticity of demand is that it is indicative of what is likely to happen to the enterprise's revenues when it changes the price of an item that it sells. Enterprise managers may not explicitly compute elasticity ratios, and they may not use the term elasticity of demand. However, we may infer that they must have employed an elasticity thought process in making a rational decision to change price if their enterprises have survived and are profitable.
To this point we have assumed that the demand curve is linear, but only for purposes of simplicity. Since only one point on a demand curve exists at any moment (all other points are only hypothetical or virtual), it can be argued that the shape of the demand curve away from the extant point (whether curved, bent, kinked, etc.) is really a non-issue. But, even if the demand curve is curvilinear, all of the elasticity formulas introduced in this chapter can be applied to compute or estimate the elasticity of demand. Graphically, whether demand is elastic or inelastic at a particular point on a non-linear demand curve can be discerned by observing the characteristics of a tangent drawn to the curve at the point.
The demand curve for an item may take any slope, although a negative slope is expected according to the law of demand. Negatively-sloped demand curves that approach the vertical, as illustrated in panel (b) of Figure 8-2, are often said to be "inelastic demand curves." It would be more accurate to note that the
Figure 8-2. "Elastic" and "inelastic" demand curves.
relevant price range spans only the inelastic portion of the demand curve. There is an elastic range (off the vertical axis scale), but it is irrelevant under current pricing conventions. We should also note that the marginal revenues associated with points on the visible portion of this demand curve are all negative. This point is important because it is not possible for an enterprise to reach a profit maximizing equilibrium in the inelastic range of its demand curve since its marginal cost can never be negative (more about this in Chapters 11 and 16).
A similar consideration should also be noted in regard to demand curves with very shallow slopes, approaching the horizontal, as illustrated in panel (a) of Figure 8-2. While such demand curves are often described as being "highly elastic," it would be more accurate to say that the relevant quantity range encompasses only the elastic range of the demand curve. There is an inelastic range, but only at quantities that are unattainable under current market and supply conditions. Marginal revenues associated with elastic points on such shallowly sloped demand curves will be positive, and thus can accommodate a profit-maximizing equilibrium solution for the enterprise.
Elasticity Formulas
Our discussion of elasticity to this point has focused on the own-price elasticity of demand, but elasticity is a more general concept not restricted exclusively to own-price. The demand elasticity ratio can be computed with respect to any relevant demand determinant, including own-price. Letting the symbol "X" refer to an unspecified demand determinant, its elasticity can be computed by any of the following formulas, given the requisite information:
A simple algebraic rearrangement of this elasticity formula yields
If the limit concept of the calculus is applied,
at the limit as DX approaches 0.
The net of this formula development process is that X elasticity can be computed as the product of the derivative of the demand function with respect to X, and the ratio of the amount of X to the quantity Q. If there are other relevant demand determinants than X, the X elasticity ratio should be computed as a partial (rather than a simple) derivative, i.e.,
This formula is referred to as the point elasticity formula because it can be computed from information about one point on the X demand curve if the equation of the demand curve is known.
Alas, this latter condition, i.e., that the equation of the demand curve must be known, may constitute a serious barrier to the employment of the elasticity ratio as a decision criterion because the equation often is not known, or cannot be satisfactorily estimated. However, an approximation to point elasticity, known as arc elasticity can be computed if information about two points along the X demand curve are known, even if the equation of the X demand curve is not known. Formula (5) can be constructed from formula (2):
where the subscripts refer to the two points identified as points 1 and 2. The expression (Q2 - Q1) constitutes "DQ," and the expression (X2 - X1) is "DX". We note that point 1 is taken as the base or starting point for the computation. However, this particular formulation exhibits a deficiency in that different values for the computed X elasticity ratio emerge if the identities of points 1 and 2 are reversed. This deficiency can be relieved by estimating the average elasticity over the arc of the demand curve between points 1 and 2 using formula
where (Q2+Q1)/2) constitutes the average of Q2 and Q1, and ((X2 + X1)/2) is the average of X2 and X1. Finally, formula (6) can be simplified because the 2s in the denominators of the ratio cancel each other, resulting in
This final formulation, the so-called "average arc elasticity" formula, can be computed if only two points on the X demand curve are known, but it must be recognized as only an approximation to the true elasticity at either known point, or any point on the arc between the known points. Depending upon the shape (i.e., concavity) of the X demand curve, the average arc elasticity ratio may be an over- or understatement of true point elasticity. The reader is invited to explore the conditions resulting in over- or understatement.
Elasticity and Other Demand Determinants
We now explore the conceptual sense of several specific X-demand elasticity ratios. The so-called "income elasticity of demand" may be computed if information about the clientele's income is known and other demand determinants remain unchanged. Any of the elasticity formulas elaborated in the previous section may be employed simply by substituting income for X in the selected formula, e.g.,
The computed income elasticity of demand for a normal good is expected to be positive, while that for an inferior good is expected to be negative. But conclusions should never be assumed before conducting empirical research. From this perspective, a computed positive income elasticity of demand ratio may be taken as the basis for an inference that the item is a normal good; likewise, a computed negative income elasticity ratio implies that the item is an inferior good. But even if the item is deemed normal, the value of the elasticity ratio may contain useful information. Positive income elasticities less than unity imply that the demand for the item is relatively inelastic (i.e., unresponsive) with respect to income changes. Income elasticities greater than unity suggest that the demand for the item is relatively elastic with respect to income changes. The reader is invited to review the earlier section of this chapter that suggested reasons for managerial preferences to produce normal and inferior goods.
The management of the firm may have chosen to take an aggressive approach to the demand for its item by mounting a promotional effort. The relevant question in this regard is whether the demand for the item is elastic with respect to the promotional expenditure (e.g., the advertising budget for a particular medium). The relevant elasticity formula can be expressed as
The management might be pleased to find a positive advertising elasticity ratio greater than unity. The reader is left to imagine the management's reactions to advertising elasticity ratios less than unity (or, heaven forbid, negative!).
Finally, we consider the sense of the so-called cross (or cross-price) elasticity of demand ratio. This term may be understood in comparison with the term "own-price" elasticity of demand. A cross-price demand curve shows the graphic relationship between the quantity demanded of one item, say x, relative to the price of another item, y or z. As noted earlier, y and z may refer to substitutes and complements, respectively, for x. The cross-elasticity of demand for the substitute good y can be expressed as
and that for complement good z as
The sign of the substitute cross elasticity ratio is expected to be positive: when the price of y rises, less of y will be demanded, but more of its substitute x will be demanded. And the sign of the complement cross elasticity ratio is expected to be negative. Again, neither substitutability nor complementarity should be assumed; empirical evidence should be compiled to reveal whether two goods appear to be substitutes or complements, and the magnitudes of the computed ratios (in absolute value, greater or lesser than unity) should indicate how good or strong is the relationship. The substitute cross elasticity ratio has been proposed as an index of the ability of a competitor to penetrate the market of the enterprise by cutting price (or the ability of the enterprise to insulate itself from competitor's price changes).
We have now considered the managerial implications of own-price, cross-price, income, and advertising elasticity of demand. The principles underlying these concepts are applicable to demand elasticities of yet other determinants that have not been specified. Each item can be expected to have a set of demand determinants that are specific to it, and which may not be pertinent to many or any other items.
While demand elasticity can be computed for any demand determinant for which sufficient information is available, we do not mean to suggest that successful managers must make explicit demand elasticity computations before each and every demand decision. Rather, the concept of demand elasticity is the economist's explanation of a thought process through which the successful manager must have passed in making the decisions that resulted in the success of the enterprise. Whether or not any demand elasticity ratio has been computed, the manager has to have asked the question of whether a contemplated demand determinant change is likely to result in a larger or smaller percentage change in the quantity demanded of the item. We shall subsequently discover that the elasticity concept can be extended into the realm of supply, production, and cost.
The Empirical Estimation of Demand
Ideally, the enterprise manager should predicate pricing decisions upon an accurately-formulated demand function for each item that the enterprise sells. This ideal is feasible only for enterprises that sell one or only a small number of items. The task of estimating a demand function is sufficiently arduous and costly that few firm managers are willing to devote the necessary resources to the task when demands for more than a few items must be estimated. In extreme cases, for example the grocery retailer or hardware wholesaler who stocks literally thousands of items, the task of estimating demand for all items becomes a physical and economic impossibility. We shall consider alternative approaches typically employed by such multi-item enterprises in Chapter 17.For the moment we shall focus upon the procedures for estimating the demand for a single item, for example dozens of grade A large eggs, or half-gallons of 2% butter-fat milk. The first step in specifying a demand function is to model the relationship between quantity demanded as dependent variable, and all demand determinants that the analyst thinks might affect quantity demanded as independent variables. The modeling process should follow the procedures outlined in Chapter 3 to select the possible independent variables and the likely form of relationship of each (linear, polynomial) to the dependent variable and to other independent variables (additive, multiplicative). The modeling process should also hypothesize the expected sign of the coefficient of each independent variable, e.g., negative for own-price, cross-price of a complement, and income in the case of an inferior good; positive for cross-price of a substitute and income in the case of a normal good.
Once the function has been modeled, the manager can estimate the parameters of the function in a manner similar to Fritz Machlup's educated guess based upon a summing up of the situation compared to experience with similar situations in the past ("Marginal Analysis and Empirical Research," in Essays in Economic Semantics, W. W. Norton & Company, 1967, p. 167). Or, he can engage in the more-formal process that we shall elaborate in the remainder of this section. The Machlup-like seat-of-the-pants method is likely what managers do most of the time and in regard to most of the items that they sell, especially when their enterprises sell large numbers of items. Although no explicit equation results from this process, an implicit demand equation does underlie each educated guess of the number of units salable, given various values of the relevant demand determinants. This informal approach may be the only one possible in the case of a new item for which no current information or historical data can be obtained.
The following discussion of the formal estimating procedure is important both because the manager may indeed wish to estimate the demand function for some of the items sold by the enterprise, and because knowledge of the formal procedure can be beneficial to the informal summing-up process even if the demand function is not explicitly specified.
The formal estimating procedure culminates in an explicit equation that can be used to compute (i.e., predict, estimate) the unit sales of the item under various demand-determinant conditions. The equation may be linear or polynomial, additive or multiplicative, and may include as many independent variables as the analyst deems significant to the explanation of unit sales. The typical form of such a linear, additive demand equation is
where X1 through Xn are such demand determinants as own-price, cross-prices, incomes of prospective clients, advertising expenditures, etc.
If there is only one demand determinant, say own-price, the equation will be of the slope-intercept format similar to that of equation (1) of Chapter 6. However, if there are more determinants than one in the equation, the constant a cannot be interpreted as an intercept parameter for any one of the demand determinants.
A typical second-order (or quadratic) demand equation including only one independent variable would take the following form,
Higher-ordered terms for X1 can be present, and terms for other variables (X2, X3, ...) can be included to any order (squared, cubed) as deemed important.
Once the demand function has been modeled, and assuming that the item is already being sold so that pertinent data can be obtained, the usual procedure for estimating the parameters of the demand model is regression analysis as elaborated in Chapter 4. The associated inference statistics provide means for assessing the statistical significances of the estimated coefficients of the included variables. The analyst should attempt to include in the model as independent variables as many demand determinants as are likely to make significant contributions to explanation of the behavior of the quantity demanded. Then, any variables for which estimated coefficients are judged not to be statistically significant can be deleted from the model before it is respecified.
Occasionally the analyst will find data appropriate to the demand specification process published in industry or trade sources, or compiled by government or private agencies. More often than not, however, demand data for individual items in specific locales do not exist, and must be captured as a matter of original field research. The first field research decision that the analyst must make is whether to capture the data cross sectionally (i.e., across a number of subjects at a point in time), or as a time series (i.e., for the same subject over a period of time). A cross-sectional approach is preferred if it is thought that demand determinants not explicitly included in the model might change over time. However, a cross-sectional approach might require access to competitors' demand information, which they are likely to be reluctant to provide voluntarily.
If the analysis must be restricted to a time-series approach, the analyst should take care to include within the model all demand determinants that are likely to change over time. The analyst may also include so-called "dummy variables" (values of 0 and 1) as a means of quantifying such qualitative conditions as type of outlet (e.g., convenience store vs. full-line grocery store) or whether or not a special promotion is in effect.
Specification Errors and the Identification Problem
A so-called specification error is often indicated by a coefficient of multiple determination (R2) which is substantially below unity. The specification error occurs either because one or more important determinants of demand were omitted from the model, or because an included variable was raised to the wrong power (e.g., linear instead of quadratic or cubic).Another type of specification error, an identification problem, may not be indicated by any inference statistic. The best indicator that an identification problem may have occurred is a sign on an estimated regression coefficient that is different than expected, e.g., a positive sign on the own-price regression coefficient. The cause of an identification error is a simultaneous relationship between the dependent variable (quantity demanded) and some determinant (e.g., consumer income) that was omitted from the model.
As an illustration of the problem, let us suppose that a cross-sectional data capture process yielded the quantity and price data in columns (1) and (2) of Table 8-1. The row-wise pairs of observations in the quantity and price columns serve as coordinates for plotting points A, B, C, D, E and F in Figure 8-3. Because these points scatter around an upward-sloping curve, D1, the coefficient of determination is quite low, 0.07, so a specification error may be indicated. Also, the slope of the curve D1 is positive, thus suggesting a violation of the law of demand. The problem is that points A, B, C, D, E, and F do not lie along a common own-price demand curve. Each point lies on a separate own-price demand curve that differs from the others because another determinant which has not been included in the model, income, has varied from observation to observation. These separate own-price demand curves are illustrated in Figure 8-4.
Table 8-1. Data for specification of a demand function.
Figure 8-3. Price and Quantity Data Plotted on Coordinate Axes.
Figure 8-4. The Identification Problem Revealed.
Additional data, shown in column (3) of Table 8-1, were subsequently obtained for the average incomes of the clients at stores where the original price and quantity data were collected. Column (4) of Table 8-1 contains an index of the income data; a convenient income observation was selected to serve as the index base. The column (4) index numbers were then used to adjust the column (1) quantity data (the adjustment is analogous to the process of deflating a money-value series by a price index) to remove the effects of the income variations. The adjusted quantity data are recorded in column (5) of Table 8-1. Now, when the adjusted quantity data are plotted against the price data from column (2), points F, G, H, I, J, and K emerge in Figure 8-5. A curve D2 has been fitted through these points that yields a coefficient of determination of 0.86. Also, the slope of D2 is negative as expected from the law of demand.
Figure 8-5. An Income-constant Demand Curve.
The curve D2 in Figure 8-5 can be interpreted as an income-constant demand curve. Curve D1 exhibits an identification problem because, since the points lie on different demand curves due to the income variation, the true locus of the own-price demand curve could not be identified. The identification problem occurred because of the simultaneous change between own-price (included in the model) and income (not included in the model).
The Identification Problem and Demand Elasticity
Suppose that an analyst estimates a demand function like curve D1 in Figure 8-3, but fails to recognize the presence of an identification problem. If the own-price elasticity of demand is computed at any point along D1, it will have a positive sign, which indicates a perverse own-price demand elasticity. However, if the identification problem is eliminated using a procedure similar to that described in the previous section so that own-price elasticity can be computed for curve D2 in Figure 8-5, the expected negative own-price elasticity ratio will result.In many cases, however, an unexpected sign of a computed elasticity ratio or the wrong slope of the estimated demand curve may not occur as a clue to the presence of an identification problem. Figure 8-6 illustrates a downward-sloping path of plotted demand data points, but the
Figure 8-6. An elastic demand expansion path.
simultaneous occurrence of change of income causes a shift of the true income-constant demand curve from locus D3 to D4 and then to D5.
The path traced out by points K, L, and M constitute not a true demand curve, but rather a demand expansion path. If a demand equation is estimated from data for points K, L, and M, it will have the expected negative slope, but the slope will be shallower than that of a the true demand curve at any of its loci. Also, if average arc elasticity is computed from information about points K and L, the elasticity ratio will be negative as expected, but will imply that demand is far more elastic than it truly is along any locus of the true income-constant own-price demand curve. In fact, the implication may be that own-price demand is elastic when it truly is inelastic. A price decision maker who bases a price change decision on such an erroneously computed elasticity ratio will likely lower price when it should be raised.
The moral of the story is that the analyst should take great care to be sure that the demand function is being estimated from points along a common, fixed-locus, own-price demand curve (i.e., one which exhibits no identification problem). Great care should be taken to ascertain that the two points from which the average arc elasticity ratio is computed do lie along the same demand curve.
The concept of the demand function provides the economist with a formalized vehicle for analyzing the demand for an item. Enterprise managers usually function to "size-up" and estimate the quantity demanded of an item without formally estimating a demand function. But more sophisticated managers who require more accuracy in their demand estimates may be willing to devote the necessary time and effort to the formal estimation procedures that we have outlined in this chapter. In Chapters 12 through 15 we shall see how demand and cost analyses can be brought together to assist the rational manager in his effort to maximize the profits of the enterprise.
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APPENDIX 8A. THE ECONOMIC TASKS OF MARKETING
Marketing is one of the four functional areas of business administration (management, finance, accounting, marketing), and as such is a variant of applied economic policy in the microeconomic arena. Marketing is concerned with the cost side of microeconomic decision criteria only in providing the demand enabling conditions for spreading overhead costs in the short run and exploiting scale economies in the long run. From an economic theory perspective, there are three tasks for marketing to accomplish in regard to demand:
(2) subsequently, to shift the product demand curve to the right, or prevent it from shifting leftward; and
(3) to improve the attitude of the demand curve or prevent its attitude from deteriorating.
1. When a new product is introduced, whether in a home or foreign market, virtually nothing is known ex ante the introduction about the locus of the product's demand curve in that market. This may be illustrated graphically in Figure 8A-1A by a demand curve that is coincident with the vertical (price) axis. The immediate marketing problem is to conduct research to gain information adequate to determining where the demand curve might lie in price-quantity coordinate space at the startup of sales of the product in the new market. For an absolutely new product never before marketed, the information resulting from market research may be little more than speculation. For products that have been sold before in markets with characteristics similar to the target market, the procedure may simply be extrapolation of what is known about the established markets to the new target market, with appropriate adjustments to account for environmental and cultural differences between the established markets and the new target market. The problem is compounded for foreign target markets since environmental and cultural settings may be sufficiently different from those of established markets that simple adaptive tranference of information is not effective. In such circumstances the product may have to be actually marketed or test marketed at the new site in order to generate the first information upon which reliable demand analysis may be based. Figure 8A-1B shows a hypothetical location of a demand curve for a new product upon its initial offering in a new market.
Figure 8A-1A.
Figure 8A-1A.
Once a "fix" can be gotten upon the properties of the product demand curve in the new market, it should be possible to assess price elasticity of demand over some range of product prices. Price elasticity of demand may be measured as a percentage change in quantity demanded divided by the percentage change in price, assuming no other causative factor has changed. Price elasticity of demand information can serve as criteria for determining an appropriate price relative to the firm's behavioral objectives (e.g., profit maximization or satisficing, growth measured by volume of sales, sales revenue, performance relative to recent history, or share of market, or yet other behavioral objectives). If demand is elastic, the firm can increase its revenues only by lowering price; if demand is inelastic, revenues are increased by raising price.
Demand elasticity is accurately measured over an arc (i.e., between two points) on a single demand curve that has not shifted. A matter that may cause assessment difficulties with measures of price elasticity of demand is that causative factors other than the product's price may have caused the demand curve to shift simultaneous with a change of product price. This problem is referred to by economists as an "identification problem" since with points on two different demand curve locations a single demand curve is not uniquely identified. Depending upon whether the demand shifted right or left when price is decreased, measured elasticity will tend to be over- or understated.
2. The second task of marketing is manipulation of the locus of the demand curve. With the passage of time, changing non-price determinants of demand can be expected to shift the demand curve, with consequent changes in price elasticity of demand. On-going monitoring of price elasticity of demand should enable rational price change decisions. For example, as illustrated in Figure 8A-2, increases of demand (illustrated as rightward shifts of demand curves) tend to render demand less price elastic at any established price level. Decreases of demand (leftward shifts) cause demand to become more elastic at the going price. In Figure 8A-2, point A on curve D1 is in its elastic range. To increase revenue the firm would have to lower price. As demand shifts rightward toward D2, elasticity progressively decreases. From point B on D2 in its inelastic range, the firm can increase revenue by raising price.
Figure 8A-2.
The firm may choose to respond passively to favorable shifts of demand, e.g., rightward shifts attributable to population growth and rising incomes. Firms that are oriented toward growth rather than profitability will be inclined toward aggressive marketing efforts designed to shift their product demand curves to the right. Rightward demand shifts lower elasticities of demand and facilitate price increases. Adverse shifts of product demand may occur in response to economic contractions or intensifying competition. Should the demand for one of the firm's products shift adversely due to changing conditions, demand tends to become ever more elastic at the established price level, and militates in favor of cutting prices. The marketing task is to mount an appropriate campaign to reverse or slow the pace of the adverse shift.
3. The "attitude" of a demand curve is its slope. A demand curve with a fairly shallow slope has a relatively poor attitude from the perspective of managerial decision making because demand is highly elastic over the relevant output range. This means that management has little pricing discretion. It also means that the firm must be prepared to cut price in order to increase revenues. From a managerial decision perspective, the attitude of the demand curve may be improved by doing something to cause it to become more steeply downward sloping. Even if the demand for a product is not increasing (or cannot easily be increased by marketing promotion), it may be possible to design a marketing program to enhance perceptions of the image of the product in the public mind to the end of rendering the demand curve more steeply downward sloping. As a demand curve rotates to become more steeply downward sloping (left to right), elasticity at any given price level will decrease toward inelasticity.
This may be an especially important matter under certain circumstances, e.g., when demand is fairly shallowly sloped and below average total cost (ATC) as illustrated by D1 in Figure 8A-3. Point A lies at the mid-point of the linear demand curve, below which marginal revenue (MR1) is zero. Demand is of unit elasticity (absolute value equal to 1) at the midpoint. Demand above and to the left of point A is in the elastic range (absolute value greater than 1). Given this locus of demand curve D1, the firm is obviously operating at a loss, but can minimize the loss by finding Q1 where marginal revenue is equal to marginal cost. Of course, if price falls below the firm's average variable cost (not shown), it should shut down operations and suffer only the fixed (overhead) costs. In order to achieve profitable operation the firm needs to be able to raise price relative to average total cost. However, a price increase will decrease revenue; only a price cut will increase revenue, but it won't solve the firm's problem in this case.
Figure 8A-3.
But suppose that the firm can mount a marketing effort to enhance the perception of the product in the public's eye sufficient to improve the attitude of the demand curve. So that it cannot be construed as a demand shift, let us suppose that in Figure 8A-4 the marketing effort succeeds in rotating the demand curve around its former midpoint at A to the new locus designated D2 with corresponding marginal revenue curve MR2. The new profit maximizing output is now Q2, only slightly lower than Q1. However, demand curve D2 now rises above the ATC curve to enable profitable operation, and the profit maximizing price is P2, is substantially higher than P1. Point F is the midpoint of D2 where demand is unit elastic. At point C, the profit maximizing point on the demand curve, demand is still elastic, but less so relative to midpoint F than was point B on demand curve D1 relative to its midpoint at A. The marketing effort has succeeded, not in shifting the demand curve, but rather in improving its slope attitude to enable increasing price enough to achieve profitable operation.
Figure 8A-4.
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CHAPTER 9. PRODUCTION IN THE SHORT RUN
Production is the central function of the enterprise. In fact, the possibility of engaging in production activity is the reason that enterprises are organized. The occasion for production activity follows directly from the existence of the economic problem: scarcity and the hope of relieving it by concerted, organized effort.
Varieties of Production Activity
In the broadest possible sense, production activity encompasses nearly all of human effort. Even if life were characterized by abundance, the things desired for consumption would still have to be gathered and transferred or transported to the point of consumption, and then possibly held until the propitious moment. The gathering, transporting, and holding activities certainly are forms of production activity.The act of production is the transformation of raw substances (including human labor itself) into other forms that are distinguished by their more desirable functional, locational, or temporal characteristics. Production of tangible goods encompasses gathering, extracting, refining, combining, assembling, packaging, transporting, and distributing activities. Production of services includes performance activities as well.
Organizing Production
Any single person can produce a variety of goods and services that are more desirable than the natural substances from which they were produced. Why go to the trouble to interact with other human beings to cooperate in a production process? Such effort is warranted because of the potential inherent in specialization and division of labor to improve the efficiency of the production process. Boiled down to its essentials, the economic problem is to use the scarce resources as efficiently as possible in the effort to alleviate the insatiability of demand.Efficiency is the name of the economizing game. Efficiency is served in either of two ways: by producing a larger volume of output from a given amount of inputs, or by employing smaller amounts of the inputs in the production of a target output. Experience has demonstrated that in both cases organized human effort is typically more efficient than is isolated effort.
Managerial Problems in the Production Process
Suppose that all production resulted as a matter of individual effort. In an economic system organized around markets, the market itself provides the mechanism for distributing the results of the productive effort. Since the market can perform this function, what justifies the appearance of such authoritarian organizations as business firms to undertake the production process? Experience has demonstrated that organized productive effort under hierarchical control (i.e., managed from the top down) often is more efficient than are individual efforts. The business enterprise, in several of its organizational guises (proprietorship, partnership, corporation), has provided the vehicle for the organization and control of production in modern society. As R. H. Coase has noted, commercial enterprises are established and thrive where it is less costly (i.e., more efficient) to organize production in centralized, authoritarian power structures than via interaction among individuals participating in market transactions. [R. H. Coase, "The Nature of the Firm." Economica, New Series, Vol. IV (1937), p. 393.]The essential entrepreneurial functions are the perception of an unfilled market demand and the assumption of risk in organizing a productive process to exploit the market potential. The three crucial managerial problems are (1) to select an appropriate technology for implementation of production, (2) to discern the right volume of output to meet the market demand, and (3) to choose the optimal combination of inputs to produce the target level of output. Associated with these three broad problem areas are a myriad of detailed functions ranging from choosing the site for the production facility, procuring inputs and scheduling production, and packaging and distributing the final product.
Real-world production processes may be quite detailed and complex. Our task in this chapter shall be to discern general production decision criteria that can be transferred to specific production situations. What we are about is learning how to think about production problems rather than what to do in specific situations.
PRODUCTION PRINCIPLES
The Relevant Questions
Every production decision maker must confront four basic questions:
b. What size plant should be constructed to implement the selected technology?
c. At what volume of output (or rate of production) should the constructed plant be operated?
d. What are the appropriate quantities of input to combine to produce the target output.
These fundamental production questions will not always be addressed in the same sequence. Some of them must be confronted simultaneously. The perceived market demand ultimately constrains the answer to the volume-of-output question and suggests a response to the size-of-plant question. The target production volume may then limit the eligible range of technologies. We shall defer consideration of the volume-of-output question to Chapters 9 and 10. Assuming that the target volume is known, we shall address the technology question later in this chapter. Our immediate task is to confront question (d), the appropriate quantities of inputs to be combined to produce output.
The Production Function
The analysis of production requires an examination of how inputs are combined to produce output. The analysis may also be directed to the effects upon the volume of output of changing any of the employed inputs. Economists have adopted the functional notation conventions of the mathematics to describe production relationships. Letting broad categories of physical inputs be represented by the symbols,
R = resources
K = capital
then a generalized production function can be represented as,
where Q is the volume of output.
But equation (1) is an incomplete specification of the production function. There are two possible ways to complete it. One is to further specify additional aspects of production that are represented as implicit inputs:
Here the symbols T, E, and M stand for technology, entrepreneurship, and managerial capacity. They are grouped together and separated from the list of physical inputs by the semicolon because they are not per se physical inputs. Rather, they both enable and constrain the combination of the physical inputs in the production of outputs.
In recognition that T, E, and M are not physical inputs, some analysts prefer the following representation of the production function:
(4) f = g ( T, E, M ).
This representation clearly indicates the relationship between physical inputs and output in equation (3), but signifies with equation (4) that the production function itself is a function of other conditions, i.e., technology, entrepreneurship, and managerial capacity.
While these are abstract production function representations, a production function that is specific to a particular production process might include in its input listing various types of labor, materials, and capital. An example of a production function to which almost anyone can relate is any kitchen recipe for the preparation of an edible dish. Boiled down to essentials, a production function is nothing more than a list of ingredients together with instructions for combining them in the preparation of a desired output.
The Production Surface
In order to examine production input-output relationships, it will be convenient to envision three-dimensional surfaces that represent output (Q) on the vertical axis, and two inputs, such as labor (L) and capital (K), on the horizontal (or floor) axes. The functional notation for such a surface may be given as
where the slash is the conventional indication that all items in the input list appearing to the right of it (in this case, "all other variables") are assumed constant.
Four hypothesized shapes for the three-dimensional production surfaces are illustrated in Figure 9-1. The four panels show, respectively, the following output patterns as the quantities of the inputs are increased:
(b) output increases at a constant rate;
(c) output increases at a decreasing rate; and
(d) output increases at varying rates in the sequence of increasing, constant, and decreasing rates of increase.
There are of course other possible patterns that might be imagined, including an absolute decrease of output consequent upon employing more of the inputs. The output-decrease possibility is a logical extension of patterns (c) and (d) for excessively large increments to the inputs.
Not all of these hypothesized shapes are plausible representations of real-world production relationships. Panels (a) and (b) illustrate two patterns that are thought to be inconsistent with observed production phenomena over any but the shortest ranges of the inputs. It is thought that most real-world production processes exhibit the behaviors represented by panel (c), or possibly the generalized shape of panel (d) which incorporates over limited input ranges all three of the other hypothesized shapes.
The Long and Short-Run Time Frames
The three-dimensional surfaces illustrated in Figure 9-1 imply that production decision makers might enjoy a great deal of freedom in varying the two inputs, or in choosing any eligible combination of inputs represented by the coordinates of points in the floors of the diagrams. In reality, such freedom of choice is constrained by the time-frame setting of the decision context.
Figure 9-1. Hypothesized shapes of production surfaces.
In the analysis of how input variation affects output, given a selected technology, economists distinguish three situations: (a) a single input is changed vis-a-vis fixed quantities of all other inputs; (b) all inputs are changed (positively or negatively) by the same proportion (greater or lesser than 100 percent); or (c) inputs are changed in varying proportions vis-a-vis each other. The first case describes the analysis of returns a variable input; the second describes returns to scale; the third describes the general situation, variable proportions, inferences about which may be drawn from an analysis of the first two situations. We shall defer consideration of returns to scale and variable proportions to a later section of this chapter.
The realm of returns to a variable input permits us to distinguish the short run from the long run. In the long run, all inputs are presumed to be variable. The analysis of returns to scale thus belongs to the long-run. A change of a single input, given fixed quantities of other inputs, is then clearly an analysis of the short run. The short run can be described as the period of time during which at least one of the inputs cannot be changed. The duration of the short run is until the yet-unchanged input can be changed. In the real world, production decision makers may plan for the long-run changes that they intend to make, but all decisions are made in short-run settings, even the decisions to make long-run changes. In this sense, then, the freedom of the decision maker to vary inputs is constrained by the temporal setting.
It is tempting to identify capital as the input class that typically is fixed in the short run, but we must recognize that this concept is not descriptive of all real-world situations. An example of this caveat consists in the family-owned business (a farm or a commercial establishment) where the labor force is the fixed input (mom, pop, children, cousins, etc.). The relevant input question in the short run is how much land or capital equipment to use (rent, buy), not how much labor to employ.
THE VERTICAL SLICE APPROACH
[This is one of two possible approaches, the other being a "horizontal-slice" approach. The author has chosen to elaborate the vertical-slice approach in the body of this chapter because he believes it to be less abstract and to lead to more operational decision criteria than does the horizontal slice approach. Instructors who prefer an isoquant-isocost approach may find an elaboration of it in the appendix to this chapter.]
We now have in place all of the conceptual tools so that we can begin the analysis of production in the short run. Our objective is to identify the relevant criteria that may be used to guide production decision making by rational and perceptive production decision makers. Because of its behavioral inclusiveness, we shall adopt the generalized shape of the production surface illustrated in Figure 9-1, panel (d). It is reproduced in an enlarged format in Figure 9-2. We should note two essential caveats before proceeding with the analysis. First, many real-world production processes may satisfactorily be modeled with the simpler linear or second-order shapes illustrated in panels (b) and (c) of Figure 9-1. Second, the smooth, continuous surface illustrated in Figure 9-2 is only an heroic representation of what certainly are discontinuous real-world relationships. In fact, no more than a few points on or near such a surface may be observable for any real-world production process.
Figure 9-2. A labor-variable section through a production surface.
The Vertical Slice
A short-run production perspective may be analyzed in Figure 9-2 by taking a vertical slice through the surface, parallel to either floor axis. Let us assume that some quantity of capital, K1, is available from an already-constructed plant, so that the vertical slice is cut parallel to the labor axis, and emanating from the point K1 on the capital axis. We shall repeat this analysis shortly, but with a vertical slice taken parallel to the capital axis.The problem for the production decision maker is to choose an appropriate amount of labor to employ with capital input K1. The analysis may be conducted by assuming alternate labor-employment decisions that follow the path across the floor of the diagram from L1 through L2 and L3. Theoretically, any other quantities of labor along this path might have been chosen; these are simply a few representative quantities. But, the real-world production process might be characterized by a few, discrete labor-quantity choices, such as L1 or L3.
As the labor employed with capital K1 is increased from L1 toward L4, output increases along the path on the surface from Q1 to Q2, Q3, and Q4. Given the adopted shape of this production surface, it is apparent that over the labor input range from L1 to L2, output increases at an increasing rate (the surface is concave upward) from Q1 to Q2. Point Q2 in the surface path is near what mathematicians would call the inflection point, i.e., where a curve changes concavity, in this case from being concave upward to being concave downward. As the labor input is further increased from L2 to L3, output continues to increase to Q3, but at a decreasing rate of increase. Further increases of the labor input from L3 to L4 yield additional output, also at a decreasing rate over the Q3 to Q4 range. It should be clear that the DQ3 output increment is smaller than the DQ2 output increment. This phenomenon of output increasing at a decreasing rate continues some beyond Q4, and until the output path peaks around Q5 and turns downward.
The labor input range from K1 to L2 is described by economists as the increasing returns range. It is thought to be an early or temporary phenomenon in the production process, and may not be observable in most real-world production situations. This range is missing entirely in the surface illustrated in panel (c) of Figure 9-1.
The Governing Principle
The labor input range from L2 to L5 is described by economists as the range of diminishing returns. Its essential characteristic is that output increases at a decreasing rate as the labor input increases. Its graphic illustration is the downward concavity of the production surface, and the output path formed by the vertical slice through the surface. Note that the range of diminishing returns to the variable input ends at the peak of the output path. Beyond L5 and its associated Q5 in Figure 9-2, output can be expected to decrease in absolute terms as the then-excessive quantities of labor greater than L5 are employed.The principle of diminishing returns is thought to govern all real-world production processes. Diminishing returns may not be evident in the very early stages of production characterized by low levels of labor employment, but it becomes obvious as progressively more labor is employed. It is simply implausible to believe and unreasonable to expect that output can continue to increase at increasing or even constant rates forever as the labor input is progressively increased vis-a-vis a given plant size. This physical relationship was recognized earliest in agricultural settings and subsequently in engineering situations. It has been adopted by economists as the fundamental behavioral premise in the explanation of input-output relationships. Although diminishing returns are rarely subject to direct examination or empirical testing, the essential truth of the principle may be verified by the logical process of reduction to absurdity.
As an example, consider a typical peasant farm in South Asia, perhaps 15 acres in size, equipped with a fixed amount of capital equipment including a yoke of oxen and a wooden plow with metal tip, and perhaps two or three other digging or cultivating implements. The peasant farmer by himself can exact some volume of agricultural production from the 15 acres. It is likely that the farmer and his son, working together, can produce more than twice what the farmer alone could produce (the range of increasing returns). As successive additional workers (usually family members) are employed on the farm, output can be expected to continue to increase, but eventually at a decreasing rate, and ultimately to actually decrease if too much labor is employed. In case the reader is skeptical of this conclusion, we invite him to think about the possibilities of employing 5 workers on the 15 acres, then 10 workers, 15, 20, 50, 100, 1000, 1 million workers on 15 acres. Is there any doubt that the principle of diminishing returns has to be true and applicable (at least, eventually) to every real-world production process?
Total, Average, and Marginal Products
Theoretically, any number of different vertical sections, parallel to the labor axis, could be cut through the production surface of Figure 9-2. Each one would differ from the others by the amount of capital (i.e., the size of plant) in use. Practically, the number of discrete plant sizes that can be built is likely to be rather small. For the time being we shall continue to analyze the representative section illustrated in Figure 9-2 by extracting it from the surface and laying it out on a set of two-dimensional coordinate axes in panel (a) of Figure 9-3. Here the production function section traces out a path that economists refer to as a total product (TP) curve. This TP curve is specific to a given technology, entrepreneurial ability, managerial capacity, and plant size; variation along it is accounted for solely by variation in the labor input.
Figure 9-3. Total, Average, and Marginal Product Curves.
Employing analytical techniques first noted in Chapter 6, we can now trace out in panel (b) of Figure 9-3 the average product (AP) and marginal product (MP) curves that correspond to the TP curve in panel (a). The average product of labor may be defined and computed as the amount of output, Q, divided by the quantity of labor, L, employed in its production, given all other inputs, i.e.,
for the ith amount of labor employed. For example, the average product of the L2 volume of labor employed is Q2/L2. With this concept in mind, we should be able to discern the behavior of the labor AP curve by observing the slopes of rays drawn from the origin to successive points on the TP curve. This is so because the slope of the ray drawn to a point on the TP curve is the hypotenuse of a right triangle formed by the horizontal axis and a vertical erected from the labor quantity point on the axis to the TP curve. Then, the trigonometric tangent of the angle so formed is the ratio of the opposite to the adjacent sides of the triangle, e.g., Q2/L2, which we have already defined as the average product of the L2 quantity of labor. In panel (a) of Figure 9-3, rays to the successive points along the TP curve have progressively steeper slopes until Q3 is reached, beyond which the rays become shallower of slope. Thus we can draw the AP curve in panel (b) as rising from the origin to a peak at the L3 quantity of labor, beyond which it falls back toward the horizontal axis. The vertical axis units in panel (b) have been expanded relative to those in panel (a) so that the behavior of AP can be made quite obvious. The relationships among the computed average products for the points along the TP curve illustrated in Figure 9-3 are:
The average product of the variable input is relatively easy to measure; the only information required is the amount of output and the corresponding quantity of the input required to produce the output. Because it is easy to measure, the AP of the variable input is a tempting criterion for production decision making. However, economists usually reject it in favor of the MP of the variable input. The average product of labor does find usefulness in aggregate production settings where it is commonly referred to as the output per capita of the labor force. The downward-sloping range of the aggregate AP of labor curve has been compared to the hypothesized subsistence level of income in neo-Malthusian studies.
The marginal product of labor (MPL) may be defined as the ratio of an increment of output (DQ) divided by the smallest possible increment of labor (DL), i.e.,
This definition should be suggestive of an application of the calculus: the first derivative of the TP function with respect to the labor input, i.e., dQ/dL, may be used as a measure of MPL. If there are other inputs present, a partial derivative must be computed. The MPL measures the rate of change of TP, and can be illustrated graphically as the slope of a tangent to the TP curve at a selected point.
This concept provides the means for discerning the behavior of the MPL. Tangents have been drawn to each of the representative points on the TP curve illustrated in panel (a) of Figure 9-3. As the labor input is increased, and output consequently increased, the slopes of the tangents become progressively steeper. The maximum steepness is reached at point Q2, beyond which they become shallower until a zero slope is reached at Q5. Beyond Q5 the slopes of tangents to points on the TP curve are negative. Thus, we draw the MP of labor curve as rising from the origin to a peak at the L2 level of labor input, then falling until it is zero at the L5 level of labor input, beyond which it is below the horizontal axis.
Since the APL and the MPL curves are superimposed in panel (b) of Figure 9-3, we may note the corresponding behaviors of the two curves. Over the initial range of labor input, MPL rises much faster than does APL. For example, at Q1 the slope of the tangent is steeper than the slope of the ray to Q1. MPL remains greater than APL even after the peak of the MPL curve is reached. MPL decreases and passes through the peak of the APL curve at the labor input level L3. Here, the tangent to the TP curve at Q3 is coincidental with a ray from the origin to Q3. For all labor input levels greater than L3, MPL is both decreasing and less than APL. The slope of the tangent at Q4 is shallower than the slope of the ray drawn to Q4.
For reasons that shall become apparent in subsequent discussion, economists advocate the use of MP as a production decision criterion. However, the MP is a more abstract concept than is the AP, and the true marginal product of a variable input is substantially more difficult to measure and compute than is the average product. In order to compute the marginal product, the equation of the TP function must be known or estimated before the derivative can be computed. The equation of a function can be guessed at, "eyeball" fashion, but the generally accepted means of equation estimation is statistical regression analysis of historical data for the Q and L variables. The data for the regression analysis may have been generated by experimental procedures or captured by observing natural production processes in operation. These procedures are troublesome, time-consuming, and costly. It is no wonder that real-world production decision makers have an aversion to using the MP as a production decision criterion.
Economists make a distinction between the marginal product and the incremental product (IP) of a variable input. While the true MP may be measured as the limit of the ratio DQ/DL as DL approaches zero, the incremental product may be measured as the ratio, DQ/DL, for any measurable DL. With reference to Figure C3-3, panel (a), the incremental product of labor over the L2 to L3 input range can be computed as
In this sense, the incremental product may be measured as the slope of a chord connecting any two points on the TP curve. This is so because the chord forms the hypotenuse of a right triangle drawn to the two points.
Although the true marginal product of a variable input is troublesome to compute, the incremental product is relatively easy to compute. The only data needed are the quantities of output and labor input for the two points on the TP curve. It is important to note two caveats in this regard. First, two observed production points may not be on the same TP curve if one or more of the other (than L) determinants of output have changed (i.e., there may be an identification problem). If the two points happen to be on different TP curves, the computed IP ratio will over- or understate the IP that might have been computed for points on the same TP curve. Second, even if the two observed points are on the same TP curve, the computed IP will over- or understate the true MP computed by differentiation for a point at either end of the chord connecting the two points.
Where does this leave us? MP is the ideal production decision criterion (we shall substantiate this point shortly), but it is troublesome to compute. IP is in practical terms both measurable and computable with relative ease, but it is likely to over- or understate the true MP. The production decision maker is urged to go to the trouble to compute MP if it is not too costly to do so; otherwise, the IP may be computed and used as a decision criterion, subject to the recognition that it is only an approximation to the true MP of the variable input.
The Productivities of Other Inputs
Thus far we have illustrated a vertical slice through the production surface, parallel to the labor axis, on the premises that capital is the fixed input and labor is the variable input in the short run. But we have also noted the possibility of the opposite identities of the fixed and variable inputs in a short-run setting. Any number of vertical slices may be taken through the production surface, parallel to the capital axis, thus simulating fixed quantities of labor, with variable quantities of capital. We could also repeat all of the discussion on the last several pages, but in reference to capital as the variable input. We shall decline to reproduce this discussion, but we invite the reader to study Figure 9-4, which depicts a labor-constant, capital-variable slice through the production surface, in order to confirm the applicability of the analysis to the alternate situation.
Figure 9-4. A capital-variable (labor-constant) section of the surface.
The Stages of Production
Now that we have demonstrated the applicability of the production principles to either labor or capital as the variable input, the stage is set to identify the so-called relevant range of production. To this end we reproduce in Figure 9-5 the surface and vertical slice through it illustrated in Figure 9-2, but with obvious alterations. We retain the assumption that capital is the fixed input with plant K1 in place; the slice parallel to the labor axis implies that labor is the variable input in the short run.
Figure 9-5. Each point on a total product curve for labor is also on a total product curve for capital.
Any point like Q2 on the production surface lies on both a TP curve for labor as variable input and a TP curve for capital as variable input. Thus we have drawn line segments cross-wise to the path of the slice at each of the selected points along the labor-variable TP curve. These cross-wise line segments represent tangents to the surface, the slopes of which measure the marginal products of capital. Even though the quantity of capital does not change, we should be able to compute for every different amount of labor employed both the MP of labor and the MP of capital.
How do the marginal products of labor and capital vary with respect to each other? Figure 9-6 illustrates a TP curve for labor as a variable input, assuming one unit of installed capital. In this illustration, the TP curve is carried to the point where so much labor has been employed that output has fallen to zero. For purpose of illustration, we assume that the horizontal axis between the origin and the point at which TP returns to zero can be divided into ten equal labor units. In panel (b) of Figure 9-6 we represent the explicit labor-variable MP and AP curves that correspond to the TP curve, and further plot selected points along implicit MP and AP curves for capital as if it were the variable input. Along the horizontal scale we note that even though the labor input increases explicitly from zero to ten units, the capital input remains constant at one unit.
Figure 9-6. Marginal productivities in the stages of production.
In Figure 9-6 we may examine the results of explicitly decreasing the labor input from ten toward zero units. When this happens, the quantity of capital employed per unit of labor implicitly increases from 1/10 of a unit to 1/9 of a unit, then to 1/8, 1/7, and so on. Conversely, when the quantity of labor is explicitly increased from one unit to two units, the quantity of capital per unit of labor is implicitly decreased from 1/1 unit to 1/2 unit. Recognition that the relative quantity of each fixed input does implicitly change consequent upon an explicit change of a variable input is essential to an understanding of how the marginal products change vis-a-vis each other.
As may be seen in panel (b) of Figure 9-6, over the initial range of labor input, the MP of labor increases to a peak, then begins to decrease; but the MP of capital is negative. Economists identify this range as the Stage I of production for labor, but the Stage III of production for capital. Likewise, moving from right-to-left as the quantity of capital is implicitly increased, the MP of capital rises to a peak and begins to decrease; but the MP of labor is negative. Economists identify this range as the Stage I of production for capital, but the Stage III of production for labor. A rational and perceptive production decision maker would not choose to operate in either Stage I or Stage III. In labor's Stage I (capital's Stage III), labor is underutilized while capital is overutilized (implied by the negative marginal productivity of capital). In labor's Stage III (capital's Stage I), labor is overutilized (implied by the negative marginal productivity of capital) while capital is underutilized.
We may thus identify Stage II (common to both inputs) as the relevant range of production. Within Stage II the marginal products of both inputs are positive, although they vary in opposite directions. The boundaries for Stage II for each input are found at the point of zero MP for the other input, which coincidentally correspond to the intersections of the MP and AP curves for each of the inputs.
Some very important behavioral relationships may now be noted. Within production Stage II, as either input is increased in quantity, its MP decreases, but the MP of the other input (which explicitly does not vary) increases. Conversely, if the quantity of either input is decreased, its MP will increase, but the MP of its complement(s) may be expected to decrease. Knowledge of this relationship enables us to answer a very important question for the production manager: how can the (marginal) productivity of labor be increased? Two answers are possible: either by decreasing the labor input, or by providing labor with more capital equipment. The former response is typically regarded as a short-run adjustment, the latter as a long-run change.
The Equimarginal Principle
But where within Stage II should the production manager choose to operate? It is tempting to pick the intersection of the two MP curves, but this would be the appropriate point only in a very special circumstance. To answer the question, we need two additional pieces of information, the prices per unit of the two inputs. Then, whatever happens to be the ratio of the unit prices of the two inputs, it follows logically that a corresponding ratio between their marginal products would be warranted, i.e.,
Following this decision criterion, if the MP per dollar's worth of capital is greater than the MP per dollar's worth of labor, the production decision maker should employ more capital and/or less labor. By so doing, the MP of capital will fall and the MP of labor will rise, thereby tending to bring about an equality of the marginal product per dollar's worth of the two inputs. We leave it to the reader to explore alternate possibilities. In Figure 9-6, if the price of a unit of capital is twice the price of a unit of labor, then approximately 5.2 units of labor should be employed to operate the one unit of capital since at 5.2 units of labor the MP of capital is approximately twice the MP of labor.
Cost Minimization vs. Profit Maximization
The equimarginal Principle as elaborated in the previous section can serve only as a decision criterion for finding the least-cost combination of the factor inputs. It cannot however find the resource input combination that maximizes profits because it encompasses only the physical productivities of the resources and their prices or, from the perspective of the firm, their costs. It fails completely to account for the firm's revenue possibilities. As we shall confirm in Chapters 12 and 15, cost minimization and profit maximization are unlikely to occur at either the same level of output or with the same resource input combination.A variant of the equimarginal Principle can be specified to enable discovery of the input combination that maximizes profits. To do so, we must define a new concept, marginal revenue product (MRP). The MRP of a resource is the addition to the firm's total revenue due to selling the additional output resulting from using one more unit of the resource. In a purely competitive context (as defined in Chapter 12), MRP can be computed as the marginal product of the resource multiplied by (evaluated at) the price per unit of the product (i.e., MRPR=MPR x P). In an imperfectly competitive situation, because the firm's product demand curve slopes downward from left to right, the MRP is computed as the marginal product of the resource multiplied by the marginal revenue resulting from selling the additional product, or
We note in Chapter 12 that MR=P in the purely competitive context, so specification (13) is good for both the purely competitive and imperfectly competitive contexts. The schedule of MRP values for different quantities of the resource used by a firm constitutes its demand curve for the resource, DR=MRPR, as illustrated in Figure 9-7.
If the firm purchases the resource in a competitive market, the resource price, PR, is the firm's marginal factor cost (MFC); the firm's MFCR curve would be horizontal and coincident with its resource supply curve at the level of PR. But if the resource is bought in an imperfectly competitive market, the MFC of employing an additional unit of the resource is greater than its price. This is so because the firm has to offer successively higher prices to purchase larger quantities of the resource, and the higher prices normally apply to all units of the resource purchased, not just the additional units. In an imperfectly competitive resource market the resource supply curve slopes upward. The marginal factor cost schedule also slopes upward and lies above the resource supply curve as illustrated in Figure 9-7.
Figure 9-7. Resource demand and supply in an imperfectly competitive market.
These resource market relationships enable specification of the criterion for finding the resource utilization level for any single resource that maximizes the firm's profits, given all other resources:
At any resource utilization level for which MRPR > MFCR, e.g., Q1, the firm can by using one more unit of the resource add more to its total revenue when the additional output is sold than will be added to its total costs by employing the resource unit. Or, if MFCR > MRPR, e.g., at Q2, the firm should reduce its utilization of that resource. This will decrease it total revenues and total costs, but total costs will fall by more than total revenue will decrease. The firm should stop making adjustments to its level of utilization of the resource as soon as there is nothing more to be gained, e.g., at Q3, where
When this equality is attained, profit is maximized. This relationship can be rearranged as
While this criterion is appropriate to a single resource input, given all others, it can be extended to multiple variable inputs as
If any inequality emerges anywhere in this string of relationships, an adjustment to the resource input combination needs to be made. Such an inequality may emerge as technologies, product prices, or resource supply conditions vary. For example, suppose that one of the resources, L, becomes more abundant and its price to the firm falls. This will decrease MFCL, the denominator of the first ratio, thereby causing the value of the ratio to increase. In this scenario the firm should adjust its input combination to use more of the resource L, or less or of other resources. Using more of L will have the dual effect of decreasing its marginal productivity and bidding its market price up. Both effects will cause the ratio MRPL/ MFCL to fall until the string of equalities is reestablished.
Two points need reiteration. First, the resource input combination resulting in the equalities of MRP/MFC across all of the inputs and equal to unity (1) will be the profit maximizing resource input combination. Second, the profit maximizing input combination found by equating the MRP/MFC ratios will not necessarily (in fact, not likely) coincide with the cost minimizing combination of resource inputs that is found by equating the MP/P ratios across all inputs.
Modeling the Production Process
Our purpose is this section is to elaborate the potential usefulness of modeling in the analysis of production relationships.We shall examine a generalized third-order equation of a production function with a single variable input, L, assuming all other inputs constant,
a graphic display of which is illustrated in the top panel of Figure 9-8. In this representation, the power 3 in the third term on the right side of this function makes it a third-order equation. The constant in this equation is missing, implicitly having a value of zero, so that the graphic depiction of the production function passes through the origin. The signs on the coefficients of L2 and L3 indicate that as L increases from the origin, Q at first increases at an increasing rate, then eventually increases at a decreasing rate (the range of diminishing returns) until Q reaches a maximum value, beyond which Q decreases. The average and marginal functions to the Q function are displayed in the bottom panel of Figure 9-8.
Figure 9-8.
Suppose that the value of the coefficient of the L3 term decreases from -0.05 to -0.045 so that the equation of the production function becomes
Figure 9-9 illustrates graphic depictions of the total, average, and marginal functions. It is apparent that all of the curves have shifted upward and outward from the origin consequent upon the change in the coefficient of the L3 term.
Figure 9-9.
As we have noted in Chapters 8 and 9, the loci of the firm's production function curves may change either because wear or weathering (i.e., depreciation) results in capital consumption, or because the management of the firm implements changes in the technologies employed in the firm's production processes. Capital consumption may be expected to shift the product curves downward and to the right. If the technology changes are output-increasing, they will shift the product curves upward. If they are input-saving they will shift the product curves to the left; input-using changes will shift the product curves to the right.
The management of an organization may gather output data via its production and inventory accounting systems; its research staff may perform regression analyses upon the data to estimate the parameters of its production functions. With this information in hand, the management of the firm may model the equations of its total, average, and marginal product functions.
What's Ahead
In this chapter we have examined the implications of changing one input while all other inputs remain constant. This has been essentially short-run analysis. In the long run, all inputs are variable, and it is to this possibility that we turn in Chapter 10.
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APPENDIX 9A. THE HORIZONTAL-SLICE APPROACH
In this appendix we pursue the alternative approach to that elaborated in Chapter 9 for developing the Equimarginal Principle. In the following discussions we shall not attempt an exhaustive exploration of the approach, but shall develop only those concepts necessary to reaching the objective.
The Horizontal Slice
We could choose to analyze any of the production surface shapes illustrated in Figure 9-1. Following the convention established in Chapter 8 we shall focus on the generalized surface shape illustrated in panel (d) of Figure 9-1. Figure 9A-1 illustrates such a production surface where a plane, abcd, parallel to the floor at quantity altitude Q4, has been passed through the production surface tracing out the horizontal slice, efgh. The path, e'f'g'h', in the floor of the surface is the vertical projection of the slice through the urface. Slice efgh is only one of an infinite number of slices that could be taken through the surface at different quantity altitudes.
Figure 9A-1. A horizontal slice through a production surface.
The Isoquant Map
Figure 9A-2 shows a two-dimensional view from a perspective above the surface illustrated in Figure 9A-1. In effect, the three-dimensional surface appears to be collapsed into the floor when viewed from above, but the path e'f'g'h' represents the slice through the surface at quantity altitude Q4. Economists refer to the e'f'g'h' path as an isoquant (meaning same quantity) because it represents a sequence of points, the (K,L) coordinates of which are the input combinations that can produce the Q4 level of output. For example, output Q4 can be produced with the L1 quantity of labor employed with the K1 quantity of capital. Output Q4 can also be produced with less capital, K2, if a larger labor quantity, L2, is utilized. This suggests that labor and capital are to some extent substitutable for one another. Since path e'f'g'h' is drawn as a continuous curve, the implication is that there are an infinite number (or as many as there are points along the path) of combinations of K and L that can produce the Q4 output. In reality, technological considerations may limit the effective number of such combinations to a relatively small number.
Figure 9A-2. An isoquant.
Suppose that instead of selecting a (K,L) combination represented by a point along the isoquant the production decision maker chooses to use the K2 quantity of capital with the smaller L2 quantity of labor, reaching point j on the production surface in Figure 9A-1, and j' in Figure 9A-2. It should be apparent that the smaller quantity of labor working with less capital will produce some output smaller than Q4.
Figure 9A-3 is an elaboration of Figure 9A-2 to show the paths of several other "representative" isoquants that could be generated by horizontally slicing the surface at altitudes other than Q4. It is now apparent that the L1 quantity of labor using the K2 capital input can produce only the Q3 output, which is less than Q4. Theoretically, any number of such isoquants could be generated by slicing the surface at different altitudes so that the floor of the surface might appear "dense" with concentric isoquants. The collection of representative isoquants may be referred to as an isoquant map. The isoquant map may be likened to the collection of isotemp or isobar lines on a weather map, or to the contour lines on a geological or military map.
Figure 9A-3. An isoquant map.
Suppose that the horizontal slices taken through the surface to generate the isoquant map illustrated in Figure 9A-2 were taken at successively higher quantity altitudes that are equal quantity increments apart. In this case, (Q2- Q1) would be equal to (Q3- Q2), and so on. When viewed from above the surface in Figure 9A-1, the isoquant map illustrated in Figure 9A-2 betrays the likely shape of the surface that cannot be seen explicitly in Figure 9A-2. From isoquant Q1 up to isoquant Q4 the isoquants appear to be getting closer together, implying that the surface is increasing at an increasing rate in the quantity dimension. From isoquant Q4 through isoquant Q7 the isoquants appear to become farther apart, suggesting that output is increasing at a decreasing rate. The reader is invited to analyze the likely shapes of the isoquant maps that could be generated from the surfaces illustrated in panels (a), (b), and (c) in Figure 9-1.
The Marginal Rate of Technical Substitution
The slope of an isoquant at any point may be measured by the slope of a tangent drawn to the point, or it may be approximated by the slope of a chord connecting two points near to each other along the isoquant. For example, the slope of the Q4 isoquant over the f' to g' range in Figure 9A-3 can be approximated by the slope of the chord from f' to g', or
The technical name for this slope is the Marginal Rate of Technical Substitution (MRTS). The MRTS is interpreted as the rate at which the firm can substitute labor for capital (i.e., use more labor and less capital) while remaining at the same level of output. Over the f'g' arc of the Q4 isoquant, the firm can maintain output at the Q4 level as the capital input is reduced from K1 to K2 only by increasing the quantity of labor used from L1 to L2. It should be obvious that between f' and g' the MRTS is negative since K2 is less than K1. The MRTS will normally be negative over the economic range of production (we shall identify production Stage II toward the end of this appendix). It will be instructive to examine the right triangle formed by the points f', g', and j'. As we have just noted, the ratio of the sides of this triangle, f'j'/j'g', measures the slope of the third side (or hypotenuse), which forms the f'g' chord. The diagonal movement from f' to g' may be regarded as two separate adjustments represented by the vertical and horizontal sides of the triangle. Specifically, the movement from f' to j' is a decrease in the use of capital (-DK) which, other things remaining the same, would decrease output from Q4 to Q3, or -DQ1. The movement from j' to g' is an increase in the use of labor (DL), which by itself would cause output to increase from Q3 to Q4, or DQ2. DQ2 is of the same magnitude, but opposite sign, as DQ1, so we shall use DQ without sign or subscript to refer to both quantities. Identification of the output changes allows us to specify the marginal products of capital and labor as
Further, we may note that the ratio of the marginal product of labor to the marginal product of capital also measures the MRTS:
This point will prove of value in subsequent discussion.
The Capital Outlay Budget
The isoquant map provides information about production possibilities, but by itself cannot provide the production decision maker with a criterion for selecting an optimal input combination. Additional information is needed in the firm's production budget and the prices of the two inputs, K and L. Suppose that the prices of Labor and Capital are PL and PK, and the firm's management has determined that the production cost outlay must be limited to the dollar sum C. This information can be brought together in the following equation:
The sense of this equation is that the product of the number of units of labor utilized (L) times its price (PL) plus the number of units of capital consumed (K) times its price (PK) cannot exceed the budgeted outlay (C). The firm could underexpend its budget, but sup-pose that the management has decided to commit the entire budget to the purchase of quantities of labor and capital so that the inequality symbol may be ignored. What quantities of each input should the firm employ?
Equition (4) can be usefully rearranged in the following format:
Equition (5) is linear and in the slope-intercept format, y = a + bx, where the slope of the line that represents the equation is the ratio of the price of labor (PL) to the price of capital (PK). It should be noted that this ratio is negative. The conceptual interpretation of this slope is the rate at which the firm can substitute labor for capital while remaining within the budget. The vertical axis intercept is the ratio of the budgeted outlay (C) to the price of capital (PK), which determines the maximum amount of capital that could be purchased by the firm if it purchased no labor at all. Equition (5), henceforth referred to as the budget line, can be plotted on the same set of coordinate axes containing the isoquant map. We may suppose that the values of C, PL, and PK are such that the budget line is plotted as in Figure 9A-4.
Figure 9A-4. An isoquant map and a budget line.
The Optimal Resource Allocation Criterion
At what point along the budget line should the firm choose to employ a combination of labor and capital? As the reader has likely already guessed, the relevant decision criterion is a comparison of the slopes of the isoquant and the budget line, i.e., whether
Point m' is one option involving a large capital input used with a small amount of labor. At point m' the slope of the isoquant, though negative, is very steep, implying that if the firm were to give up the (K3- K4) quantity of capital, it could purchase the (L4- L3) quantity of labor while remaining within its budget. This additional quantity of labor is a great deal more than the firm would have to have to remain at the Q2 level of output. In fact, to exchange the (K3- K4) quantity of capital for the (L4- L3) quantity of labor would enable the firm to move to a higher level of output on isoquant Q3 at point n'. This is obviously a good move that the firm should undertake. The reader is now invited to repeat this analysis using point n' as the departure point.
Suppose that the production decision maker had first determined to try the input combination represented by point s'. At this point the firm employs a relatively large quantity of labor with substantially less capital. The MRTS at point s' is negative, but quite small (i.e., the slope of the isoquant is shallow). The production decision maker is considering replacing the (L5- L6) quantity of labor with additional capital. Only a small amount of additional capital will be needed to allow the firm to remain at the same level of output, Q3. However, by giving up the (L5- L4) quantity of labor the firm can still remain within its budget by purchasing the (K6 - K5) quantity of capital, which will enable it to increase output almost to the Q4 level. This is a good move that the firm should undertake.
As may be readily deduced, the production manager will find an output-increasing incentive to reallocate labor and capital by moving downward along the budget line from points such a m' and n' until the incentive disappears. Likewise, a similar incentive will be found to move upward along the budget line from points such as r' and s' until the incentive is eliminated.
When does the input-reallocation incentive expire? This occurs when a point is reached along the budget line where the slope of the budget line is just equal to the slope of the isoquant. At such a point, e.g., f' in Figure 9A-5, the conceptual interpretation is that the rate at which the firm can substitute labor for capital while remaining at the same level of output (the MRTS) is just equal to the rate at which the firm can substitute labor for capital while remaining within its capital outlay budget (PK/PL). This is the point of tangency of the budget line with an isoquant. It is also the highest output-level isoquant that the budget line can reach. At this point the production manager will have found the output-maximizing combination of labor and capital, given the limitation of the budgeted capital outlay. It is then also the cost-per-unit minimizing combination of labor and capital that can be accommodated by the capital-outlay budget.
Figure 9A-5. The Stages of production in isoquant analysis.
The Equimarginal Principle
Cost minimization occurs at the point representing the input combination that meets the criterion,
And since we have already shown in equation (3) that MRTS also measures the ratio of MPL to MPK, equation (7) can also be expressed as
Stages of Production in Isoquant Analysis
Before we leave the horizontal slice approach, we should also note that the stages of production can be identified on an isoquant map by specifying two ridge lines. One ridge line follows a path formed by the points on the isoquants where they are vertical, the path r1r in Figure 9A-5. At any point below r1r an increase of the capital input will increase output because a higher isoquant will be reached. This implies that the MPK is positive. However, at any point above r1r an increase in the capital input will decrease output (lower quantity altitude horizontal slices will be reached), implying a negative MPK. We may infer then that the region above r1r is Stage III for capital, while that below r1r is capital's Stage II.We leave it to the reader to examine the logic leading to the inference that at any point to the left of r2r the MPL is positive, while at any point to the right of r2r the MPL is negative. This recognition then identifies Stages II and III for labor. The final step is to recall from discussion in Chapter 8 the coincidences of Capital's Stage III with labor's Stage I, as well as that for labor's Stage III and capital's Stage I, and the isoquant stage analysis is complete. The MRTS at any point along an isoquant in Stage II will be negative, and the marginal productivities of both inputs in Stage II will be positive. Outside of Stage II, the MRTS will be a positive slope, and the marginal productivity of one or the other of the inputs will be negative.
Extensions of Isoquant Analysis
There are several other avenues of inquiry in regard to isoquant analysis that the interested reader may wish to pursue. Two of these are the implications of resource price changes, and the possibility of finding the least capital-outlay budget required to produce a target quantity of output. The interested reader is invited to pursue these and other isoquant-related topics by further reading in any standard microeconomic theory text.
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CHAPTER 10. PRODUCTION IN THE LONG RUN
The Long- and Short-Run Time Frames
As we noted in Chapter 9, the three-dimensional surfaces illustrated in Figure 9-1 imply that production decision makers enjoy a great deal of freedom in varying the two inputs, or in choosing any eligible combination of inputs represented by the coordinates of points in the floors of the diagrams. In reality, such freedom of choice is constrained by the time-frame setting of the decision context.In the analysis of how input variation affects output, given a selected technology, economists distinguish three situations: a single input is changed vis-a-vis fixed quantities of all other inputs; or all inputs are changed (positively or negatively) by the same proportion (greater or lesser than 100 percent); or inputs are changed in varying proportions vis-a-vis each other. The first case describes the analysis of returns to a variable input; the second describes returns to scale; the third describes the general situation, or variable proportions, inferences about which may be drawn from an analysis of the first two situations. It is to the second and third cases that we now turn in Chapter 10.
The realm of returns to a variable input permits us to distinguish the short run from the long run. In the short run, some (at least one) inputs may not be changed. In the long run, all inputs are presumed to be variable. The analysis of returns to scale thus belongs to the long-run. In the real world, production decision makers may plan for the long-run changes that they intend to make, but all decisions are made in short-run settings, even the decisions to make long-run changes. In this sense, then, the freedom of the decision maker to vary inputs is constrained by the temporal setting.
To this point we have taken the short-run view that some quantity of one or another of the inputs is fixed while quantities of other inputs are variable. Over the long run, quantities of all of the inputs into the production process can vary. While some can be varied almost continuously (for example, labor), others can be adjusted only in discrete increments (for example, sections of land, additions to warehouses, new assembly lines).
Variable Proportions and Returns to Scale
We shall describe the more general case where the quantities of the inputs change in different proportions vis-a-vis each other as the case of variable returns or variable proportions. Variable proportions encompasses the possibility that quantities of some inputs decrease as others increase. While this is certainly the typical case in the real world, let us first consider the special case wherein all of the physical inputs are assumed to change in the same direction and by the same proportion, i.e., to the same scale. This is the phenomenon of returns to scale.Returns to scale can be analyzed with graphs of production surfaces similar to those illustrated in Figure 9-1. As we did in Figure 9-2, we shall focus on the generalized production surface in panel (d) of Figure 9-1. Again we shall cut a vertical slice through the surface, but along a linear path emanating from the origin at some angle (any, it does not matter) with the labor and capital axis. The angle with respect to either axis is the 90-degree complement of the angle with respect to the other axis. In Figure 10-1 the path to be followed on the floor of the surface (a ray from the origin) is 0ABCD. The corresponding path traced out on the surface is 0Q1Q2Q3Q4.
Figure 10-1.
A Constant Capital-Labor Ratio
The angle chosen for the ray from the origin implies a certain capital-labor ratio that remains fixed as long as the line input path is followed, that is,
If the firm has been producing Q1 by employing the L1 quantity of labor in a K1 size plant, the firm can increase its scale of operations by increasing both inputs (and all others not explicitly included in the three dimensional diagram) by the same factor or proportion. For example, it might double both the plant size and the employed labor force to reach point B where it will employ the L2 labor force in the K2 plant that will enable it to produce the Q2 output. To reach output Q3 while maintaining a fixed capital-output ratio, the firm would have to increase both of its capital and labor inputs by another 50 percent (the same absolute increments as previously) to reach point C. To produce the Q4 output would require another one-third increase (again, the same absolute increment as in the earlier examples) of both inputs to arrive at point D.
Returns to Scale
As the scale of operations has increased while the capital-labor ratio has been preserved, what has happened to output? Consequent upon the shift from point A to point B in the floor of the diagram (a 100 percent increase in both inputs), output has increased by (Q2-Q1), which appears to be a nearly 400 percent increase. We may describe the A to B input change as an output range of increasing returns to scale. The B to C input shift (an increase of 50 percent for both inputs) resulted in an output increase, (Q3- Q2), of about the same proportion, 50 percent. We can describe the B to C input change as an output range of approximately constant returns to scale. We leave to the reader to classify the nature of the returns to scale associated with the C to D input change.We are now in a position to specify some general principles with respect to returns to scale. For any particular change of all inputs in a production process by the same proportion, if the output change is in the same direction and
b. of the same proportion as the input change, this is a case of constant returns to scale.
c. of larger proportion than the input change, this is a case of increasing returns to scale.
It may be quite difficult for production decision makers to perceive the effects of returns to scale. In Figures 8-2 and 8-4 we sliced the production function parallel to one of the input axes in order to describe the phenomenon of diminishing returns to a variable input, given some quantity of a fixed input. In Figure 9-1 we sliced the production function diagonally along a ray from the origin in order to discuss the effects of returns to scale. But a real-world production process will likely involve a meandering path across the floor of the production surface, or possibly a path with a stair-step appearance implying a sequence of short-run adjustments situated within a longer-run time frame. The consequence is that it may not be possible to separate those output changes which are a result of diminishing returns from those that are attributable to changes of scale.
Scale and the Production Function
The mathematical properties of a production function may now be easily specified. Returning to the production function specification (1) introduced in Chapter 8, suppose that all of the inputs are multiplied by the same factor, v (a positive or negative real number that may be larger or smaller than 1), and output changes in the same direction by proportion u ,
The production function exhibits,
b. constant returns to scale if u is equal to v; or
c. increasing returns to scale if u is greater than v.
However, a single production function may have mixed orders for the various inputs, for example linear in K but second order in L:
Because different inputs may be present in the production function to different orders, it may be difficult to say whether to expect constant, increasing, or decreasing returns to scale from any particular function. We may indulge in a few broad generalizations. If the equation is linear in all included inputs, we may be confident that it will exhibit constant returns to scale over all ranges of the included inputs. It will then have a pyramidal or conical appearance when graphed in three dimensions. If the highest ordered term for all included terms is second, the equation will exhibit increasing or decreasing returns (but not both), depending on the signs (positive or negative) of the included terms. Such a second-order equation might plot as illustrated in panel (a) of Figure 8-1, but it is more likely to have the decreasing-returns appearance of that in panel (c). Finally, if the highest-ordered terms for all inputs included in the equation are cubic (third order), the production function can be expected to exhibit increasing, constant, and decreasing ranges of returns to scale as illustrated in panel (d) of Figure 8-1 (we note that the opposite sequences of ranges is possible but highly unlikely in real production circumstances). In a production function with mixed orders of the included terms, the nature of returns to scale will depend upon the angle of the ray from the origin that determines the capital/labor ratio.
Equitions (1), (2), and (3) are additive in the sense that the effect on Q of all of the inputs is simply the sum of the independent effects with no mathematical interaction among the inputs. If interaction among the included terms is likely, then a multiplicative equation form may be more appropriate. A commonly-used equation format of this type is the so-called Cobb-Douglas production function:
This function can be modeled by ordinary least squares regression in the transformed format
where the parameters a, b, and c can be estimated by the regression procedures. In this multiplicative power-equation form of the production function, the returns to scale depend entirely upon the values of the powers b and c.
The Cobb-Douglas production function exhibits
b. constant returns to scale if (b + c) is equal to 1; or
c. increasing returns to scale if (b + c) is greater than 1.
A decreasing returns Cobb-Douglas production function has the appearance of the surface illustrated in panel (c) of Figure 8-1. Since it never quite reaches a peak (rather, it approaches some output level asymptotically), it has no production Stage I or III. All input combinations for a Cobb-Douglas production function lie in Stage II.
Changes in Technology, Entrepreneurship, Managerial Capacity
All of the production functions illustrated thus far have been specified assuming some particular technology, given amounts of managerial capacity and entrepreneurial ability. This point is incorporated in the functional notations (2), (3), and (4) of Chapter 9. If there is any significant change in any of these enabling conditions, the production function must be respecified, and the geometric surface representing it redrawn. Failure to do so may lead to an identification problem (introduced in Chapter 7) in the production context, with the consequence that production decisions may be based upon erroneous criteria.Some technological, entrepreneurial, or managerial changes will have the effect of shifting the production surface upward (in the output dimension) or downward while preserving its essential shape. A technological change that shifts the production surface upward is an advance that improves productive efficiency in the sense that a larger volume of output can be produced with any combination of the inputs. A downward shift, perhaps because the firm has lost managerial capacity or deliberately chosen to retrench to some simpler or more primitive technology, constitutes a decrease in productive efficiency.
Some technological changes may have the effect of twisting or warping the production surface instead of simply shifting it. Such changes may have the effect of using more intensively one factor of production (and hence, less intensively the other factors). The firm's management may deliberately choose such a surface-twisting technological change if, for example, factor supply conditions change in such a way as to make one factor significantly more costly or another less costly. An example of the former might be the union organization of the firm's labor force that results in rising wage rates, thereby inducing management to install labor-saving technologies when the occasion arises for capital replacement. An example of the latter might be found in a technological advance that renders a previously uneconomic resource now commercially exploitable, e.g., new technologies enabling the extraction of shale oil or the gasification of coal.
This leads to a consideration of the criterion for selecting an appropriate technology in any commercial setting. Given market conditions, the best technology is not necessarily the most recently developed, the most "advanced," the most complex, or the one used most commonly by other firms or in other countries. Rather, the appropriate technology for implementing any productive process is the one that employs extensively the most abundant (cheapest) factors of production, and conserves most on the scarcest (dearest) factors of production. Failure to recognize or abide by this criterion has on too many occasions led enterprises in developing countries (which often are labor-abundant and capital scarce) to adopt the most advanced, capital-intensive technologies available in the West.
Technological changes are almost always implemented via capital investment. Capital replacements are almost always current-technology instead of the earlier vintage being replaced. Likewise, capital expansions typically opt for a later technology than that already in place. Care should be taken by management when any capital replacement or expansion is underway to question whether some technological change is also being effected. If so, the firm's production functions should be respecified in order to avoid erroneous production decisions that may result from an unrecognized identification problem.
In earlier discussion of returns to scale, we described the phenomenon but failed to indicate why it occurs. We are now in a position to suggest that even if all of the physical inputs (labor, capital, materials) are variable in the same or varying proportions, there still must be some ultimate enabling or limiting conditions that govern the scale phenomenon. We may speculate that these enabling and limiting conditions are the entrepreneurial ability, managerial capacity, and technologies that can be understood and implemented by the firm. The firm may possess or acquire abilities far beyond those that it presently is using, so that all of the physical inputs can be utilized more effectively at a larger scale. But eventually the scale of operations can exceed the ability of the management's abilities for coordination and control, with the result of decreasing returns to scale.
The Empirical Estimation of Production Functions
As in the estimation of demand functions (Chapter 7), it should be possible to apply regression analysis to empirical data for output and inputs in order to estimate the parameters of a best-fit equation. For many reasons, the job of estimating a production function may be even more difficult at the microeconomic level of the firm than at the macroeconomic level of the aggregate economy or even an industry.An immediate problem is that most firms produce a variety or range of products and some are joint products resulting from a common production process. If the firm produces several products in independent productive processes, a separate production function may be needed for each of the processes. Where joint products result from a common production process, it may be necessary to identify output as a product mix that is measured in value rather than quantity terms.
Another problem is that the production function by its nature assumes quantities of resources used and output produced such that measures of flows of inputs and outputs are needed for modeling purposes. Example of flows are labor hours employed and capital consumed (i.e., used up) in the production process. But flows are much more difficult to measure than are stocks, such as the number of laborers employed or the number of machines or value of capital invested. Where data for flows are unavailable or too costly to generate, the analyst may attempt to use available data for associated stocks as proxies for the missing flows data.
The management of the firm may need a short-run production function, i.e., for the particular plant that can be assumed to be in place and unchangeable. In this case the hypothesized relationship can be given as
so that the only data needed for the regression analysis are for the output flow, the volume of labor (L) utilized and materials (R) consumed, and various other inputs (X1,...,Xn) such as energy that vary with the level of output. The subscript indicates "gross" output in the sense of total number of units or total value of output produced. If the management can accept a value-added-by-manufacture (or processing) as the measure of net output, then the materials and other variable inputs can be assumed to be given (or at least to be enabling), so that the functional-notation representation of the production function becomes:
In this case, only data for value-added (as the measure of Qnet) and labor used are needed in order to estimate the production function via regression analysis.
If the management needs a long-run production function (that is, for plant-size and all other physical inputs variable), then K must be moved to the left of the slash,
or
Data for capital consumed in the production process are also needed.
Yet another potentially serious problem consists in the quantity of data required by the regression analysis for estimation of a statistically significant production function model. Cross-sectional data can be used only if data are available for other, similar production processes, i.e., production by other firms that are likely to be competitors. As a practical matter, competitors are usually quite reluctant to share such sensitive internal information as production volume and input requirements data, except possibly under the auspices of a trade or manufacturer's association. Even if data from other firms or other plants within the same organization are available, they are likely for different plant sizes (not a problem if a long-run production function is to be estimated), or different technologies, managerial capacities, or entrepreneurial abilities. If any of these differences are present in the cross-sectional data, then an identification problem is likely to emerge because the data will be for points on different production functions rather than a common production function.
The potential for an identification problem can be minimized by using data only for the firm itself, but this requires the use of time-series data instead of cross-sectional data. The use of time-series data opens other problems. If monetary values (instead of quantity units) are to be used, they should first be adjusted for changes in price levels (i.e., deflated or inflated), and this begs the question of the appropriate price index to use as deflator, if indeed an appropriate index even exists. When this problem is surmounted, there remains yet another problem. If a short-run production function is to be estimated the time series must be short enough that the size of the plant has not changed. Or if a long-run production function (encompassing plant size changes) is to be constructed, in order to avoid an identification problem the analyst must still restrict the range of the time series so that no significant changes in technology, managerial capacity, or entrepreneurial ability have occurred. The effect of restricting the length of the time series may be that too little data are available to estimate a statistically significant production function model.
The thrust of the foregoing discussion may suggest the heroic nature of an effort to estimate a production function from empirical data. It is a difficult, but not an impossible, task. Our purpose is to alert the analyst to the requisites and potential pitfalls so that they may be accounted for or avoided as required.
Managing Production
Suppose that the firm's management has been successful in estimating production functions for as many of its production processes as are needed. How can these production functions assist the management in its production decision making? The answer of course is to use the production function equations as models to simulate changes in the resource inputs. Since the cost-minimizing or profit-maximizing combinations of inputs are rarely self-evident, management may use the models to try a "what-if" approach to understanding the likely effects of alternatives to the present input combinations.The firm's management should be sensitive to the effects upon its production processes of changing input supply conditions, technological advances, and the gains or losses of managerial or entrepreneurial capacities. In addition to responding passively to such changes that impinge upon the firm, the management may aggressively determine to try to alter its productive processes by acquiring different technologies or managerial or entrepreneurial abilities.
On a closing note, we should assert that even if the management never undertakes or succeeds in adequately modeling any of its productive processes, an acquaintance with the concepts that we have examined in this chapter should provide the basis for more effective production-related decision making.
BACK TO CONTENTS
CHAPTER 11. COSTS IN THE SHORT RUN
The Inevitability of Costs
Costs, the age-old plague of the production manager, are a necessary evil--something you can't live with, but you can't do without. "You've got to spend money to make money."The manager of any production process, whether formally organized as an enterprise or informally conducted as in household cookery, must come to terms with the cost phenomenon. What should be the manager's attitude with respect to costs? Any production process where scarce resources are employed must incur costs. But the incurred costs offset the realized benefits (including revenues if the product is sold in a money-using economy). That is, the costs diminish the net benefits (including profits in the money-using economy) and may render them negative. Why not just get rid of the costs or avoid them? We can't...the necessary evil! If output is to be produced by combining scarce resource inputs, costs are going to be incurred. So, the inevitable must be accepted...incur more costs to get more output. But this suggests a direct and causative relationship: costs vary with output, and increasing output results in greater costs. It also begs the question of whether the additional benefits (revenues) will be as great the incurred costs.
We show in this chapter that while there is a tendency for costs to rise as output increases, the relationship between output and costs is not a one-for-one correspondence. And costs are a consequence of production, not a cause of it. The manager would do better to regard costs as something to control rather than something to manipulate as a causative factor in producing output.
What is the fundamental nature of costs? Why do they exist? Why can't we get rid of them? The existence of costs of production is attributable directly to the existence of scarcity. We may recall from introductory economics courses that scarcity exists if there is less of something (a consumable good or a productive resource) than people have or want. A price greater than zero is a certain indicator of the existence of scarcity. And since anyone's price is someone else's cost, the scarcity of the resources used in productive processes means that costs will plague the productive enterprise.
A short digression about an admittedly unrealistic condition may prove helpful. Suppose that the world were characterized not by scarcity, but rather by its opposite, abundance. There is enough of everything (consumable goods and productive resources) to "go around" so that no one has to pay anyone else for anything. Everyone can have as much as he or she needs of anything simply for the taking, and enough will be left for everyone else's use. The prices of all things in this unrealistic world are at highest zero (we admit the possibility that they may be negative). Suppose that all things have precisely zero prices. Again, since everybody's price is someone else's cost, all costs in this world of abundance will also be zero. Not only would the economic problem be solved: so also would that of the production manager. In fact, in a world of abundance we would need neither economists nor managers.
Unfortunately for society (although fortunately for the employment needs of economists and managers) the world is not so characterized by abundance. Because they are scarce, the prices of most things are positive, and nontrivial costs are incurred by productive processes. However, there are a few things (or substances) in nature that are, for all intents and purposes, abundant relative to wants, and that are also absolutely essential to production. The prime example is the air (containing oxygen) which is a necessary input in any internal combustion engine. There are no (we should stipulate "explicit") costs of using common air. However, should commonly-available air begin to contain too little oxygen or too much of certain impurities, even this example will cease to be useful.
Relevant Cost
We shall proceed upon the operating premise that any aspect of a production process that has negative implications for the production decision maker is a cost of production that is relevant to the production decision. We may also identify the corollary premise that any aspect of production with a positive implication for the decision maker is a relevant benefit (or revenue if the benefit is denominated in money terms). We should note that this premise could be germane to a barter economy (where no money is used to effect transactions) as well as to the monetized economies with which we are familiar. This means that even in a monetized economy where we are accustomed to denominating costs in money terms, some costs of production are essentially personal, or emotional, or psychic, and hence are not (easily) quantifiable and expressible in pecuniary equivalents.Implicit Costs. We shall refer to nonpecuniary costs as implicit costs, and those that are regularly incurred in money terms as explicit costs. A hypothetical example of an implicit cost might be the negative sense that a production manager feels when he purchases an input from a party whom he personally dislikes (perhaps because he is an alumnus of the state university that is the arch-rival of the production manager's alma mater), even though the money price per unit is lowest from that supplier. Such negative feelings, or psychic costs, could be so substantial as to induce a production decision maker to indulge in the apparently irrational decision to procure inputs from a well-liked supplier at higher prices.
Aside from such psychic implicit costs, economists identify opportunity costs as another category of implicit costs. An opportunity cost is incurred when a decision maker either knowingly (for non-economic reasons) or unwittingly opts for a lower-valued opportunity than the highest-valued alternative available. The classic text-book example is that of a single proprietor who chooses to continue to run his own business while realizing an accounting profit (to be defined shortly) that is less than the salary that he could realize in managing one of his chain-store competitor's outlets. We admit that the negative feeling experienced by a production decision maker that induces him to forego the lower-priced inputs in favor of those from a fellow alumnus is in effect also an opportunity cost.
Explicit Costs. Another term commonly used for explicit cost is accounting cost by virtue of the fact that such money-denominated costs are visible, readily monitored, and hence easily included by accountants when they design accounting systems. Accountants should be congratulated upon their meticulous efforts to account for all of the "hard" (i.e., money-denominated) costs incurred by a productive enterprise. By the same token they may be chastised for their reluctance to address those nonpecuniary psychic or opportunity costs and benefits that are no less relevant to the production decision. Because such non-pecuniary or psychic costs are excluded from formal cost accounting systems, it is up to the production decision maker to recognize them and account for them in the decision-making process.1
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1One reason that accounting systems are designed to account only for the explicit costs is that this is the requirement of the tax authority that the accounting profit (i.e., explicit revenues minus explicit costs) can be identified and taxed.
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Accounting costs may be subdivided into two categories: disbursement and non-disbursement costs. Disbursement costs are those that result in money out-payments from the enterprise to parties who provide services or resources to the enterprise. Examples are the payroll, payments for energy used, and the disbursements to the vendors of the raw and partially processed materials, components, and subassemblies brought together in the production process.
There is one type of non-disbursement accounting cost: depreciation (the macroeconomic equivalent is "capital consumption"). Depreciation is an allowance for the decline in the value of the capital stock that is attributable to the using-up of part of the enterprise's capital equipment during the production (usually the accounting) period. Such using-up or consumption of capital may occur as wear on the equipment or by weathering (exposure to the elements), whether the capital is used or not. These processes gradually diminish the production capabilities of the capital equipment. The phenomenon of obsolescence due to technical advance should not, however, be treated as a depreciation or capital consumption phenomenon. Obsolescence may reduce the market value of a piece of capital equipment, but it does not per se diminish the physical productive capacities. Nor should a disaster (e.g., fire, flood, earthquake) be regarded as a capital consumption phenomenon even though it may suddenly and catastrophically diminish both the market value and productive capability of the equipment.
An allowance for depreciation is not paid out (disbursed) to any party outside the enterprise; rather it is in a sense paid to the enterprise itself for the use of the capital equipment owned by the enterprise. Because it is not paid-out, but still is allowed as an expense against money revenue in computing the taxable profits, the enterprise's tax liability is thereby reduced. For this reason, depreciation may be regarded as a means of outlay recovery, supplying funds internally to the enterprise to finance subsequent reinvestment in its capital stock. But we should be careful to note that capital consumption is a real phenomenon that occurs whether or not a tax authority exists, and regardless of the tax authority's rules for computing the depreciation allowance.
Because it is impossible to know in advance what will be the actual life of any piece of capital equipment, and because the tax authority may change the depreciation-allowance rules for macroeconomic reasons (i.e., in an effort to stimulate or retard the growth of the economy), it is highly likely that any tax allowance scheme designed by the accountant or permitted under the tax authority's current rules will diverge from the real phenomenon of capital consumption. The depreciation allowance could either exceed or be less than the real wearing out of capital. In the former case, the capital equipment will cease to function before the full amount of the capital outlay has been recovered ("written off"). In the latter case, the capital equipment continues to function productively even after it is fully depreciated. The important point to be recognized by the production manager is that the accounting allowance may not closely match the real weathering and wearing process. Since it is the real process that contributes the relevant cost, the production manager must be prepared to make decision allowances (positive or negative) beyond those designed by accountants or allowed under the tax authority's rules.
We have made more than one reference to the concept of relevant cost. We have already noted that any negative-implications phenomenon that is consequent upon the production process is a relevant cost, whether it is denominated in money terms or not. We should also note that there may be negative-implications phenomena that are not relevant to a particular decision context, but that may be mistaken as being relevant to it. For example, cost factors that do not change in response to any particular managerial decision are not relevant to that decision.
Variable and Fixed Costs
One example lies in the distinction between direct costs and overhead costs, or to use the economist's preferred terms, between variable costs and fixed costs. Variable or direct costs are those that vary with the level (or rate) of productive output. Variable costs are always relevant to the rate-of-production decision. Fixed or overhead costs are associated with the existence of the manager, the plant, and the equipment. Examples are contractual salaries and insurance premiums. They continue at the same levels or rates irrespective of the rate of production, even if it is zero. Once the plant has been put in place, these fixed or overhead costs are, so to speak, "sunk" costs, and sunk costs are not relevant to any rate-of-production decisions.
The Short Run and The Long Run
The distinction between variable and fixed costs also permits us to distinguish between the time frames of the short and long runs that we have already noted in Chapter 8. The short run is the period of time within which some contractual obligations associated with management, plant, and equipment are not alterable by changing the firm's managerial capacity or its scale of operations. The duration of the short run of course varies from enterprise to enterprise and situation to situation, and thus cannot be specified in discrete terms.In the long run all aspects of the enterprise's operations can be adjusted. All costs are variable in the long run. Yet, as we noted in Chapter 8, any long run consists of a sequence of short runs. All decisions affecting both the enterprise's scale and rate of operation are made in short-run settings, even those decisions affecting the long runs. The distinction between the short and long runs may be more pertinent to academic analysis than to operational decision making. But once we have distinguished the concepts of the short and the long runs, we can assert that the costs that are relevant to short-run decisions (i.e., the rate of production) include no overhead or fixed costs, i.e., sunk costs are "gone costs," and hence irrelevant to short-run decision making. Fixed costs, though irrelevant to rate-of-production decisions in the short run, become relevant to the scale-of-operations decisions of the long run.
Temporal Mismatchings of Production and Costs
Another example of explicit costs that may be irrelevant to decision making in a particular time frame are those that are incurred within the time frame but which affect operations in other time frames. Prime examples are maintenance and repair expenses. Preventive maintenance services are performed in one period to ensure the continuing functionality of the equipment in subsequent periods. Repair service expenses are incurred in one period due to operations in previous periods. If the enterprise is pushing hard to meet a production target or delivery schedule during one period, both preventive maintenance and some repair services may be delayed, and the resulting costs thereby deferred to a subsequent slack period. Such costs then, when they are incurred, are irrelevant to decisions of the period within which they were incurred, but are relevant to some earlier or later period. The moral of this story is that the astute decision maker may have to go to some lengths to match the relevant costs with the appropriate temporal settings, and not rely blindly upon the available cost accounting data.
Spill-Over Costs
A final example of costs that are irrelevant to current decision making consists in what economists define as social or spill-over costs. The reader may recall that our operating premise is that a relevant cost is any aspect of a production process that has negative implications for the production decision maker. But what about negative aspects of production that descend upon members of society other than the production decision maker? For example, air, water, and noise pollution are the unfortunate by-products of production processes that affect parties outside the enterprise. These spill-over costs, however, are irrelevant to the production decision context unless or until either the production decision maker experiences a twinge of conscience, or the authorities require the firm to abate, prevent, clean-up, or compensate those who have been harmed. We may say, then, that while such spill-over costs currently are irrelevant to the production decision context, they always have the potential for becoming relevant costs and should not be ignored entirely by the production decision maker.
Economic Profit
Once we have identified relevant costs (as well as relevant revenues), we are in a position to specify the distinction between accounting profit and economic profit. Accounting profit is the explicit, money-denominated revenues realized by the enterprise during an accounting period, less the explicit, money-denominated costs that are incurred in that same period. Accounting profit does not include any implicit (psychic or opportunity) costs, recognizes no divergence between depreciation allowance and the real phenomenon of capital consumption, and often makes no allowances for the temporal mismatching of production and costs. To the extent that these aspects are omitted from consideration, the computation of an enterprise's accounting profit may over- or understate its true (economic) profit and thereby lead to erroneous decisions.The concept of economic profit is the result of the economist's effort to recognize all benefits (implicit as well as money revenues) and costs (psychic and opportunity costs as well as accounting costs) accruing to the enterprise. Economic costs are all of the costs that are relevant to decision making, whether or not money disbursements were made and whether or not they are recognized in formal accounting systems. The critical significance of economic costs is that they must be paid (or at least given adequate recognition or compensation) in order to retain the services of all factors of production supplied to the firm. The magnitude of the economic cost of any productive factor is its opportunity cost, i.e., at least as large a return as it can realize in its most favorable alternative use. The consequence of failure of an enterprise to pay all of the relevant or economic costs of its factors of production will be their departure to their best alternative employments. We admit that ignorance or irrationality on the part of the owner of the resource may result in the resource remaining in its present employment in spite of economic realities. A critical distinction between a "good management" and "poor management" may lie in the ability of the decision maker to recognize the implicit costs and benefits of managerial decisions.
THE COST-PRODUCTION NEXUS
It should be clear from foregoing discussions that the phenomena of costs and production are inextricably intertwined. The analysis of the behavior of costs and the specifications of cost-related decision criteria follow directly from the production principles outlined in Chapter 8. Costs behave as they do because of the underlying production relationships. In fact, the principle of diminishing returns serves as a common governing principle in the behaviors of both production and cost relationships.
In Chapter 8 we developed the analysis of production behavior via the production function, both algebraically and graphically implemented. We may now pursue the analysis of costs via a cost function that may be developed directly from the production function of Chapter 8. We shall begin with the graphic exposition and move to the algebraic specification.
The Transition from the Production Function to the Cost Function
In order to begin our graphic analysis of costs we make three simplifying assumptions that we can subsequently drop. First we assume that the enterprise already has an installed capital base that determines its plant scale and a particular output range. Second, we assume that there is only one explicitly variable input; for convenience we choose labor, but we could choose any other. There may be other inputs such as materials and energy that must also change with the rate of output, but we can assume that supplies of them are adequate to permit them to be handled with the labor. Third, we assume that labor is hired in a purely competitive labor market such that any quantity of labor can be hired at the going wage rate. With these three assumptions in place we have the classic short-run decision question confronting the manager: how much output to produce, or at what output rate should the given plant be operated? Although we must wait until Chapters 12 and 13 to discover the possible answers to this question, we are ready to analyze the cost implications in the remainder of this chapter.We may begin our analysis of the behavior of costs in the short-run by departing from the total, average, and marginal product curves illustrated in Figure 8-3 and reproduced with only minor modification in Figure 11-1. The first step in the transition from production to cost analysis is to rotate the axes so that L is on the vertical axis and Q is on the horizontal axis. This permits us to focus on Q rather than L as the deterministic variable. As illustrated in two panels of Figure 11-2, this has the effect of reversing the concavities of the TP curve, but there are as yet no other significant changes.
Figure 11-1. Total, Average, and Marginal Product Curves.
Figure 11-2. Rotating the Axes of a Total Product Curve.
The second step in the transition from production to cost analysis is to evaluate the labor units now on the vertical axis at their unit cost, the wage rate (which, it is assumed, does not change as more labor is employed because labor is hired in a purely competitive market). The vertical axis label may now be changed to W x L in recognition of this evaluation. We note that if W is constant, the shape of the curve is not altered when we change the vertical axis units from physical units of labor to value (or cost) of labor employed. The product of W x L can also be regarded as the total labor variable cost, TLVC, or, since labor is the only variable input, simply as the total variable cost, TVC. Although we had to make several simplifying assumptions to do so, we have now accomplished the transition from the analysis of production to the analysis of costs.
Dropping the Assumptions
We assumed that labor was the only variable input, but now let us suppose that the materials input is also variable, but it varies with output independently of the labor input. For purpose of illustration, we suppose the total materials cost, TMVC, to be linear as illustrated in Figure 11-3, so that the total variable cost, TVC, is the (vertical) sum of the TLVC and TMVC. As is apparent in Figure 11-3, the TVC curve lies above the TLVC curve by the amount of the materials cost of each output level, but the shape of the TVC is essentially the same as that of the TLVC curve, which we recall was derived from the TP curve. In similar fashion, as many variable cost curves as are relevant can be brought into the analysis and summed to compose the TVC curve.
Figure 11-3. TVC as the sum of TLVC and TMVC.
These other-input variable cost curves may have a variety of shapes, but economists believe it to be unlikely that their shapes will be so perverse relative to that of the TLVC curve as to render the shape of the TVC curve fundamentally different from that of the TLVC curve. If this is true, then the principle of diminishing returns, which underlies the shape of the TP curve, also dominates the shape of the TVC curve, even if there are other variable inputs in addition to labor.
We also assumed that labor was hired from a purely competitive labor market so that W could be treated as a constant. But if labor is employed from an imperfectly competitive labor market, ever higher wages must be offered to attract successively larger quantities of labor. This phenomenon will change the locus of the TLVC curve by rotating it upward, perhaps introducing a stair-step pattern if the wage increments occur in discrete stages. But in this case as well, economists are generally of the belief that the imperfections of the labor market are unlikely to fundamentally alter the shape of the TVC curve from that dictated by the principle of diminishing returns.
The Law of Increasing Costs
In the previous section we went to some lengths to convey the notion that the principle of diminishing returns dominates the shape of the TVC curve. But we also noted that in the transition from the analysis of production to the analysis of costs, the concavity of the curve is reversed. In the production context, as the labor input is increased, output may initially increase at an increasing rate; but corresponding to this Stage I phenomenon, variable costs tend to increase at a decreasing rate. In the production context we noted that beyond some point, further increases of the variable input resulted in output increasing at a decreasing rate, i.e., the phenomenon of diminishing returns. And corresponding to this Stage II phenomenon, costs will increase at an increasing rate. Economists refer to this phenomenon as a revelation of the law of increasing cost. The law of increasing cost is the cost analysis variant of the production principle of diminishing returns.
Average Variable Cost
Diminishing returns and increasing costs can also be illustrated with marginal and average functions derived from the TVC function. The average variable cost (AVC) curve, illustrated in panel (b) of Figure 11-4, may be derived from the TVC curve in the same fashion that the AP curve was derived from the TP curve in Chapter 8. Specifically, AVC at any level of output, Q1, may be measured as
Figure 11-4. AVC and MC curves derived from the TVC curve.
The ratio of TVC/Q may be measured graphically as the slope of a ray from the origin to the TVC curve at the selected Q. For successively larger outputs, it can be seen in panel (a) of Figure 11-4 that the rays from the origin at first decrease in slope, reach a minimum at Q3, and then increase in slope as output increases beyond Q2. Correspondingly, the AVC curve illustrated in panel (b) of Figure 11-4 decreases to a minimum at Q3, and then increases beyond Q3. The increase of AVC beyond Q3 is attributable to the principle of diminishing returns, and is illustrative of the law of increasing costs.
Marginal Cost
Likewise, the marginal cost curve, MC, illustrated in panel (b) of Figure 11-4, may be derived from the TVC curve in the same fashion that the MP curve was derived from the TP curve in Chapter 8. Marginal cost may be computed as
for a DQ of any magnitude.
Graphically, IC may be measured as the slope of a chord connecting any two (near-neighborhood) points along the TVC curve such as the chord AB in panel (a) of Figure 11-4. MC may be measured as the slope of a tangent to the TVC curve (the tangent to the curve is the limiting position of a chord as either end-point of the chord approaches the other end-point). The shape of the MC curve then may be inferred by observing the slopes of tangents to successive points along the TVC curve as Q increases. It is apparent in panel (a) of Figure 11-4 that the slopes of the tangents to points up to B decrease (mathematicians refer to a point like B as the "inflection point" where the curve changes concavity). For ever-larger quantities beyond point B, the slopes of tangents to points like C, D, and E become progressively steeper. Correspondingly, the MC curve illustrated in panel (b) of Figure 11-4 falls to a minimum at Q2, then rises as output increases beyond Q2. The increase in the MC beyond Q2 is attributable to the principle of diminishing returns, and is illustrative of the law of increasing costs. We may assert that the phenomenon of increasing costs starts at the output level for which MC is minimum (Q2 in Figure 11-4).
What are the managerial significances of AVC, IC, and MC? The average variable cost is easiest to compute (only two pieces of information are needed, the current total variable cost and the quantity being produced), and for this reason it is tempting to try to base output decisions upon it. Indeed it can be used as an output decision criterion if the goal of the enterprise is to minimize per-unit variable costs. But we asserted in Chapter 8 that the circumstances of cost minimization, revenue maximization, and profit maximization are unlikely to coincide (we will demonstrate this point in Chapters 12 and 13).
If the goal of the enterprise's management is profit maximization, then AVC is an inadequate criterion; the appropriate cost-related decision criterion for profit maximization is marginal cost (we shall also demonstrate this point in Chapters 12 and 13 when we bring revenue and cost conditions together). But here is a problem, because MC is rarely observable (i.e., for a one-unit change of output). It can be computed mathematically (differentiation) if one has an equation that adequately represents the cost function. However, to develop such an equation by statistical means requires information about an adequate number of cost and quantity combinations (usually 20 or more).
In lieu of such extensive information, the IC can be computed from four pieces of information: quantities produced at two points in time (preferably very close to each other in time and involving as small a quantity change as possible), and the corresponding totals of the direct production costs. Even for a very small DQ, the IC will be at best only an approximation to MC because it will over- or understate MC, and may thereby lead to erroneous output-change conclusions.
Where does this leave us? MC is the ideal cost-related decision criterion, but is hardly observable and may be very costly to compute. Even IC, its approximation, though cheaper to compute, may lead to erroneous conclusions. AVC, though not acceptable as a cost-related decision criterion when the goal is profit maximization, is easily computed from a minimal amount of readily-observable information. There is a circumstance, however, under which AVC may serve satisfactorily as a profit-maximizing decision criterion: as we shall demonstrate in Figure 11-6 of Chapter 11, if TVC is linear (or approximately so), then AVC decreases and approaches MC, which is constant. As it turns out, empirical data for many industries suggest that TVC may in fact be approximately linear across a wide range of output in the vicinity of the commonly-produced output level.
Relationships among Total, Average, and Marginal Cost
We may now observe the unique relationships among the curves illustrated in Figure 11-4.
b. MC reaches its minimum point at the Q for which TVC reaches its inflection point; at its minimum, MC is less than AVC.
c. AVC reaches its minimum point at the Q for which a ray from the origin to the TVC is of minimum slope (point C in panel (a) of Figure 11-4). Coincidental, the ray from the origin to this point is a tangent to the TVC, so MC and AVC are equal at this output level (Q3 in Figure 11-4). MC is less than AVC up to this point.
d. For all output levels beyond the minimum of the AVC, both AVC and MC increase, with MC rising at a faster rate (i.e., MC lies above AVC).
e. Neither TVC nor AVC nor MC is ever negative (this seemingly trivial point will find its significance in Chapters 15 and 16).
Although the reader may not at this point see the significance of the relationships outlined in this section, the astute production manager will find a knowledge of these relationships to be invaluable as criteria for production decisions.
Relationships between Cost Functions and Product Functions
In Chapters 13 and 14 we shall be addressing the question, "What is the appropriate level of output for the enterprise to produce in order to meet its goals?" Once the answer to this question is determined, and subsidiary question must be addressed: "What are the appropriate amounts of inputs to use in producing the target level of output?" Since these two questions are so closely related, it is now appropriate to review certain relationships between cost and production functions. The reader may confirm the following relationships by comparing Figures 9-3 and 11-4.
2. The output levels at which AVC and MC are at minima correspond, respectively, to the variable input levels at which AP and MP are at maxima.
3. The output range over which TVC is increasing at an increasing rate (and MC is rising) corresponds to the variable input range over which TP is increasing at a decreasing rate (and MP is falling).
The reason that these relationships between the cost function and the production function are so significant is that our understanding (or theory) of the behavior of costs is based so exclusively upon the principle of diminishing returns. If the principle of diminishing returns is not true, or not descriptive of the way the world really is, then our understanding of the behavior of costs is also defective and will lead to erroneous production decisions. The other side of this coin is that if we do have an adequate grasp of a principle that truly is descriptive of the way the world works, then production managers need to know how their costs are related to the principle.
Overhead Costs in the Short-Run
We already have at hand enough information about costs in the short-run context to proceed on to the analysis of Chapters 13 and 14. We shall take up the nature of overhead or fixed costs in this section, but we run the risk of conveying a misimpression to the reader about the significance of fixed costs to short-run decision making. So, at the outset of this discussion we repeat our assertion from an earlier section of this chapter that overhead costs are "sunk and gone," and are thus costs that are not relevant to short-run production decision making. We shall be examining the nature of fixed costs in the short-run context purely for information, and not as prospective decision criteria.Overhead costs, usually fixed by contractual obligation at the same level as long as the existing plant, equipment, and management are in tact, can be illustrated in panel (a) of Figure 11-5 as a horizontal line TFC, at the altitude of the total of the fixed costs. Then, to the fixed costs can be added the total variable cost at each level of output to measure the total cost, represented by curve TC in panel (a) of Figure 11-5. It should be apparent that the TC curve lies above the TVC curve by a constant vertical distance (the magnitude of TFC), and that the two curves are parallel to each other along verticals. This means that along any vertical that crosses both curves, a tangent to either curve will be parallel to a tangent to the other curve. The significance of this relationship lies in the fact that a common MC curve, already illustrated in panel (b) of Figure 11-4 and reproduced in panel (b) in Figure 11-5, serves both the TC and TVC curves.
Figure 11-5. The TC and ATC curves.
The same methodology, i.e., drawing rays from the origin to points along the total curve, can be used to ascertain the behavior of the average fixed cost, AFC, which can be computed as
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2It may also appear to approach the vertical axis asymptotically, but in reality it begins at a finite point where Q=1 and at altitude = TFC.
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In similar fashion to finding the position of the TC curve by adding TVC to TFC, the locus of the average total cost curve, ATC, can be determined in panel (b) by vertically summing the AVC and AFC curves. The reader should confirm that any level of output the ATC curve lies above the AVC curve by the amount of the average fixed cost at that output level, which is also the altitude of the AFC curve. It may also be noted in passing that the MC curve passes through the minimum point of the ATC as well as the minimum point of the AVC curve, but that the minimum of the ATC lies somewhat to the right of the minimum of the AVC. This latter relationship is true because in panel (a) of Figure 11-5 the tangency of the ray from the origin to the TC curve occurs to the right of the tangency of the ray from the origin to the TVC curve.
In panel (a) of Figure 11-5, the TC and TVC curves appear to converge toward the upper end. However, they do so only in the horizontal dimension; the vertical distance between them is maintained constant. But as illustrated in panel (b), the ATC and AVC curves do tend to converge in both the horizontal and vertical dimensions because of the spreading of the overhead as Q increases.
To return to the caution issued at the beginning of this section, what are the short-run significances of the TFC, the TC, the AFC, and the ATC curves constructed upon recognition of the overhead costs? Before the making of short-run output and pricing decisions, they should be ignored as irrelevant costs; after the point of decision, they may be regarded purely as information to be considered in any forth-coming long-run decision set. Particularly, the decision maker should not attempt to set price to cover overhead costs or total costs (including overhead); the output decision should not be oriented specifically toward the spreading of the overhead.
What's Ahead
The criteria for appropriate pricing and output decisions are developed in Chapters 13 through 16. After the fact of selecting the price and output upon appropriate criteria, the manager may in retrospect observe whether or not total costs were covered, and by how much the overhead was spread across the number of units produced. If the total costs were not covered, or the overhead costs were not met, then a long-run change may be warranted. It is to costs in the long run that we turn in Chapter 12.BACK TO CONTENTS
APPENDIX C6A. SIMULATION MODELING OF COSTS
Suppose that empirical research and regression analysis has yielded parameters for a third-order total cost function (TC) with equation
It is the power 3 in the fourth term on the right side of this function that makes it a third-order equation. The constant in this equation, 120, is a scale value that may be interpreted as the firm's total fixed cost and serves as the vertical axis intercept for the total cost function. The equation of the total variable cost function (TVC) may be given as
A graphic display of these functions is illustrated in Figure 11A-1. Since the constant term in the TVC equation is missing (implicitly zero), the TVC curve passes through the origin. The bottom panel of Figure 11A-1 illustrates the average and marginal cost functions derived from the total cost functions.
Figure 11A-1.
As illustrated in Figure 11A-2, the constant value has been changed from its initial value of 120 to the larger value, 180. The revised TC equation is
The TVC equation remains unchanged. The loci of the new total and average total cost functions illustrated in Figure 11A-2 lie higher in coordinate space than those illustrated in Figure 11A-1. Since the TVC equation did not change, the TVC, the AVC, and the MC curves remain unchanged.
Figure 11A-2.
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As we have noted in Chapters 10 and 11, the loci of the firm's cost functions may change either because in the short run the costs of the inputs into the production processes change, or because in the long run the management of the firm implements changes in the technologies employed in the firm's production processes. A short-run increase in input costs may be expected to shift the cost functions upward; if input costs fall, the cost functions will shift downward. If the long-run technology changes are output-increasing, they will shift the cost curves to the right; if they are input-saving they will shift the cost curves downward.
The management of an organization may gather cost data via its cost accounting system; its research staff may perform regression analysis upon the data to estimate the parameters of its cost functions. With this information in hand, the management of the firm may model the equations of its total, average, and marginal cost functions. When any of these functions shift either by deliberate actions of the management or due to matters beyond the control of the management, it may analyze the effects of such shifts by making appropriate changes to the respective functions.
BACK TO CONTENTS
PART D. THE COMPETITIVE ENVIRONMENT
CHAPTER 13. THE COMPETITIVE ENVIRONMENT
Now that the theoretical foundations for the analyses of both revenue and costs are in place, we can proceed to bring the two together and begin an examination of goal-oriented decision criteria. To begin this analysis we assume that the decision maker is deliberately trying to maximize the economic profit of the firm. Along the way we shall give consideration to alternative behavioral objectives (costs, production scheduling, inventory control, employment, social responsibility, etc.) and behavior patterns (minimization, optimization, satisficing, etc.).
The decision options of the enterprise manager are constrained by the types and intensities of competition confronting the enterprise in the market for its products. We shall describe a range of competitive types along a continuum between two extremes. In broad terms, the two extremes represent a maximum intensity of competition and no effective competition at all. We readily admit at the start that very few industries and markets in the real world can be characterized by conditions at either extreme. Our objective in this chapter and the next is to identify and describe the limits of the competitive spectrum so that Chapters 15 and 16 can be devoted to examination of decision making under the more realistic conditions between the extremes.
THE MAXIMUM-COMPETITION EXTREME
We can imagine the descriptive characteristics of a market at the highly competitive extreme of the continuum:
(2) The single product that they produce and market is essentially homogeneous across the member firms.
(3) The member firms have virtually identical managerial capacities; they use essentially the same technologies; no one of them has or can acquire any special expertise that is not available to all of the others.
(4) All participants in the market have access to the same information about changing market conditions.
Given these descriptive characteristics, we can deduce likely consequences and behavioral patterns for firms in the purely competitive market:
(b) Exit from the market is likewise easy, i.e., the firm can dispose of its capital assets quickly and with very little loss of value.
(c) Once a decision has been made to enter the competitive market there is likely be very little incentive or effort to exercise further entrepreneurship, except the decision to exit the market.
(d) The atomistic size and limited financial resources of the competitive firm militate against its acquisition of any special managerial or technical expertise; firms are unable successfully to differentiate their products, and no firm can attain any position of market dominance.
(e) Because of the common knowledge of changing market conditions, all participants in the market become aware of such changes simultaneously, and all adjust at approximately the same rates.
(f) Because of the large number and atomistic size of sellers, competition is essentially anonymous; no seller is aware of or concerned about the identities of other sellers.
(g) A common price likely emerges in the market, and no market participant finds incentive to try to charge any price higher or lower than the market price.
(h) Due to the absence of successful product differentiation, there is little or no point in advertising the firm's product characteristics or its price.
(i) Supernormal and subnormal profits in the competitive market, although they may occur, are fleeting; profits tend toward the economically normal level of opportunity cost (what the firm can realize in the next best alternative application of its resources).
Short-Run Adjustment in the Competitive Industry
Figure 13-1 illustrates in panel (a) the market conditions for a purely-competitive market. Market prices will adjust toward an equilibrium at price P1 and quantity Q1 as explained in Appendix 13A. Because all firms in the market are similar to one another and significant differences are unlikely to emerge, we can analyze the behavior of a "representative firm" in panels (b) and (c). No single firm in the competitive market will find incentive to charge any price but the market price, P1; at any higher price no one will buy from the firm; the firm can sell all that it can produce at the market price. Therefore, the firm is what we call a "price taker;" it exercises no discretion concerning price except to get into line with the market price when it changes. For this reason, the representative firm's demand curve is drawn as a horizontal line at price P1. We can deduce from principles described in Chapter 7 that when demand is linear and horizontal, total revenue, TR, is a straight line emanating from the origin of its axes, and the marginal revenue curve, MR, is coincident with the demand curve.We are now in a position to analyze the effects upon the firm of decisions to produce at selected output levels. Output quantities q1 and q2 are variable-cost break-even levels. At outputs smaller than q1 or larger than q2, total variable cost is greater than total revenue; likewise average variable cost exceeds average revenue. At any output between q1 and q2 the firm covers all operating costs and makes some contribution to covering overhead costs and profit.1 Output q3 is one of the output levels between q1 and q2 for which revenue exceeds variable costs, TR > TVC, and makes a contribution to overhead costs and profit. At q3, a small increase of output will increase total revenue by more than it will increase total cost. We can discern this relationship graphically in panel (c) because the slope of the TC curve is shallower than is the slope of the TC curve at output q3. This relationship can be verified in panel (b) of Figure 13-1 where at q3 the marginal revenue curve (coincident with the demand curve) lies above the marginal cost curve. If the decision maker's goal is profit maximization, it is clear that an increase of output from q3 will add more to total revenue than to total cost, and thereby either increase profit or diminish loss.
The appropriate decision criterion is a comparison of marginal revenue and marginal cost. If marginal revenue is greater than marginal cost, MR > MC, then output should be increased. Output q4 is also in the range of q1 to q3, but at q4 marginal cost is greater than marginal revenue. An increase of output from q4 will have the effect of adding more to total cost than to total revenue, thereby diminishing profit or increasing loss. A decrease of output will decrease both total revenue and total cost, but total cost will decrease by more than total cost decreases, thereby decreasing loss or increasing profit. Again, if the goal of the manager is to maximize profit, the firm should decrease output when marginal cost is greater than marginal revenue, i.e., MR < MC.
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1We do not at this point show the locus of the total cost curve in panel (c) or the average total cost curve in panel (b) of Figure 13-1 because fixed costs are not relevant to short-run decision making. All that the manager should attempt to discern in the short run is whether, after the fact of the decision, the operating costs are covered. An appropriate long-run consideration is whether revenues also cover the overhead costs and make a contribution to profit, hence the concept of a "contribution margin."
Figure 13-1. A Firm in a Purely Competitive Industry.
We could examine other output levels between q3 and q6 to draw inferences similar to those drawn for q3. Likewise, we could examine other output quantities between q4 and q6 in order to draw inferences similar to those drawn for q4. The general principle that should govern output decision making when the goal is to maximize profit is to increase output if marginal revenue is greater than marginal cost, MR > MC, but to decrease output if marginal cost is greater than marginal revenue, MR < MC. Marginal revenue is easy to identify in the purely competitive market because it is equal to price, and the MR curve is coincident with the demand curve. However, we recall from Chapter 12 that marginal cost is not directly observable. It can be computed for any output level if the equation of the TC or MC curve is known, but knowing either of these equations probably required the exercise of a costly data collection and model specification and estimation process. Incremental cost can be computed more cheaply from data for two different output levels, but it is only an approximation to true marginal cost.
It is tempting then to look at average revenue and average cost as possible decision criteria because it is so easy to compute both at any level of output. Average revenue at any output level such as q2 can be computed as TR2/q2, but in the purely competitive market, average revenue is also equal to the price of the product. Average variable cost is easily computed as TVC2/q2 at output level, q2. These magnitudes, AR2 and AVC2 are so easy and cheap to compute, what would be the problem in using them as the output decision criteria? It should be apparent in panel (b) of Figure 13-1 that the profit-maximizing output level cannot be found simply by comparing AR and AVC unless all possible outputs between q1 and q2 are examined. Another way to say this is that the comparison of AR and AVC can reveal whether or not the firm is covering its operating costs, but can yield no guidance about whether to increase or decrease output. The comparison between AR and AVC can serve as a useful decision criterion, however, if the goal of the management of the firm is to minimize per-unit costs (this occurs at output level q5 in Figure 13-1), or if the goal is simply to operate at any output level for which revenues cover operating costs.
The moral of this story is that MR and MC are the appropriate decision criteria if the goal of the firm is to maximize profit. A qualification to this principle should be noted. In the event that the total cost curve is also linear as described in Chapter 12, Figure 11-6, the marginal cost curve will be linear and horizontal, paralleling the linear and horizontal marginal revenue curve. In this case neither averages nor marginals can provide any guidance in regard to profit maximization or cost minimization. If TR lies above TC (MR also will be above MC and be parallel to it), the firm can always increase its contribution to over-head and profit by increasing output. But it is unlikely that TC will be linear forever as output increases; eventually the principle of diminishing returns will have its way with the firm's costs, but the firm may have grown beyond the confines of pure competition.
The Operate vs. Shut-Down Criterion in the Short Run
Zero is also a possible level of output that may be chosen in the short-run, and it may be rational to shut-down operations if the revenue generated by selling the output cannot cover even the operating costs (or variable costs) of producing the output. Assuming cubic production and cost functions, the shut-down criterion can be illustrated in panel (b) of Figure 13-1 at any output for which AR < AVC, or in panel (c) at any output for which TR < TVC.2 Graphically, TR would lie completely below TVC, and P=AR=MR would be below MC at all output levels. In these circumstances, the firm should not operate because the revenue resulting from operation would not cover all of the operating costs, and could make no contribution at all to the overhead costs.3 In shut-down mode, the firm minimizes its losses by incurring only the fixed costs. The fixed costs, which continue in the short run whether the firm operates or not, can be saved (or avoided) only by exiting the industry, a long-run decision.__________
2As depicted in Figure 11-6, a linear TVC function has a linear and horizontal AVC curve. In this unlikely case, the shut-down criterion obtains when the slope of TR becomes less than the slope of TVC, such that the horizontal AR curve lies below the horizontal AVC curve. As depicted in Figure 11-5, a second order (quadratic) TVC function has a linear and up-sloping AVC curve that never reaches a minimum. In this more likely case, the shut-down vs. operate criterion fails because AR can never (in Quadrant I) become less than AVC.
3It is tempting to think that the shut-down criterion should be the failure of revenues to cover overhead costs, but as we have stipulated earlier, overhead costs are not relevant to short-run decision making. The identification of the proper shut-down criterion is another reason that we have declined to draw the TC and ATC
curves into Figure 13-1.
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There are many exogenous phenomena that may impinge upon the firm in the short run but are not under the discretionary control of the firm's management. For example, as we noted in Chapter 11, the variables X1,..., Xn in the cost function may include the prices of the inputs (labor, materials, energy, etc.). A change in the price of an input will have the effect of shifting the firm's short-run cost curves upward or downward and may thereby create a shut-down or restart situation. Such a short-run change may create the need or basis for a long-run decision to exit the industry if the problem cannot be satisfactorily remedied by short-run adjustment. In the long run, revenues must cover all costs of production because there are no fixed costs in the long run. The long-run exit criterion applies to any output in panel (b) of Figure 13-2 for which AR < ATC, which also corresponds in panel (c) to any output for which TR < TC.
Figure 13-2. Purely Competitive Adjustment in the Long Run.
Short-Run Industry Adjustment of the Competitive Industry
Figure 13-2 is an extension of Figure 13-1 to include the TC curve in panel (c) and the ATC curve in panel (b). We may recall from Chapter 10 that TC is greater than TVC by the amount of the total fixed costs, and ATC is greater than AVC by the average fixed cost at each level of output. Under the circumstances illustrated by P1 and TR1, firms presently operating in the market can cover all of their variable and fixed costs and enjoy a profit at the current market price. When these profits are perceived by outsiders, and if these profits are greater than can be earned in other markets, the outsiders may exercise their entrepreneurship to enter the market and try to share in the supernormal profits. This entry into the market will have the effect of increasing market supply, shifting it to the right to some position like S2 in panel (a) of Figure 13-2. As a result, market price will fall toward P2, which will become the new locus of the demand and marginal revenue curves as well. Correspondingly, the TR curve will rotate downward to its new position, TR2. As consequence, the firm's profit-maximizing output level will change to q7, and the profit earned by the firm will be smaller.Theoretically, this adjustment process, driven by continuing entry into the market, could continue until the price falls to P2 and the total revenue curve rotates to position TR2; here, supernormal profits are eliminated and the market price just covers the firm's variable and fixed costs, allowing only a normal return to the firm's ownership interest. The important point is that with no effective way for firms to prevent entry into the market, all super-normal profits will be competed away. But no firm in the market will be suffering because each will be paying or earning normal returns for all of the resources under its employ. Capital and entrepreneurship, having entered the market, will continue in their present occupation until the prospect of supernormal profits appears elsewhere.
Perfect market knowledge is never a fact in the purely competitive market. Suppose that there is a time lag in the dissemination of information so that potential entrants into the market fail to realize that enough new firms have already entered the market to cause price to fall to the level of ATC. Continued entry by new producers who are yet unaware that supernormal profits are no longer possible in the market will cause price to fall to below the minimum point of ATC, and the total revenue curve to rotate downward to TR3, which lies below TC. Now firms in the market are realizing insufficient revenue to cover all of their costs. At price P2, all of the direct or variable costs are covered, and a contribution is being made toward the overhead or fixed costs, so the firm should keep on operating in the short run. However, if due to excessive entry into the market price should happen to fall below the minimum point of AVC, the firm should then shut down and suffer only the fixed costs.
If the situation persists, the management of the firm should give thought to making the long-run decision to exit the market. The managements of some firms will decide to do just this; their exit from the market will decrease market supply, causing market price to rise toward the level where all costs, direct and overhead, can again be covered, and the firms remaining in the market can once again earn normal profits. The competitive market is in equilibrium when all firms still in the market are realizing normal profits, and there are no supernormal profits to tempt entry or subnormal profits to induce exit.
Long-Run Adjustments in the Competitive Industry
In the short run the firm's management is limited to making output-related adjustments. Output is adjusted by changing the amounts or rates of utilization of inputs. We can bring together the functional-notation relationships of Chapters 9 and 11 as follows:
Costs are a function of output; output is a function of the variable inputs (labor, materials, etc.), given the existing plant and the productive environment. The productive environment is a function of the available entrepreneurial capacity, managerial ability, and the technology in use. The latter three plus plant size constitute the long-run parameters that the firm's management may alter.
The decision options of the long-run extend to
(b) adding to the firm's plant or equipment, disposing of capital assets, or letting them depreciate to non-functionality without replacement;
(c) building a larger or smaller plant of the same technology;
(d) choosing a different technology, and consequently an appropriate plant size to implement that technology; technologies new to the firm may be acquired externally by licensing, purchasing new equipment, or hiring new personnel, or they may be developed internally through research and development (R&D) efforts;
(e) gaining of managerial capacity internally by experience and training or externally by employment of new personnel; or losing managerial capacity through retirement, death, or movement of personnel to other firms; or
(f) gaining or losing entrepreneurial ability.
A change of plant size within the same technology is amenable to analysis using the long-run average total cost curve introduced in Chapter 11. Such a plant-size change may have scale economy or diseconomy implications if the LATC curve is U-shaped. If the management can discover enough about the shape of its LATC curve, it may devise a long-run (capital investment) strategy to change plant size in anticipation of exploiting scale economies or avoiding scale diseconomies. Also, as market demand changes, the managements that know enough about their costs in the long run may seek to construct plants of more optimal capacity to meet market demands.
These points can be illustrated with the ATC and LATC curves depicted in Figure 13-3. Suppose, for whatever historical reason, the firm has constructed the plant represented by ATC1 and MC1. At price P1 it maximizes profits by producing the q1 output. But we note that there is a more optimal plant for producing the q1 output. This plant is ATC2, the one for which average total cost curve is tangent to the LATC curve at q1. The profit-maximizing output for plant ATC2 is not q1, but rather q2 where MC2 crosses the MR curve. However, there is an even lower-cost plant that could be constructed to produce the q2 output level, ATC3, but the profit maximizing output level for ATC3 is q3. Points a, b, and c are on the respective marginal cost curves and lie directly below the points of tangency of the respective ATC curves with the LATC curve. These points trace out a path that can be construed as a long-run marginal cost curve, LMC.
Figure 13-3. Long-Run Costs for a Purely Competitive Firm.
Unless the firm's managers have perfect knowledge of the firm's long-run cost conditions (i.e., they know the loci of all of the possible short-run cost curves), it will be through a process of discovery that the firm will eventually be led to build the ATCm plant and operate it at the qm level of output where the firm will maximize profits. Given market price P1, plant ATCm is the plant that will yield the largest mass of profit for the firm. At output level qm, the short-run ATCm curve is tangent to the LATC curve; there is no other plant that is more appropriate for producing the qm output. Theoretically, this plant can be found at the intersection of the LMC curve with the MR curve. The appropriate plant then is the one whose MC curve crosses MR at the intersection of the LMC curve with the MR curve.
Let us suppose for a moment that the manager of the competitive firm does have perfect knowledge of its production and cost functions, but completely lacks foresight of likely future market changes. Given price P1 and assuming that it will persist forever, he makes the long-run decision to build plant ATCm, intending to operate it at qm level of output. Managers of many other competitive firms do likewise. This phenomenon, plus the effect of entry of new firms into the market to try to capture a share of the super-normal profits can be expected to bid the market price down toward Pe in Figure 13-4, for which demand curve De and marginal revenue curve MRe happen to be tangent to the minimum point of the LATC curve. When prices reaches Pe, the appropriate plant size is described by ATCe, which is tangent to the LATC curve at its minimum point. And the manager who opted for plant ATCm when price was P1 can now be seen to have been both naive and short-sighted because plant ATCm incurs unit costs (even at its minimum point) that are greater than market price Pe.
Figure 13-4. A Competitive Firm in Long-Run Industry Equilibrium.
Managers who committed to plants like ATCm or ATC1 may find their firms realizing losses relative to firms whose managers more astutely chose to build a least-cost plant. They are stuck with plants that are too small or too large for the duration of the lives of the plant and equipment. Their short-run options are to continue to operate while suffering losses if Pe happens to exceed their average variable cost, or to shut-down if Pe is less than their average variable cost. If price remains as low as Pe, the firms that are realizing losses have the option of exiting the market. Exit from the market will likely involve capital losses if the plant and equipment cannot be economically converted to other applications, or if they must be sold at prices below their depreciated book values.
In reality, managers of competitive firms have neither perfect foresight of market conditions nor perfect knowledge of their production and cost functions. Collectively they will be led through processes of discovery to the construction of optimal plants (ATCe in Figure 13-4) as market price falls toward Pe. Some will build suboptimal plants and others will build superoptimal plants. It is these who will prematurely exit the market. The ones who survive and remain in the market are those who through exceptional knowledge of their own long-run cost possibilities, astute understandings of future market dynamics, or sheer good luck, are induced to build the right-sized plants and operate them at the right levels of output. Competition smiles upon those who learn enough about their costs and are knowledgeable of market dynamics. Competition ruthlessly dismisses those who are ignorant of their costs or naive of market realities.
Our purpose is to examine decision-making criteria from the perspective of the manager, but in passing we shall note that from the perspective of society as a whole, plant ATCe operated at output level qe when price is pe is also a socially-optimum condition. Competitive firms are induced to build least-cost plants and operate them at least-cost output levels while covering all economic costs but realizing no supernormal profits. The market price of a good can be interpreted as society's valuation of the good; the marginal cost of producing a good can be interpreted as the cost to society of using the resources to produce the good rather than other goods. Because in competitive equilibrium the firm's marginal cost of producing the output is just equal to market price, it may be said that the social cost of using resources to produce the output is just equal to the social valuation of the output produced. From this may be drawn the inference that the resources used in the production of the output are efficiently allocated. Enough, but not too much, of the output is being produced.
Finally, it may be noted that the functioning of the competitive market has brought about a coincidence of social welfare and private profitability.
The Managerial Implications of Pure Competition
It may be possible to capture supernormal profits in a highly competitive market that can be easily entered with small amounts of capital and commonly available technologies. Entrepreneurs who perceive such possibilities should be aware that those supernormal profits will be fleeting at best. Good advice would be to "gather ye rosebuds while ye may" and "make hay while the sun shines." Only normal returns (no greater than the returns that can be realized in other opportunities) can be earned in the competitive market in the long run.The competitive firm manager would be well advised to take pains to identify and build the least-cost plant for the long run, even if there appears to be a more appropriate plant size to build under current conditions. It is better to take smaller profits from a plant that can be operated through its physical life than to take maximum profits this month from a plant that may have to be shut down next month and disposed of next year.
Since no manager can know in advance and with precision what is absolutely the correct rate of output at which to operate its existing plant in the short run, the manager should expect to proceed iteratively, i.e., to try one rate of production and then another higher or lower rate, using as decision criterion whether marginal cost (or an approximation to it) is greater or lesser than marginal revenue (price in a competitive market.
We entered this chapter with a disclaimer: the extremes of the competitive spectrum are hardly representative of real-world situations. Are there no examples of pure competition in the real world? A search for good examples of pure competition is likely to be fruitless, but this may only mean that we have asked the wrong question. A better question, given a market in which we are already operating or considering entering, is whether the decision-making characteristics of the market can best be analyzed with the purely-competitive model or some other model that will be introduced in subsequent pages. Is the DVD movie rental business a good example of a purely competitive market? We can't say. Is the purely competitive model an appropriate vehicle for analyzing the DVD movie rental business? Possibly.
At the beginning of this section we specified the descriptive characteristics of the purely competitive market. We then noted the consequences and behavioral patterns that follow from the characteristics. These consequences and patterns rather severely limit the range of entrepreneurial discretion to the choices to enter or exit the market. It limits the range of managerial discretion to choosing the right plant size in the long run, and the right rate of output in the short run.
If there ever were a purely competitive market, it would likely cease to be such rather quickly because of the inherent differences of entrepreneurial capacity and managerial abilities from firm to firm. Entrepreneurs of exceptional ability will discover new markets to enter, new product lines to produce, and new, more efficient technologies to employ; they will discover how to make their products more appealing to consumers by differentiating them from other products. And in so doing they will gain competitive advantage over other firms in the market. This of course means that the market can no longer be characterized as purely competitive. What are the managerial implications? As one wag has put it, the way to get ahead in life is to be a goat while everyone else is being a sheep. A goat in the middle of a flock of sheep is a natural leader. Being a goat amidst a flock of sheep is what entrepreneurship is all about.
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CHAPTER 14. PURE MONOPOLY
At the other extreme of the competitive continuum from pure competition is the market structure that economists designate as pure monopoly. Its descriptive characteristics are as follows:
(2) There are no close substitutes for the product(s) sold by the firm, i.e., the product is significantly differentiated from all others.
(3) There are several possible bases for the monopoly position, including
(b) a technological uniquity that may have been developed (internally, by research and development) or acquired (externally, from the inventor);
(c) the grant of an exclusive position by government, e.g., by franchise, patent, trademark, or copyright;
(d) a resource-control uniquity; and
(e) predatory or acquisitive behavior leading to the demise or absorption of former competitors.
The maintenance of a monopoly position may involve a combination of these bases.
These descriptive characteristics of a pure monopoly lead to a number of consequences or behavioral patterns:
(2) Exit from the market may be equally difficult; if the monopolist has attained large enough scale, exit may be possible only by failure and dissolution.
(3) The monopolist has exclusive control over the market price of the product. However, this does not mean that the firm can charge "any price it wishes," or can send prices "out the ceiling" as may be a common misconception. The monopolist is still subject to the discipline of market demand; there is some revenue-maximizing price, some profit-maximizing price (probably different from the revenue-maximizing price), and some price that is high enough that the public won't (or can't) buy any of his product, even if it is the only source of it.
(4) Supernormal profits and control over its situation are the two prominent benefits that monopoly position confers upon a firm. Supernormal profits are not a certainty, even for a monopolist, but if they are achieved, it may be possible to sustain them indefinitely if effective competition can be forestalled and entry into the market blocked. But even if supernormal profits cannot be achieved (as appears to be common for some utilities), the control over the market, the comforts of entrenchment, and the absence of a need to compete may be sufficient rewards for the monopolist.
Short-Run Adjustments by the Monopolist
Figure 14-1 illustrates the short-run revenue and cost curves for a pure monopolist. The reader is invited to compare these with those in Figure 13-1 for a representative firm in pure competition. There are two obvious differences. First, the market demand and supply curves illustrated in panel (a) of Figure 13-1 are apparently missing from Figure 14-1. They are in fact present in Figure 14-1, but a separate set of coordinate axes is not needed to house them. This is so because the monopolist's demand curve is the market demand curve when there is only one seller in the market. And the market supply curve consists of one of the monopolist's short-run cost curves, depending upon the monopolist's behavioral objective.
Figure 14-1. Cost and Revenue Curves for a Pure Monopolist.
The second obvious difference between Figures 13-1 and 14-1 is that the monopolist's total revenue curve, TRm, is drawn as a parabola opening downward (rather than a straight line), and its demand curve (which is also its average revenue curve), Dm, slopes downward from left to right. The marginal revenue curve, MRm, as was noted in Chapter 6, diverges from the demand curve and lies below it when the total revenue curve is a parabola.
The practical reason that D slopes downward is that the monopolist, in order to increase sales, finds it necessary to lower the product price (or do something to cause the demand curve to shift to the right). The conceptual reason that marginal revenue is always less than average revenue (i.e., MR lies below D) is that the lowered price applies to all units that are sold, not just to the additional unit sales resulting from the price decrease. Since marginal revenue is the addition to total revenue consequent upon selling more units, marginal revenue decreases because total revenue increases at a decreasing rate. This can also be stated in the opposite direction: when TR increases at a decreasing rate, MR decreases. Because marginal revenue eventually reaches zero and negative values, total revenue correspondingly reaches a peak and becomes negatively sloped beyond the peak.
The cost curves illustrated for the pure monopolist in Figure 14-1 have essentially the same appearances as those illustrated for the pure competitor in Figure 13-1 Short-run cost relationships are not the real differences between the pure competitor and the pure monopolist. In a local market, or in the case of a newly-invented product, the pure monopolist could be physically as small a firm as we assume a pure competitor to be, in which case the cost curves could be identical. We usually imagine the monopolist to be a gigantic firm, having gotten so by growth and exploiting economies of scale. In this case, the quantity units scale on the horizontal axis may cover a much larger range than would be expected of the small-firm pure competitor, but we can still expect the short-run cost curves to be of similar shape, only to spread horizontally across the larger range.
The thought process that the pure monopolist must use in selecting the right output level is virtually identical to that of the pure competitor. The same decision criteria are pertinent to both pure competition and pure monopoly. Output should be increased if marginal revenue exceeds marginal cost because more will be added to total revenue than to total cost, thereby increasing profit (or diminishing loss if the firm is operating unprofitably). Such is the case at output level Q1 in Figure 14-1. If marginal cost is greater than marginal revenue, as at output level Q2, output should be decreased; the resulting decrease in total cost will be less than the decrease in total revenue, so that profit will be increased (or loss diminished).
The major difference between the pure monopolist and the pure competitor lies in the fact that the pure monopolist has at least two realms of decision discretion whereas the pure competitor has only one. The pure competitor is a price taker; it has no alternative but to accept market price as a given. The pure monopolist not only can alter market price if it wishes; it must change market price if it wishes to change the quantity that it sells. For example, suppose that it has been selling the Q1 quantity at price P1 (point A in Figure 14-1). The manager realizes that since marginal revenue is greater than marginal cost output should be increased to Q2. If the manager now does not also lower price to P2, a larger quantity will be produced than can be sold at the unchanged price, resulting in an inventory accumulation of Q2-Q1, or the line segment AC in Figure 14-1. It would certainly be nice to be able to sell the larger quantity, Q2, at the unchanged price, P1, but point C does not happen to be on the firm's demand curve. In fact, to increase output without correspondingly decreasing price will result in increased total costs but no increase in total revenue. The impact on profit would be precisely the opposite of the desired effect.
To accomplish the desired objective of increasing profits, the monopolist must move along the demand curve to some point like B. Such a movement is a "change of quantity demanded," which any student who has had a course in principles of economics knows to be caused by a change of price. In order to get to a point like C, the monopolist would have to effect a "change of demand," i.e., to shift the demand curve to the right. This may indeed be possible by mounting an effective promotional effort.
Even if the monopolist does not have perfect knowledge of the shapes and loci of his revenue and cost curves (management almost never will), an iterative process (trial and error) employing as decision criteria the comparison between marginal revenue and marginal cost (or their proxies) can lead the monopolist toward the profit maximizing price and output levels, P3 and Q3 in Figure 14-1. Output level Q3 is that for which marginal revenue is equal to marginal cost. Given the locus of the demand curve at Dm, there is no other quantity sold at any alternative price that can yield any more profit than can the Q3 output sold at the P3 price. In addition to Q3, there are other output levels that are also notable:
Q5, the output that minimizes average variable cost;
Q6, the output which minimizes average total cost;
Q7, the upper break-even output level;
Q8, the maximum output at which all variable costs are covered;
Q9, the lower break-even output level.
Each of these is notable because it could be a decision objective of the firm in lieu of profit maximization. For example, suppose that the objective of the firm is growth rather than profit. Output Q7 is the largest quantity that can be produced and sold without incurring loss. Output Q8 is the largest output that can be produced and sold while covering all variable costs, but sustaining a maximum loss equal to the average fixed costs. Output Q9, the lower break-even output, could be an objective if the firm is attempting to present a low profile to the antitrust authorities: it is the smallest output that can be produced and sold without incurring a loss.
In Chapter 2 we noted that the manager of the firm might pursue a satisficing behavioral strategy with respect to profits. One form of satisficing is to select a target rate of return (TROR) on invested capital. For example, if the firm has $1 million invested in plant and equipment and the management wishes to earn 10 percent on this investment, it must realize a profit of $100,000. This sum can be represented as a vertical line segment of an appropriate length relative to the vertical axis scale. This vertical line segment can then be moved into Figure 14-2 until it just "fits" between the TR and TC curves, thus "finding" the minimum output level, Q10, which will just satisfy the TROR requirement. Alternately, it may be fitted to the right side of the lens-shaped area formed by the TR and TC curves to find Q11, the maximum output that is compatible with the TROR requirement. In either case the management would further have to estimate the market price at which each output could be sold, but there are no marginal decision criteria that can help him in this respect. However, if the management has enough information about cost and revenue relationships to permit estimation of cost and revenue functions, it could solve the difference between the two functions (TR-TC) for the Q that just meets the TROR requirement.
Figure 14-2. A Monopolist's Profit-Satisficing Level of Output.
Before we leave the realm of short-run decision making for the monopolist, we should note that it has even more decision-making discretion than just price and output. There is a wide variety of non-price determinants of demand that the marketing decision maker can manipulate in the effort to shift the demand curve, i.e., to effect a "change of demand." In regard to Figure 14-1 we noted that the effort to get to point C will be unproductive if the demand curve lies at position Dm. But by creative advertising or other promotional effort, the marketing staff may succeed in shifting the demand curve to the right until it does pass through point C. Then the firm could produce the larger output Q3 and sell it at the unchanged price P1. The additional revenue will be offset by the increased promotional expense. Both the revenue and the cost curves will be shifted by such an effort, thus establishing a new profit-maximizing price-output combination. At any time that such changes occur, the cost and revenue functions should be respecified either intuitively or by empirical estimation. The problem is that when such a change is effected, no historical data for the altered situation exist to permit the empirical estimation. The manager is then in the position of making "best-guess" intuitive modifications to the parameters of the cost and revenue functions until enough new data can be compiled to enable empirical reestimation of the functions.
Long-Run Adjustment by the Monopolist
The monopolist's long-run average total cost curve is more likely to be flat-bottomed or to slope downward from left to right as depicted in Figure 12-4, rather than to have the classic U-shape depicted in Figure 12-3. The monopolist's demand and marginal revenue curves are downward-sloping as depicted by curves D1 and MR1 in Figure 14-3. If market demand, D1, is still small relative to scale economy possibilities, the monopolist should select plant size ATC1, for which its marginal cost curve crosses the long-run marginal cost curve at the latter's intersection with MR1.
Figure 14-3. Long-Run Adjustment by the Monopolist.
Although it may be heroic for the monopolist to know so much about its revenue and cost possibilities as to be able to find such an intersection, there is no more efficient plant for meeting the D1 demand than the ATC1 plant. However, selection of plant size ATC1 could be short-sighted if there is prospect for market demand to shift to the right from position D1. It might do so if the economy is growing and the income elasticity of demand for the product is positive. The monopolist may also promote its rightward shift by engaging in effective marketing activity. If either of these prospects is significant, the monopolist might be wise to build a plant to meet the demand forecasted for some number of years into the future, even though it may yield suboptimal profits or even losses at present demand levels. The right-ward shift of demand through time may enable the monopolist to exploit potential scale economies if LATC slopes downward. By the time that demand has shifted to position D2, plant ATC2 can be constructed and operated profitably. It will yield lower unit costs and extend to a larger output range than can be attained by plant ATC1. The exploitation of scale economies as demand increases can contribute to the profitability of the monopolist.
Some industries grow, but others contract with technological advances or the dynamics of comparative advantage. Sometimes a monopolist is faced with contracting demand conditions. In these circumstances, a firm that has built a plant like ATC2 in Figure 14-3 may find demand to have collapsed to some level like D1. Given demand D1, there is no level of output at which plant ATC2 can be operated profitably. The monopolist's options are to continue to operate plant ATC2 as long as output can be sold at a price above average variable cost, or to shut down when price falls below AVC. The manager can then given consideration to exiting the market or building a smaller plant, such as ATC1.
The Managerial Implications of Pure Monopoly
From the perspective of the manager of the commercial business firm, monopoly would seem to be the most desirable position to be in. Except for governmental interference, the monopolist can exert greater control over his own destiny than can managers of firms in any more competitive environments. This position is not without cost, however. It must be maintained, defended, and protected on a continuing basis. The monopolist must be ever vigilant, not only for attempts at entry, but also for changes in demand and technology that can provide opportunity for growth or threaten the firm with failure. Although the monopoly position can be comfortable, its operations seem inevitably to attract the attention of the public or the authorities. Once the monopolist comes under the scrutiny of an antitrust authority that decides either that its existence or its behavior are not in the public interest, the monopolist's position may cease to be so comfortable.
Competition vs. Monopoly
The market structure of choice for the manager of the business firm would surely be pure monopoly, but it can be argued that the interests of society are best served by pure competition. As we noted at the beginning of this chapter, industries in the real world are rarely at either extreme of the competitive continuum. We have devoted Chapters 13 and 14 to an examination of the extremes so as to describe the limits within which real-world market structures lie. We now proceed to Chapters 15 and 16 for elaboration of two more realistic market structures, monopolistic competition and oligopoly.
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CHAPTER 15. MONOPOLISTIC COMPETITION
In Chapters 13 and 14 we considered what life would be like for the manager of a firm operating at either extreme of the competitive continuum. We noted that both extremes were unrealistic relative to what is typical of commercial relationships in late-twentieth century western societies. But perhaps we should not so hastily dismiss the extremes, because at some earlier time both may have been more realistic than they seem to be today.
Prior to the middle of the nineteenth century when the corporate form of business organization became more popular, most business enterprises were organized as proprietorships or partnerships, and were generally of quite small scale. Under these circumstances the hypothetical construct that economists have labeled "pure competition" may have been more than adequate to the task of analyzing circumstances and providing criteria for managerial decision making.
With the popularization of the corporate form of business organization during the latter half of the nineteenth century, the scale of the enterprise could grow very rapidly. And business entities competed fiercely during the late nineteenth century, driving some of their competitors out of business and combining with others to effect what economists came to understand as "pure monopoly." Indeed, Alfred Marshall's first edition of Principles of Economics in 1890 contained essentially complete expositions of both pure competition and pure monopoly, but mentioned nothing in between. Very little has been added to our understandings of pure competition and pure monopoly since 1890. But perhaps these two model types were entirely adequate for describing and analyzing most real-world commercial and industrial contexts of the day.
As business organization, management, competition, and particularly governmental involvement in the commercial and industrial sectors evolved in the twentieth century, economists became ever more acutely aware that their theories of competition and monopoly represented polar extremes. These theories served progressively less satisfactorily to describe and analyze the emerging competitive situations between the extremes. By the 1930s, economists were attempting to devise theories to fill the void between the extremes, and the adjective "pure" became the common descriptor of the theories at the ends of the competitive continuum.
By the late 1940s the emerging intermediate theories became classified into two broad categories to be known as "monopolistic competition" and "oligopoly," the latter term implying a small number of sellers in the market. We should pause at this point to distinguish American usage from British terminology. An American economist, Edward Chamberlin, and an English economist, Joan Robinson, almost simultaneously, but independently, proposed virtually identical explanations of competition with monopolistic elements. Chamberlin described his theory as that of "monopolistic competition," but Robinson called hers "imperfect competition." American economists and textbook writers naturally adopted the term "monopolistic competition" while British economists became accustomed to talking about "imperfect competition," although when American and British economists got together they became aware that they were talking about the same phenomenon going by different labels.
American practice found a use for the term "imperfect competition" that was likely not intended by Robinson or her English associates. In American economic parlance, the term "imperfect competition" came to refer to everything between the extremes of pure competition and pure monopoly, including both monopolistic competition and oligopoly. But when she described imperfect competition, Robinson had in mind a very specific set of characteristics that did not encompass what we today know as oligopoly. The title of this chapter follows the American practice.
Decision Making under Monopolistic Competition
The descriptive characteristics of monopolistic competition in its modern incarnation are as follows:
(2) Unlike pure competition, the firms produce similar but not identical products, although they are enough alike to be regarded by the public as very close substitutes in use. The products may be differentiated in fact by color, texture, structure, function, etc., or only in the imagination of the consuming public. In a sense, monopolistic competition may be said to be like pure monopoly in that each seller is a monopolist of his own product design and brand name (hence the "monopolistic" part of the term).
(3) Like pure competition, firms in the market have comparable managerial capacities and use approximately the same technologies, but unlike pure competition, individual firms may develop or acquire managerial distinctives that are sufficient to enable the pursuit of market strategies. They may also develop or acquire technological variations that are sufficient to differentiate each firm's product.
(4) As in pure competition, all participants in the market have access to the same information about changing market conditions.
With these descriptive characteristics in mind we can deduce the likely consequences and behavioral characteristics of monopolistic competition. Since monopolistic competition is so much more like pure competition than pure monopoly, we shall be focusing on the consequential differences between monopolistic competition and pure competition.
(b) Exit from the monopolistically competitive market is also easy, as it is in pure competition.
(c) Because of the possibility of developing managerial distinctives and market strategies, there may be significant incentive for managements of monopolistically-competitive firms to exercise entrepreneurship in order to distance themselves and their products from other competitors and their products.
(d) In spite of the small size and limited financial resources of the monopolistically-competitive firm, it may seek to gain special managerial abilities and technological variants in order to try to achieve some measure of market dominance.
(e) Even with ready access to commonly available knowledge of market conditions, and because of the possibility of managerial distinctives, monopolistically competitive firms may react differently from their competitors.
(f) But like pure competition, monopolistic competition is essentially anonymous; each monopolistic competitor perceives changes only in "the market," and thus reacts only to "the market" rather than to the particular actions of any specific competitor whose identity can be known (we stress this point now because this is be one of the significant differences between monopolistic competition and oligopoly).
(g) Because of the ease of entry into the monopolistically-competitive market, there is a tendency toward convergence upon a common price. Because of the great number of competitors supplying very close substitute products, the monopolistic competitor's demand curve is highly elastic (though not perfectly elastic as in pure competition). The downward slope of the monopolistic competitor's demand curve, however slight, provides the manager of the firm some small measure of pricing discretion, and from time to time he may be tempted to experiment with price. Most of the time, however, he will perceive himself to be adjusting to a changing market price rather than initiating a new price.
(h) Because of the possibility of differentiating the product, either physically or only in the perceptions of prospective clients, the manager of the monopolistically competitive firm will be prone to advertise or otherwise promote his product extensively in the hope of attracting the attention of the consuming public. Any promotional effort incurs an expense that is like an overhead cost because once a commitment has been made to the promotional program, its cost is in effect "sunk." It will be the same level of outlay whether successful or not, i.e., whether the firm produces and sells a larger or smaller volume of output.
(i) As in pure competition, super- or subnormal profits will be fleeting due to the ease of entry and exit. Profits will tend toward the economically normal level of opportunity cost.
Short-Run Adjustments in the Monopolistically-Competitive Market
In the discussion of pure competition in Chapter 13, we spoke of a "representative firm in the market." This terminology may not be appropriate to monopolistic competition because products are not homogeneous, and because monopolistic competitors may develop managerial distinctives. The differentiated products, however, are enough alike to be construed as being within the same market group. We shall analyze the operation of a typical firm in the monopolistically-competitive market group.Figure 15-1 represents the revenue and cost curves for such a typical monopolistic competitor. The cost and revenue curves for the typical monopolistic competitor illustrated in Figure 15-1 differ from those for a representative purely competitive firm illustrated in Figure 13-1 in that the market is not separately represented, the demand curve slopes downward from left to right (even if only slightly), the MR curve diverges from the AR curve, and the TR curve has some downward concavity. The Figure 15-1 curves are actually quite similar to those for the pure monopolist as illustrated in Figure 14-5 with the exception of the relative shallowness of the slope of the AR and MR curves, and the fact that the TR curve is of such slight concavity that its peak and downward-sloping range lie well beyond the total cost curves.
Figure 15-1. Revenue and Cost Curves for a Monopolistically Competitive Firm.
We shall not impose upon on the reader a "replay" of the Chapter 13 discussion of the process that the manager of the firm might go through in finding the output Q1 and the corresponding price P1 for which the monopolistically-competitive firm maximizes profits. Suffice it to say that the comparison of marginal revenue with marginal cost serves just as well for the manager of the monopolistically competitive firm as it does for the pure competitor or pure monopolist in discovering whether to increase or decrease output.
If the monopolistically-competitive firm depicted in Figure 15-1 is typical of all such firms in the market group, the large amount of supernormal profit realized at the profit-maximizing price and output level will not go unnoticed by entrepreneurs presently outside the market. There will likely ensue a rush to enter the market in order to likewise reap such handsome above-normal returns, but they will surely be competed away just as in pure competition. How this happens requires further elaboration.
Chamberlin employed two demand curves, similar to those depicted in Figure 15-2, to explain the market adjustment process. The demand curve of Figure 15-1 is reproduced in Figure 15-2, and was intentionally labeled with a lower-case letter "d" so that Chamberlin's other demand curve could be introduced and labeled with the capital "D" in Figure 15-2. Chamberlin referred to demand curve d as the firm's "species" demand curve because it is specific to the particular firm; it is the one with respect to which the manager must plan most of its short-run strategies. But the manager cannot avoid giving consideration to the other demand curve, D, which Chamberlin referred to as the "genus" demand curve because it is generic to the market group.
Figure 15-2. Genus and Species Demand Curves in Monopolistic Competition.
Suppose that the entire market demand, Dm, for all of the close-substitute products that comprise the market group can be identified, and that there are n such typical firms in the market group. Unless any of them can distinguish itself and its product to capture a larger share of the market demand, each can expect to exploit a 1/nth share of the market demand, or D = (1/n)Dm. When, in response to the perception of the supernormal profits being realized in the market, k additional firms enter the market, each firm in the market (new as well as old) now can count on only a 1/(n+k) share of market demand, or D' = (1/(n+k))Dm.
Thus, the firm's generic demand curve shifts to the left consequent upon the entry into the market, and according to Chamberlin carries with it the firm's species demand curve as we have illustrated it in Figure 15-2. The leftward shift of each firm's set of demand curves consequent upon a diminishing share of the market induces each firm's management to accept a progressively lower price consistent with the goal of maximizing profits. The effect of the decreasing market share and falling price is to decrease the profits of each of the typical firms. Theoretically, enough additional firms, j, will enter the market until all supernormal profits have been competed away, and each of the typical firms is left in a state similar to that depicted in Figure 15-3. This state may be described as market (or group) equilibrium.
Figure 15-3. A Monopolistically-Competitive Firm in Industry Equilibrium.
This result is similar to the market equilibrium in pure competition in that the typical firm in the market is covering all of its economic costs, including normal returns to the entrepreneur and management, but is not realizing supernormal profit. It is different from the purely competitive conclusion because the typical firm operates at an output rate, Qm, which is below that at which the pure competitor would produce, Qc, and sells at a price that is slightly higher than that of the representative pure competitor in market equilibrium.
Carried into the long run, which we will leave to the reader to analyze with reference to Figure 15-3, the manager of the monopolistically- competitive firm will be led to build a (slightly) too-small plant, operate it at a (slightly) too-low rate of output, and charge a (slightly) too-high price, all while realizing no more profit than would have been realized by the representative pure competitor.
With the small amount of pricing discretion implicit in the shallowly-sloped species demand curve, the manager of the monopolistically-competitive firm may be tempted to experiment with price. In the interest of increasing the market share, a price cut is much more likely to be attempted than a price increase. The highly elastic species demand (the one that appears to govern his market) leads to the belief that a small price cut can vastly increase sales, thereby to increase both revenues and profits. And this strategy would work, too, if none of his competitors noticed the price cut.
Alas, some of the competitors at first will become aware that price has fallen somewhere in the market (but because there are so many sellers, they will be oblivious to the identity of the perpetrator) and cut their prices as a defensive measure. More and more firms will meet what is rapidly becoming the reality of a new market price. As this phenomenon ensues, each firm will find itself sliding down its genus demand curve rather than traveling down the species demand curve as was the intention of the manager of the first firm to have cut price. They will all sell a few more units of the product (people do tend to buy more at lower prices), but if the movement along the genus demand curve is into the inelastic range, each firm's revenues will actually decrease and profit will fall. The perpetrator of the price cut, so full of hope that cutting price will get him a larger market share and more profit, will have gotten burned by playing with the matches of price experimentation. It is experiences like this that make managers of monopolistically-competitive firms much more amenable to non-price forms of competition and promotion.
Detractors of the monopolistically-competitive (or any imperfectly competitive) market structure speak of the "wastes of monopolistic competition," call attention to the redundance involved in "pointless" heterogeneity, note the excess capacity implicit in operating at a rate of output below the least-cost output rate. They deduce that resources are at one-and-the-same time both overallocated (the excess capacity) and underallocated (too little is produced at the too-high price) to goods produced for such a market.
Those more tolerant of the monopolistically-competitive market structure note that the slightly-higher price, the slightly-lower output, and the smaller-than-optimal plants are small prices to pay for product variety in a society that values freedom of choice (after all, a range of alternatives must be available in order to be able to exercise the privilege of choosing). Also, the excesses of monopolistic competition may seem mild in comparison with the alternatives of oligopoly and monopoly. Other things remaining the same, if society could make no-cost choices of the market structures for producing its outputs, pure competition would win hands down. But even those who think they have found an example of monopolistic competition in the real world (have they been asking the wrong question?) are hard-pressed to come up with a workable public policy for transforming the monopolistic market into a purely competitive one.
Managerial Implications of Monopolistic Competition
The entrepreneur who decides to enter a monopolistically-competitive market should do so with eyes wide open to the likelihood that those supernormal profits will disappear very quickly. The manager's only serious hope for sustaining the supernormal profits is to make the product and its support system (location, convenience, delivery, service, etc.) as distinctive in a positive way as possible, and thereby to prevent the leftward shift of the demand curve. To this end the manager of the monopolistically-competitive firm may engage in efforts to promote and differentiate the product, but not without cost.The relevant question here is whether the increased demand for the product will generate enough additional revenues to cover the costs of differentiation and promotion. Figure 15-4 illustrates a successful effort at promotion that adds to overhead costs but shifts the demand curve far enough to the right, e.g., to position D2 to yield enough additional sales revenue to both cover the promotional cost and pad the profits. But there are entrepreneurial risks in monopolistic competition, and this happy result is not guaranteed. If the manager of one typical monopolistic firm can devise an innovative marketing scheme, so too can the managers of other similarly typical firms, and their efforts may simply cancel each other out. In this case they might end up spending more and enjoying less profit, for example, if demand remains at D1 in Figure 15-4.
Figure 15-4. A Successful Promotional Effort by a Monopolistic Competitor.
To the extent that a monopolistically competitive firm is successful in differentiating and promoting its product to gain a larger-than-typical market share, it and a few other successful firms may be on their way into the realm of oligopoly, and it is to this market structure that we soon turn our attention.
Are there many (or any) good examples of monopolistically-competitive markets? We should remember from our discussion in Chapter 14 that this may be the wrong question to ask. For a particular market under examination, is the model of monopolistic competition an appropriate vehicle of analysis? This is the better question. It may be answered in the affirmative if certain criteria are met. If there is a relatively large number of fairly small sellers in an market that is easy to enter, then either pure competition or monopolistic competition is indicated. If the managements of the firms can be observed to be trying to differentiate their products, then either monopolistic competition or possibly oligopoly is indicated. But there are two acid-test criteria: if competitors are essentially oblivious of each other's identities, and if profits tend to be dissipated due to entry of new firms into the market, then monopolistic competition is almost certainly the appropriate model to apply.
On the other hand, if the competitors are conscious of each other's identities to the point of devising market strategies oriented toward specific competitors, this is a sure sign of oligopolistic competition. Profits may be dissipated in oligopoly as well as in monopolistic competition, but due to price competition rather than entry. The detection of price leadership/followership behavior might be taken as an identification of oligopoly rather than monopolistic competition, but if competitors "follow the market" without specific knowledge or concern about the identity of the perpetrator of a price change, monopolistic competition is the appropriate model.
The number of competitors was not stressed above as a critical distinction between monopolistic competition and oligopoly. This is due to the importance of an identification of the relevant geographic market. For example, in any Standard Metropolitan Statistical Area (SMSA) there are literally hundreds of retail gasoline stations that are differentiated from each other by brand name and locality. Does this sound like monopolistic competition? If the owner or manager of each station sets prices vis-a-vis the prices of those other stations within sight up and down the street, the relevant geographic market likely consists of a half-dozen or fewer stations in the near neighborhood. This renders retail gasoline distribution essentially oligopolistic.
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CHAPTER 16. OLIGOPOLISTIC COMPETITION
Chapter 15 ended with a question of whether there are any good examples of monopolistically competitive markets. It was noted that this may be the wrong question to ask. The better question for any particular market under examination is whether the model of monopolistic competition is an appropriate vehicle of analysis. If there is a relatively large number of fairly small sellers in a market that is easy to enter, then either pure competition or monopolistic competition is indicated. If the managements of the firms can be observed to be trying to differentiate their products, then either monopolistic competition or oligopoly is appropriate.
As we noted in Chapter 15, there are two acid-test criteria for distinguishing the applicability of monopolistic and oligopolistic competition models. If competitors are essentially oblivious of each other's identities, and if profits tend to be dissipated due to entry of new firms into the market, then monopolistic competition is almost certainly the appropriate model to apply. On the other hand, if the competitors are conscious of each other's identities to the point of devising market strategies oriented toward specific competitors, this is a sure sign of oligopolistic competition.
The number of competitors was not stressed in Chapter 15 as a critical distinction between monopolistic competition and oligopoly due to the importance of the relevant geographic market. We noted that in any Standard Metropolitan Statistical Area (SMSA) there are literally hundreds of retail gasoline stations that are differentiated from each other by brand name and locale. If the owner or manager of each station sets prices vis-a-vis the prices of those other stations within sight up and down the street, the relevant geographic market likely consists of a half-dozen or fewer stations in the near neighborhood. This makes retail gasoline distribution essentially oligopolistic. The critical criterion is not number of sellers, but rather consciousness of identities of competitors. Experience indicates that the majority of real-world competitive contexts are more appropriately analyzed with oligopolistic models than with monopolistically-competitive models.
Decision Making in Oligopoly
More-or-less standard specifications may be described for pure competition, monopolistic competition, and pure monopoly. oligopolistic competition, perhaps the most common form of Western industrial and commercial market structure, is the one for which the least standard analytical specification exists. In laying out its descriptive characteristics, we shall focus upon the differences and similarities with both monopolistic competition and pure monopoly.
(2) The products (goods or services) sold by the firms in the oligopolistic market may be homogeneous (examples might be asphalt once laid, concrete once poured, a grade of gasoline once in the tank) or differentiated (locale, billing practices, and levels of service distinguish even pavers, ready-mix concrete suppliers, and retail gasoline stations). But if differentiated, the products must be close-enough substitutes in use or function that prospective consumers give serious consideration to the alternative products before purchasing.
(3) Unlike monopolistic competition, in oligopoly there may occur significant differences in managerial abilities and organizational structures. Also, widely divergent technologies may be employed by different oligopolistic competitors to produce identical or close substitute products.
(4) Unlike monopolistic competition, firms in an oligopolistic market have differing levels of access to information, some of which may have been acquired by deliberate research. Some information is specific to each firm, particularly its own prices, production plans, and marketing strategies. This information is likely to be kept secret and protected so that it is not readily available to other firms. There are likely to be few enough firms competing in the market that the manager of each one can know the particular identities of each of the other competitors in the same market.
These descriptive characteristics lead to the following behavioral characteristics of oligopolsitic competition:
(b) As in monopoly, exit from the market is always possible by failure and dissolution, but oligopolists wishing to exit a market may have another option not available to the monopolist, i.e., to combine with or dispose of assets to a competitor.
(c) Unlike monopolistic competition and pure competition, oligopolistic competition is hardly anonymous. Because there are few enough sellers for each to know the identities of the others, virtually every market-oriented and productive decision needs to take into account the range of possible reactions by competitors as well as the most likely reaction. And even if no deliberate decisions are under consideration by the management of the oligopolistically competitive firm, its manager needs to monitor the activities of the competition and be prepared to react accordingly.
(d) Oligopolists, like monopolists, have a great deal more pricing discretion than do monopolistic competitors, but the pricing discretion may be severely constrained by the pricing practices of competitors and their likely pricing reactions.
(e) Because of the inherent or contrived barriers to entry into an oligopolistic market, supernormal profits may persist. Yet, price competition among oligopolists, as among monopolistic competitors, may tend to dissipate any supernormal profits even if no new entry occurs. Managers of oligopolistic firms may even deliberately initiate a price war that is intended to take profits to subnormal levels long enough to induce competitors to exit the market.
(f) As in both pure and monopolistic competition, there may tend to be a market-wide convergence upon a common price, but for different reasons in the oligopolistically competitive market. These may range from an effort to limit price to a profit submaximizing level to forestall entry into the market, through various forms of price leadership/followership behavior, to overt collusion among the oligopolistically competitive firms in the market. The oligopolist's demand curve likely will be of somewhat steeper downward slope than that of the monopolistic competitor, and it may account for some fraction of the total market demand that is greater or less than 1/n if there are n firms in the market. The steeper downward slope of the oligopolist's demand curve suggests greater pricing discretion, but this may be rather illusory for all of the firms in the market except the price leader.
(g) Difficulties with pricing strategies and price leadership/followership relationships in the oligopolistically competitive market may lead the managers to prefer non-price forms of competition that are similar to the efforts to differentiate and promote the product in monopolistic competition. But practically everything that can be said about price leadership/followership in oligopoly can be repeated for non-price competition ladership/followership. That is, there may occur design, service, or promotion competition, and a market leader may emerge in any of these areas. The leader then initiates aggressive decisions while the followers make defensive decisions of the "catch-up" or "me-too" variety.
The object of competition in oligopoly often becomes market share rather than profit or any other behavioral goal. A common problem for oligopolists engaging in non-price competition is to incur design, service, or promotion costs (fixed costs) that simply cancel out each other's efforts, leaving their market shares unchanged (the "smoking-more, enjoying-it-less" syndrome). To the extent that non-price competition has self-cancelling effects, profits are diminished. The market leader may have the best hope of gaining market share, and that may be only temporary.
For each of the other market structure types (i.e., pure competition, pure monopoly, and monopolistic competition), we were able to describe one fairly standard model generally accepted by economists. Unfortunately, this is not possible for oligopolistic competition because the circumstances and the potential for competitor reaction render each oligopolistic situation unique. Since no two oligopolistically competitive situations are alike, it is necessary to model each one to fit the specifics. There is no single oligopoly model as there is a single monopoly model. Oligopoly models are legion.
We can, however, identify a limited number of oligopolistic behavioral patterns into which nearly any oligopolistic situation can be classified. A general type of model can be specified for some of the patterns. We shall describe seven broad behavioral patterns:
(2) Managers of oligopolistically competitive firms may engage in aggressive competitive behavior, occasionally manifested by open price- (or design-, service-, promotion-) warfare or other predatory or even criminal behavior to the end of eliminating competitors so that monopoly (or more-limited oligopoly) position can be achieved.
(3) Oligopolistic managers may be so fearful of the possible deleterious effects of a ruinous price (or other kind of) war that they enter into extreme decision rigidity (e.g., price rigidity) in a "don't-rock-the-boat" or "don't-make-waves" attitude.
(4) Managers of firms in oligopolistic competition, to avoid both price rigidity and price warfare, may engage in overt (open, public) collusion (e.g., by forming a cartel). Collusion may be only occasional consultation, or it may be conducted on a continuing basis. Such overt collusion, if formalized by contract or treaty, constitutes a cartel. The monopoly model described in Chapter 13 is adequate to the analysis of the behavior and identification of decision criteria for an effective cartel. However, collusive relationships and cartel arrangements are inherently unstable because of the difficulty of maintaining discipline among the members as to agreed-upon decisions or policies. They are prone to cheating by members who engage in "under-the-table" transactions. It has been said that if a near-universal cartel exists, the best position to be in is outside the cartel in order to be able to subvert the cartel's prices, promotions, etc.
(5) If overt collusion among separate firms is frowned upon by the authorities, the same end may be accomplished by combination (acquisition, merger, forming "trusts") among the competitors to achieve monopoly position.
(6) If combination to achieve monopoly is frowned upon as well by the authorities, then competitors may try to engage in implicit or covert collusion with no apparent agreement or even contact among themselves. Such so-called "conscious parallelism of action" may be effected through the use of common rate schedules, transportation basing points, catalogs or price books, or trade-association reporting schemes. No one talks to anyone else, but everyone knows that each of the others is following a common policy. In the latter case, although the information reported is historic, there may emerge a consensus about how near-future prices may be predicated upon recent past prices.
(7) And finally, even if none of the above occurs, some type of price leadership/followership is likely to emerge. This author is of the opinion that the existence and effective administration of antitrust law inevitably causes price leadership/followership relations to become the most common patterns of oligopolistically-competitive interaction in Western industrialized nations. This is not to imply that price leadership/followership is the pattern of choice among oligopolistic competitors. Left to their own devices (i.e., without constraint or interference from governmental authority), oligopolistic competitors would choose not to compete, but rather would collude, cartelize, or combine. If these avenues to monopolistic position are foreclosed by effective antitrust administration, price leadership/followership will emerge by default. Then there remains the residual question for government authority of whether leadership/followership relationships are deleterious to the public interest, and if so, what is to be done about them. This and other questions should be of extreme interest for managers of oligopolistically competitive firms.
Models of Oligopolistic Adjustment
Patterns (1), (4), (5), and (6) may be analyzed with the pure monopoly model described in Chapter 14. If de facto monopoly is achieved through any of these avenues, then the remaining problems are those of maintaining discipline and dividing the spoils (i.e., the monopoly profits). These are essentially political problems that we shall not attempt to model with economic theory. The models that we shall describe for patterns (2), (3), and (7) can all be adequately elaborated assuming a two-firm market, duopoly. Each model could be extended to more than two firms with added degrees of graphic complexity.Price Warfare. The earliest of what might be considered oligopoly models were described by Augustin Cournot, Joseph Bertrand, and F. Y. Edgeworth during the nineteenth century. The Edgeworth variant described a simple duopoly whose managers are incredibly naive, but the model can serve to illustrate the effects of price warfare. A model similar to Edgeworth's is illustrated in Figure 16-1. The manager of Firm A, the first to set up shop, naturally assumes himself to be a monopolist who can exploit the entire market demand. He builds a plant that by assumption has constant variable costs represented by MC=ATC, and with plant capacity Q1, the output at which monopoly profits would be maximized when sold at price P1.
The second seller, Firm B, enters the market. Its manager realizes that Firm A is already in operation, and naively assumes that Firm A will continue to sell at price P1. Firm B builds a plant also with capacity Q1; the manager takes as its demand curve D1, which is half of the total market demand. The Db demand curve is represented in Figure 16-1 as a Janus curve facing left (i.e., output increases from right to left), which backs on the Dm demand curve at its vertical axis. The manager of Firm B, however, realizes that if he will undercut price P1 by a small margin, say at price P2, he can sell his whole output, invading the market of Firm A by line segment rs.
Figure 16-1. A Duopoly Model of Price Warfare.
Meanwhile, the manager of Firm A has become aware of the presence of Firm B, accepts it as a fellow duopolist, and now takes Firm A's demand curve to be Da, which also is half of the market demand. The manager of Firm A, who now makes the naive assumption that Firm B will continue to sell at price P2, cuts price to P3 and dumps Firm A's entire capacity output on the market, invading Firm B's market by amount tu.
It is easy to see that as long as each manager naively makes the assumption that the other firm will continue to sell at its current price, the competitive price cutting will continue through several more iterations until the price charged by one of the firms, B in Figure 16-1, reaches the level of its average total cost. The manager of Firm A notices (with sudden and unexplained astuteness) that Firm B has done its worst; it is dumping its entire capacity output on the market at a price just equal to ATC. It dare not go to a lower price, else it will suffer losses. So the manager of Firm A reasons that there is nothing to lose by returning to its profit-maximizing price, P1, and to produce and sell Q2. And the whole price war starts all over from P1 back down to P6.
The moral of this story is that if the managers of oligopolistically competitive firms are so naive as to assume that competitors will continue to charge the same price forever more, and if they are incapable of learning from experience, they will get into price wars where price oscillates between the preferred profit maximizing price and the level of ATC.
Real-world business firm managers are neither so naive nor incapable of learning from experience. As intelligent and perceptive decision makers, they are unlikely to lapse into such mindless competition. However, as noted earlier in this chapter, if the manager of one oligopolistically competitive firm has a cost advantage or a greater financial capacity relative to competitors, a price war may be initiated with the intention of driving price down below the AVC of the competitors, thereby to induce them to shut down in the short run, and to exit the market if the low price continues long enough.
Oligopolistic Price Warfare. In Figure 16-2, suppose that two duopolists equally share the market demand so that their demand curves are coincident and each equal to 1/2 of market demand, Dm. Firm B, however, has lower costs, represented by ATCb, AVCb, and MCb. Firm A's costs are higher at ATCa, AVCa, and MCa. Firm A would like to maximize profit at P2, while Firm B prefers the lower price, P1, for maximization of its profits. But if the manager of Firm B knows enough about both the firm's own costs and those of Firm A, he or she will realize that price can be taken as low as P4 before incurring a loss greater than average fixed costs. Price P3 is at the minimum point of Firm A's AVC curve. Firm A's options now are either to meet price P4 and go out of business in the long run (because P4 is less than its AVC), or to stay at Price P2 and lose market share as its demand curve shifts leftward far enough for it to go out of business because of declining market demand for its product. Thus, by pursuing a deliberate profit-nonmaximizing strategy in the short run, Firm B may be able to achieve monopoly position that will allow it to maximize profits in the long run. But this sort of aggressive price cutting behavior is likely to be regarded as predatory by antitrust authority.
Figure 16-2. Price warfare in a duopoly market.
Extreme Price Rigidity. During the late 1930s the prices in certain oligopolistic industries, notably tobacco products, were observed to be constant for years at a time. During the late 1930s economist Paul Sweezy proposed an oligopolistic model to explain extreme price rigidity among competitors ("Demand under Conditions of Oligopoly," Journal of Political Economy, vol. XLVII (1939), pp. 568-73). Sweezy reasoned that competitors are likely to react asymmetrically with respect to price increases and price decreases initiated by one of the firms in the market. Sweezy implicitly assumed recession economic conditions (the effects of assuming an expanding economy are explored in appendix to this chapter). Given these conditions, competitors are far less likely to follow a price increase than a price decrease. Sweezy then reasoned that demand would be relatively more elastic above the current price, but relatively more inelastic below the current price. This implied that the oligopolistic competitor's demand curve is bent or kinked at the price as illustrated in Figure 16-3.
Figure 16-3. Sweezy's Kinked Demand Curve.
If the demand curve for the oligopolist's product really is kinked at point A in Figure 16-3, then a price increase to P2 will result in a larger percentage decrease of quantity demanded (to Q2) than the percentage increase (to Q3) that will result if price is cut to P3. Assuming that demand is elastic above the kink, but inelastic below the kink, this alone will provide a revenue disincentive for the manager to change price from P1. It may be recalled from Chapter 7 that a price increase when demand is elastic will reduce total revenue; and a price cut when demand is inelastic will also reduce total revenue. The manager is in a lose-lose situation. There is no price above or below P1 at which the firm can increase its revenue. Hence, price remains rigidly at P1. A second possible explanation of extreme price rigidity lies in what is reputed to be a gap or vertical segment in the marginal revenue curve below the kink. This hypothesis is also examined in the appendix to this chapter.
There are several problems with the so-called kinked-demand hypothesis. One is that it provides no explanation of how any actual price, like P1, is established in the first place. Second, when price is increased but competitors do not follow, customers can be expected to defect from the firm's product to those of its competitors. This is an example of an unsuccessful effort at price leadership, and it constitutes a change of one of the determinants of demand, i.e., the cohort of the consumers purchasing the firm's product. The consequence of a change of such a non-price determinant of demand is a demand curve shift (in this example, to the left). The movement from point A to point B is really not along the same demand curve; rather, the firm's genus demand curve (a concept borrowed from Chamberlin's monopolistic competition model) shifts to the left as illustrated in Figure 16-4. Point B is on a relocated genus demand curve, D'.
Figure 16-4. Asymmetrical Price Leadership for Price Increases and Decreases.
The path from A to B is in this example a contraction path. The demand curve is not kinked; rather, it has simply shifted to create an identification problem (as described in Chapter 8). Point C is on the original demand curve, D, and is reached when the firm cuts its price to P3, and all of its competitors follow suit (in this case, the firm is a successful price leader). All of the firms in the market sell some more of the product at the lower price, but there is no realignment of customers with sellers, so the demand curves do not shift.
Leland Yeager has suggested that there is only one actual point, like A, on any demand curve ("Methodenstreit over Demand Curves," Journal of Political Economy, vol. LXVIII (February 1960), pp. 53-64); all others are "virtual" in the sense that they may be revealed under other circumstances (different prices). So it is not possible to be confident that a demand curve has any particular shape, whether straight, curved, or kinked, away from the single existing point.
Even if a demand curve is not truly kinked as reputed in the Sweezy model, asymmetrical responses of competitors to a firm's increases and decreases of price could result in the theorized rigidity. If the firm cuts price when demand is inelastic and other firms follow the price cut, revenues will decrease because of the demand inelasticity. If the firm raises price and other firms do not follow, the firm's revenues will decrease because its demand curve shifts left (but not because its demand is elastic). Although economists have looked very hard for empirical evidence of kinks in demand curves, virtually none has been reported in the professional literature over the past half century. This implies either that the kinked demand curve is a relatively rare circumstance, or that economists have been looking for the wrong thing (kinks rather than shifts).
Price-Leadership/Followership. We have made a case that oligopolistic competition is the most prevalent form of commercial organization in Western society; and we have asserted the most common pattern of oligopolistic interaction where antitrust laws are vigorously enforced to be price leadership/-followership. But we recognize that each price leadership circumstance is unique and demands its own model for analysis. All that we can do in this section is to select a few of the more prevalent types of price leadership to model as guides for the reader to use in encounters with price leadership circumstances.
Economists have identified four broad categories of price leadership:
(b) Barometric price leadership is where the manager of one of the oligopolistic firms establishes a reputation for perceptiveness and sensitivity to changing market conditions, and a record of making timely and successful adjustments to those perceived changes. Managements of other firms then watch the price leader's activities and attempt to emulate his decisions.
(c) Dominant firm price leadership is where the market consists of a dominant firm surrounded by a competitive fringe of smaller firms. The dominant firm behaves as a benevolent monopolist, tolerating the existence of the smaller firms and allowing them to sell any amount of the product that they wish at the price that the dominant firm prefers. The dominant firm then takes its demand as the residual of the market demand not met by the competitive fringe firms, and proceeds to behave as a pure monopolist in maximizing profits. There is no doubt that dominant-firm price leadership examples (in the automotive and computer industries, to name but two) can be found, but we venture the guess that they come into being only as a consequence of vigorous antitrust enforcement that constrains the predatory tendencies of the dominant firm. In Figure 16-5, the market demand is Dm. The competitive supply, Sc, is the sum of the marginal cost curves of the competitive fringe firms. The locus of the dominant firm's demand curve, Dd, is found by subtracting the competitive supply from Dm at each possible price. The dominant firm then sets price at P1 to maximize its profits by selling output Q1, while the competitive firms behave as purely competitive price takers to sell quantity (Q2-Q1). This form of oligopolistic market organization is quite workable, and can persist as long as antitrust law is vigorously enforced and the dominant firm behaves itself. The dominance of the dominant firm may break down when one or more of the competitive firms begins price experimentation or product differentiation/promotion in the effort to capture a larger share of the market.
Figure 16-5. A Model of Dominant-Firm Price Leadership.
(d) Differential characteristics price leadership may be based on three aspects of the constituent firms' characteristics:
(2) differences in sizes of plant; or
(3) differences in market shares.
Combinations of these differences may also be bases for price leadership.
Price Leadership based on Cost Differences. Suppose, in Figure 16-6, that there are two firms in a market, and that, as illustrated in panel (a), they initially share the market demand equally, i.e., the demand curves are coincident at Df, each of which is one-half of market demand. Firm B has a cost advantage (it hires labor or buys material inputs, components, or energy in lower-cost resource markets) than does Firm A. In order to maximize its profits, Firm B would prefer the lower price, PB, at which it sells quantity QB, than that preferred by Firm A, PA, at which it sells the smaller quantity QA in order to maximize its profits. Which firm has the potential for exercising price leadership?
Figure 16-6. Price Leadership based on Cost Differences.
If Firm A chooses to charge its preferred price, PA, ignoring Firm B's preferred lower price, PB, some of Firm A's customers will defect to purchase from Firm B. This constitutes a change of a non-price determinant of demand for both firms, i.e., the population of consumers purchasing from each firm. Firm A's demand curve will shift to the left toward position DA as illustrated in panel (b), carrying with it its marginal revenue curve toward position MRA, with the consequence that Firm A will prefer an ever-lower price. Firm B's demand curve will shift to the right toward position DB in panel (b), carrying with it its marginal revenue curve toward position MRB, with the consequence that it will prefer an ever-higher price. Theoretically, these shifts will continue until the preferred prices converge to a common price, PC, but with a significant difference: the two firms now have divergent market shares, Firm B now with a larger share than Firm A. Firm A will sell an even smaller quantity, QA', and Firm B will sell an even larger quantity, QB'.
Alternately, had the manager of Firm A been willing to meet Firm B's preferred lower price (a deliberate profit sub-maximizing strategy in the short run), it could have preserved its share of the market. Thus, the firm naturally preferring the lower price (in this case, Firm B) has the potential to be the price leader when demand or cost circumstances change. The other firm(s) may choose to follow or not; they can either go ahead and meet the leader's preferred lower price (and thereby preserve market share), or they can lose market share and end up preferring the same price as the leader.
Price Leadership based on Plant Size Differences. The same phenomenon can be seen where there is no cost or demand difference between firms, but there is a difference in plant sizes. In Figure 16-7, the two firms again have equal initial market shares. They also use the same technology and have access to the same labor and materials markets, or different markets with the same market prices. The evidence of this is that their ATC curves have the same shapes and reach bottom at the same per-unit cost levels. Firm B, however, has a slightly larger plant evidenced by the overlap of its ATC curve to the right of Firm A's ATC curve. Again, Firm B has the potential for price leadership because it naturally prefers a lower price in order to maximize profits. But in this case, the basis for price leadership lies in Firm B's larger plant.
Figure 16-7. Price Leadership based on Plant Size Differences.
Price Leadership based on Unequal Market Shares. Finally, we suppose in Figure 16-8 that the two firms have identical plants and hire labor and purchase materials from the same resource markets. These conditions are evidenced by the fact their ATC curves are coincident. Firm B, however, initially has a slightly larger market share than does Firm A. In this case, Firm A prefers the lower price in order to maximize its profits, and thereby has the potential for price leadership. In this example, the basis for price leadership lies in the smaller initial market share (we can only imagine that Firm A's sales force is pushed to be more aggressive, "We're Number 2, we try harder!"). If Firm B now does not meet the lower price preferred by Firm A, it (Firm B) will lose market share to Firm A. This process theoretically could continue until they have the same market shares and thus prefer the same market price.
Figure 16-8. Price Leadership based on Unequal Market Shares.
While the potential for price leadership can readily be discerned in each of these models, it does not follow that the actual price leader will coincide with the potential price leader. The theoretical follower could "take the bull by the horns" and undercut the price preferred by the theoretical leader in each example. But by so-doing he risks the initiation of a price war as described earlier.
The Managerial Implications of Oligopolistic Competition
We have reached the end of our survey of possible behavior patterns in oligopolistically-competitive markets, but we have by no means exhausted the range of possibilities. What should the manager of the oligopolistic firm pay attention to? It all depends upon the circumstances of the specific situation. The oligopolistic market can range from a fairly comfortable "live-and-let-live" mentality to an intensely competitive situation characterized by predatory behavior on the parts of some of the managements. Some managers thrive in such an environment while others would rather get out. Business failure will get some of the faint-hearted out of the market, while others will try to escape the intensity of oligopolistic competition by efforts to achieve monopoly. In Western societies where antitrust law exists and is effectively administered, the oligopolistic competition can count upon government scrutiny of its practices and policies.
The Societal Implications of Oligopolistic Behavior and Industry Structure
Oligopolistic industries are populated by firms that range in size from the corner gas station to the mega-buck corporation. Oligopolistic competition among gasoline retailers probably militates in the consumer's interest by ensuring the lowest possible prices and the narrowest possible profit margins consistent with the continued provision of retail gasoline distribution services. Unless collusion among competitors accomplishes a measure of monopoly control and the realization of supernormal profits, oligopolistic competition at the larger-firm end of the spectrum contributes to technological advance in productive efficiency, better product designs, and better service of the product.Competition, if not subverted by collusion, predatory behavior, the erection of barriers to entry, or the grant of exclusive position by government, can serve as a mechanism for the social control of industry and commerce. Competition doesn't have to be pure in order to exert its controlling function. Even the competition present in the oligopolistically-competitive market in the form of price leadership/followership can be an effective vehicle of social control because the threat of market share loss will induce competitors to meet the lowest price preferred by any firm in the market. Society's job in formulating public policy with respect to oligopoly then is to suppress collusive behavior that exploits consumers, prevent predatory behavior that destroys existing competitors, and disallow the creation of entry barriers that diverts potential competition.
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APPENDIX 16A. MORE ON THE KINKED DEMAND CURVE
In Chapter 16 we showed how the asymmetrical responses of competitors to price increases and decreases by one of the firms in an oligopolistically-competitive market could make it appear that the firm's demand curve was kinked. We dispelled this notion, however, by calling attention to the fact that the firm's genus demand curve actually shifts leftward when it raises price but its competitors do not follow suit, thereby tracing out a more-shallowly sloped contraction path that has the appearance of a species demand curve. A rightward-shift of the genus demand curve, however, does not follow upon a price cut by the firm that is followed by competitors. The resulting asymmetry of response by competitors theoretically renders price rigid at the current level.
Proponents of the kinked-demand model further extend it to a consideration of the marginal revenue conditions associated with the kink. As illustrated by Figure 16A-1, the marginal revenue curve is reputed to have a gap or vertical segment immediately below the kink. This discontinuity is attributed to the mismatching of the two ends of the marginal revenue curve that are derived from the portions of the demand curve above and below the kink. The gap or vertical segment is reputed to allow the firm's marginal cost curve to freely shift upward or downward within the gap without bringing about conditions that would be the basis for a price change. This phenomenon thus constitutes a second explanation of the rigidity of prices in an oligopolistically-competitive market.
Figure 16A-1. The Gapped Marginal Revenue Curve.
However, when the phenomenon is recognized to be an asymmetrical demand shift phenomenon rather than a kinked-demand phenomenon, it must also be concluded that the marginal revenue curve also shifts in an asymmetrical fashion: it does not shift rightward when price is cut and competitors follow the price cut, but it does shift leftward along with the demand curve when price is raised and competitors do not follow suit. This phenomenon is illustrated in Figure 16A-2. The marginal revenue curve is not gapped or vertical below the "kink;" it shifts in one direction but not in the other with price changes. Since there is no gap or vertical segment in the marginal revenue curve, this does not constitute a second explanation of price rigidity.
Figure 16A-2. Asymmetrical Shifts of the Marginal Revenue Curve.
The original Sweezy kinked-demand thesis implicitly assumed recessed economic conditions. To further demonstrate the implausibility of the kinked-demand, gapped-marginal revenue thesis, let us assume a buoyant economy accompanied by some inflation. In this case, competitors are more likely to be looking for an excuse to raise price than to lower it since their costs of production are probably also increasing. Under these circumstances the demand curve would have to be kinked in the opposite direction, with a zigzag marginal revenue curve as illustrated in Figure 16A-3. Here, any price other than P4 would be better than P4. Because demand appears more inelastic above the kink, a higher price will increase revenues; and because demand appears more elastic below the kink, a lower price will increase revenues. Therefore, price P4 is an unstable price. The relevant question would be whether to raise or lower price from P4.
Figure 16A-3. Kinked Demand under Inflationary Conditions.
One suggested solution is to observe where the marginal cost curve cuts the various portions of the marginal revenue curve; there are of course three such intersections. According to this suggested solution, if the leftward triangular portion is of larger area than the rightward triangular portion, the firm should raise price; it should lower price with the opposite triangular areas. Needless to say, the comparison of areas of triangles can hardly serve as a practical decision criterion. We here leave it to the reader to discern the asymmetrical demand-shift implications of price changes in inflationary circumstances.
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CHAPTER 17. EXTENDING THE MODELS
Simple Models and Complex Realities
The models that we have examined in Chapters 13 through 16 assumed the simplest possible context for a commercial enterprise: a business with a single plant, employing a single variable input, producing a single product, which is sold in a single market, and which is run by a single manager. The organization of the market varied in structure and complexity, ranging from pure competition through monopolistic and oligopolistic competition to pure monopoly. But there are very few real-world businesses that are so simple.Business enterprises typically produce a multiplicity of goods and services that often can be organized into lines of complementary and sometimes competing items. Occasionally the goods produced by the business are conglomerated in the sense that there are no apparent relationships among them. Often the multiple goods are joint products resulting from a common production process. And commercial enterprises often sell their products in a multiplicity of separable market areas. They employ a great many variable inputs bought or hired from different resource markets. It is not unusual for a business to have several production facilities or plants, and each plant may be subdivided into several assembly lines, each of which can function as a more-or-less autonomous production unit. And the management of the business may include many decision makers, each with limited areas of expertise, decision-making authority, and responsibility. They may be organized into multiple, hierarchical tiers of authority. The facets of intricacy and complexity of the modern business enterprise are almost innumerable.
How can the simple-minded models elaborated in Chapters 13 through 16 be relevant to any real-world business organizations other than those that match the models in simplicity? The great virtue of such simple contexts is that they allow us to peer through the haze of complexity in order to come to understandings of the principles governing the behaviors of revenues, costs, profit, production, and competition itself without the encumbrances of a plethora of detail. They may serve their academic purposes well, but from a practical perspective, the applicability of such simple models is still not apparent.
There are three planes upon which the models that we have been examining may be beneficial to practical decision contexts. First, the general principles discovered and learned by examining the models in an academic setting can be used as guides to what we shall call "seat-of-the-pants" decision making (see Fritz Machlup, "Marginal Analysis and Empirical Research," in Essays in Economic Semantics, W. W. Norton & Company, 1967, pp. 154-155). Here the decision maker proceeds from an accumulation of experience in similar circumstances to an assessment of the present situation. A rational decision is made by comparing the best available information about the situation to the decision criteria discerned in the academic study of the principles. While this decision-making procedure may sound a bit loose and uncertain, we believe that the vast majority of all business decision makers who have engaged in any formal study of economic principles are likely to proceed in just this fashion.
The second plane upon which simplistic models can be used is to simulate small parts of the complex business decision context. For example, if a business has one plant in each of several completely separate markets, and each plant produces several mutually-exclusive products for sale in the market where that plant is located, it should be possible to specify a revenue and a cost function for each of the products in each of the markets in order to establish the relevant marginal decision criteria. This approach becomes cumbersome and costly in the case of a wholesale distributor or a "big-box" retailer that regularly carries 30 thousand different items (in the case of screws, each combination of thread pattern, head design, finish, diameter, and length constitutes a separate item) in its warehouse. The approach breaks down entirely if some of the items are jointly-produced, or if they are produced in a single plant for sale in several markets, or if they are produced in multiple plants but sold in a single market.
On the third plane the simplistic models must be elaborated to handle the intricacies of the situation. The model builder attempts to make the assumptions underlying the model ever more realistic, the structure of the model ever more accurately descriptive of the real context that is being modeled, and the parameters of the model ever more closely tailored to the particular circumstances of the required decision. The progressive elaboration of a model inevitably increases its complexity and detail. The number of equations in the model increases, and particular equations may have to have more and higher-ordered terms in them.
On Realism, Accuracy, and Specificity in Models
Economists have traditionally valued simplicity in models, for after all is said and done a model is intended to be a simplified representation of a more complex reality. But economists have also debated the importance of the realism of assumptions and the descriptive accuracy of the structure of their models. Most inevitably have come to the conclusion that it may not be possible to construct a simulation model that is perfectly realistic in its assumptions and accurately descriptive in its structure without making it as complex as the real situation from which it is supposed to be an abstraction. This of course would defeat the purpose of attempting to structure a simplified representation of the more complex reality.Economist Milton Friedman argued that the realism of assumptions and the accuracy of the structure of a model are of lesser importance than is the predictive ability of the model ("The Methodology of Positive Economics" in Essays in Positive Economics, University of Chicago Press, 1953). The acid test for a model is how it performs in doing what it was designed to do. According to Friedman, a simplistic model based on unrealistic assumptions may perform satisfactorily; what is important is whether people behave as if the assumptions of the model are realistic, even if the assumptions bear little or no resemblance to the reality.
An economic perspective on the process of elaborating a model to make it more specific to the context being modeled would examine the benefits and the costs of the elaboration process. A more complex model based on more realistic assumptions may indeed yield better decision criteria, but the process of specifying any model is costly in terms of time and effort, and in money terms if the expertise has to be hired from outside the organization. The cost of specifying an ever more complex model probably obeys the principle of diminishing returns (or its variant, the law of increasing costs) no less so than does any other real production phenomenon. Model-building costs rise at an increasing rate the farther the model builder attempts to go in detailing the model. The relevant economic question then is whether the value of the additional effectiveness of the model is worth the extra cost of improving the fit.
Our advice is to apply Occam's Razor to the model-building context. Under this principle, one should (use the Razor to) "cut off" the unnecessary complexity of a model: let suffice the simplest model that will perform satisfactorily. When several needles are lost in a haystack, rational behavior on the part of the tailor is to search until he finds one that is sharp enough to do the sewing job, not until he has found the absolutely sharpest one. But, this is not a recommendation to make no enhancements to the model. Some models are "simply too simple" to fit the realities under analysis. Our purpose in the next section of this chapter is to point the reader in the directions of some potentially productive model elaborations. But we do caution the fledgling model builder to take an economic approach by comparing the possible benefits with the likely costs.
EXTENSIONS OF THE MODEL OF THE FIRM
Non-Price Determinants of Demand
Economists focus almost obsessively upon price as the primary determinant of demand. In Chapter 7 we postulated a more general demand function with several quantity determinants, any one of which could be moved to the head of the queue to serve as the primary determinant. Once any one of them has been designated the primary determinant, others are assumed constant. This procedure enables the construction of a two- or (at most) three-dimensional graphic model to illustrate and analyze the demand relationship. A change of any of the assumed-constant determinants (i.e., the ones not represented explicitly on any of the coordinate axes) results in a shift of the curve (in two dimensions) or the surface (in three dimensions). If such a change occurs without being recognized by the analyst, an "identification problem" arises. The decision-significance of the occurrence of an identification problem is that the decision criteria will tend to be over- or understated, and could thereby lead to erroneous decisions.Economists, in structuring the kinds of models we have examined in Chapters 13 through 16, usually assume price to be the primary determinant of quantity demanded, but it is also a convenience to have a deterministic variable that is directly comparable to average and marginal costs. Business decision makers attempting to employ the economic models should pay attention to the non-price demand determinants because autonomous changes in any of them can shift the company's demand curves in unexpected ways. While these are phenomena to be aware of and prepared to adjust to, it may also be possible to make the non-price determinants of demand into components of the firm's promotional strategy. For example, a successful advertising campaign (promotional effort is one such non-price determinant of demand) should have the effect of increasing the company's demand (i.e., shifting the demand curve to the right), or at least preventing it from decreasing (shifting left) in the face of a competitor's promotional effort.
Non-Quantity Determinants of Costs
Economists also focus almost exclusively upon quantity produced as the primary determinant of cost. But we also noted in Chapter 9 that non-quantity determinants of costs may be incorporated into the cost function. Possible candidates are the market prices of the labor and materials inputs that the firm purchases. It is a convenience to take costs primarily to be functions of quantity produced because this allows direct comparison of per-unit costs (average and marginal) with price and marginal revenue. A change in any of the non-quantity determinants of costs can be expected to shift the per-unit cost curves upward or downward.As in the case of the non-price determinants of demand, it may be possible to incorporate the non-quantity determinants of costs into the company's production and marketing strategies. For example, one way to gain a "leg-up" on the competition would be to develop a more productive (i.e., lower cost) technology, or to find or negotiate lower-priced sources of supply of the materials or labor inputs than competitors can employ. This would certainly increase the company's profits (or reduce its losses) by shifting its per-unit cost curves downward. If the company's average variable cost curve shifts far enough downward, the manager may be encouraged to initiate a price war.
Multiple Markets
The markets in which a firm sells can be classified on at least four bases: product, geographic, demographic, and temporal. We shall defer consideration of multiple products to a subsequent section. The geographic market for a particular product is the locale within which the company sells, and where there is effective competition by other companies selling closely competitive products. For most products, the geographic market is almost certainly not the world or even the whole geographic of area of a country. Most companies sell in multiple geographic markets that are separated by distance and the cost of transport so that clienteles are effectively compartmentalized. Furthermore, the company may face varying intensities of competition in its different geographic markets: it may be a monopolistic competitor in some markets, an oligopolist in some, and a nearly-pure monopolist in a few. It may need to pursue different marketing strategies according to the nature and intensity of competition faced.Varying demand conditions make price differentials among the markets feasible. The charging of different prices for the same item where there are no differences in the costs of serving the different customers constitutes price discrimination that is prohibited under law in most Western societies. By the same token, the charging of the same price where there are different costs of serving different customers is also price discrimination, but this form of price discrimination usually escapes detection or prosecution under the law. For example, many companies deliver products in their own trucks instead of using third-party shippers. Often the costs of own-truck delivery are not charged explicitly, but rather absorbed in the product prices. To the extent that this occurs, the delivered price is the same to the nearby customer as to the distant customer. Price discrimination results as a consequence of charging the same price to the different customers. The antitrust authorities would likely never finish if ever they decided to start prosecuting this form of price discrimination. Although the law usually prohibits the practice of overt price discrimination where there is no cost justification for the price discrimination, price discrimination between markets should be expected to emerge as a normal concomitant of different demand elasticities in the different markets.
The company may also sell to separate temporal and demographic markets within the same geographic market. The bases for demographic market separation may include age, race, ethnicity, religion, place of birth, citizenship, etc. Price (and any other kind of) discrimination based on race or ethnicity are usually prohibited by law. The most common demographic forms of price discrimination are by age and citizenship. Theaters typically offer lower-priced children's tickets, even though the seat is as fully occupied by the child as by an adult, and even though the adult really didn't want to see the children's feature. Restaurants as well as theaters may price differently through the day (the "luncheon menu" vs. the "dinner menu," the "afternoon matinee" vs. the "evening feature"). State universities often price-discriminate against citizens of other states who apply for admission, and denominational colleges occasionally price-discriminate in favor of their own members or the offspring of their ministers and missionaries. Airlines and hotels conventionally price discriminate by days of the week and from one season to the next.
Commercial classification may constitute yet another basis for price discrimination. Wholesalers usually identify "legitimate" retail vendors who then are eligible to buy "at wholesale" whereas members of the general public can qualify only for the higher retail price. Some wholesalers as well as some manufacturers maintain several customer classifications, each of which is eligible for a certain price level or discount from the company's standard price (wholesalers often express their price schedules as various levels of discount from manufacturer's suggested retail price). Such classification schemes break down when a buyer classed in one group has access to someone classed in another group. Most of us know "a guy who's got a brother-in-law who can get it for us at wholesale." Also, the recent advent of "wholesale buying clubs" has served to obscure the distinction between retail and wholesale.
Any of these forms of price discrimination is enabled only because demand elasticity varies among groups or from time to time, and it is not feasible for a prospective client to jump from one group or time frame to another. If clients can jump market segments, the basis for price discrimination is destroyed. It can be shown mathematically that if two conditions can be met, the company can increase its profit by price discriminating across its markets: (a) demands are of different elasticities in the different markets; and (b) there is some means segmenting markets and keeping customers in the different market segments from jumping segments or from buying for one another.
A Graphic Model of Price Discrimination
Figure 17-1 illustrates the possibility of price discrimination across two separable markets, A and B. Demand in Market A is somewhat more inelastic than is demand in Market B. When the demands are summed (horizontally), Dc (the combined demand) has the appearance of a bend where Db is joined to Da, so that the marginal revenue curve, MRc is as drawn in panel (c). The firm has a single plant for which its marginal cost curve is MC. The intersection of MC with SMR identifies the quantity Qc and price Pc that would maximize profits without price discrimination. The total revenue will be the area 0PcTQc. Suppose now that the manager of the company identifies the quantities and prices in the two markets separately for which MR in each is equal to MC, the common marginal cost. On this criterion, Q1 can be sold at Pa in market A, and Qb can be sold at Pb in Market B. Pa is higher and Pb is lower than Pc. A careful examination of total revenue rectangles 0PaRQa and 0PbSQb should reveal that the sum of their areas is greater than that of total revenue rectangle 0PcTQc. Thus, whatever the firms costs happen to be, its revenues with price discrimination will be greater than its revenues without price discrimination. Price discrimination will yield more profit than can be realized without price discrimination. A mathematical model of price discrimination that supports this contention is elaborated in Appendix 17-A.
Figure 17-1. A Model of Price Discrimination.
The managerial implications are clear. The manager of an imperfectly competitive company may by price discrimination increase the company's revenues, but only by incurring the costs of establishing and enforcing market separation, and often by risking antitrust prosecution. It may be very troublesome (and trouble translates into costs) to seal off the markets from one another. The costs of enforcing market separation may be greater than the additional revenue realized from discrimination. What does it take to certify that a person really is under thirteen years of age in order to qualify for the child's price, or over 55 years of age to qualify for the senior citizen's discount? How much does it cost to verify each prospective customer's claimed authorization to buy at wholesale? What is the probability of incurring antitrust prosecution, and what is the likely fine if the verdict is "guilty"? As with any other managerial decision, the rational approach is to compare the expected benefits with the likely costs before deciding to proceed.
Mathematical Modeling for Price Discrimination
Suppose that the manager of a company that has a single plant thinks that it might be more profitable to divide the market into two segments in order to price discriminate. In order to ascertain the appropriate quantities to ship into each sub-market and the prices at which to sell them, the company must estimate its demand functions in the form of P = f ( Q / ... ) and then find the total revenue function by multiplying the demand function through by Q, or TR = P x Q (alternately, the company might first estimate its total revenue function, then derive the average and marginal functions mathematically):
It must then compose its total profit function as TN = TR1 + TR2 - TC, so that the two marginal profit expressions can be computed by partial differentiation,
and
These marginal profit expressions may then be set equal to zero (because the slope of the profit function is zero at its peak),
and
allowing for solution of values for Q1 and Q2. Then, using these values in the estimated demand functions, values for P1, P2, TR1, and TR2 may be found. And finally, the maximized profit, TN, may be computed. An example of this process is elaborated in Appendix 17-A.
Multiple Products
As we have already noted, if the company produces multiple products for sale in as many product markets, its production and marketing operations in each product market can be modeled separately. For short-run decision making purposes, this analysis can be handled without reference to the overhead costs since they are irrelevant to the price and output decisions (in the last section of this chapter we will consider a model for pricing to cover fully-allocated costs).In the long run the allocation of the overhead costs in a multiproduct plant becomes critical to the question of whether to delete any particular items from the product line, or to add new items if excess capacity exists. In order for any item currently in the product line to continue to be produced, its price must make an adequate contribution to its overhead costs as well as cover all of the direct costs of its production. This is not an argument for price to be set to cover overhead as well as direct costs; rather, once price has been determined with appropriate economic criteria (MR, MC), the question is whether or not it covers all relevant costs. Since there appears to be no objective criterion for allocating overhead costs among multiple products, this assessment must be based upon the judgment of the decision maker who, in any case of deleting or adding products, is engaging in an entrepreneurial decision.
If the company has excess productive capacity and is considering whether to add items to its product line, the decision maker must make a prior judgment (again, in an entrepreneurial capacity) as to whether the new item can be sold at a price that is high enough to cover all of its direct production costs and make some contribution to covering the overhead costs as well. It can be argued that since the excess capacity already exists, the overhead costs are in effect "sunk costs" and thus not pertinent to the question of adding the item to the product line. Yet, even if an item is added on the basis that its price will be sufficient to cover all direct costs plus some contribution to overhead costs, for the item to be retained in the product line in the long run it will have to be judged to be making an adequate contribution to overhead costs and profit. If the company is considering adding an item when it has no excess capacity, then the appropriate criterion is that the item should not be added unless it is possible to sell the item at a price that will cover both its direct costs and the overhead costs resulting from the added capacity. In any case, the rational entrepreneur should add items to the product line in descending order of perceived profitability.
Jointly-Produced Products
The specification of decision criteria for jointly-produced products poses another difficult problem. Jointly-produced products are those that result from a common production process. Classic examples are beef and hides, gasoline and fuel oil, mutton and wool. Even where the objective is to produce one primary product, e.g., metal stampings for auto body parts, there are likely to be marketable by-products such as the metal scrap. In any short-run situation, such joint products are produced in fixed proportions. The relevant questions are what quantity of the output mix is to be produced and at what prices are the individual items in the mix to be sold. In the long run, the management often can vary the output proportions, so that the relevant question for the long run is the profit-maximizing output combination.The short-run decision problem can be analyzed with a variant on the multimarket price discrimination model. In Figure 17-2, the marginal revenue curves for the jointly produced products are summed vertically (they were summed horizontally in the price discrimination model) to construct the joint marginal revenue curve, MRJ. We note that for all outputs larger than Q2, MR1 is negative so that the MRj curve is coincident with the path of MR2. The relevant short-run decision criterion is the comparison of marginal cost with joint marginal revenue. The manager should increase output as long as joint marginal revenue exceeds marginal cost, or decrease output if joint marginal revenue is less than marginal cost. In panel (a) of Figure 17-2, if marginal cost is given by MCA, the product 1 profit-maximizing price is P1 at which output Q1 of product 1 should be sold. Price P2 should be charged for product 2, and all units of both products should be sold.
Figure 17-2. Jointly-Produced Products Produced in Fixed Proportions.
If marginal cost should fall to MCB in panel (b) of Figure 17-2, it intersects the joint marginal revenue curve to the right of where MR1 has become negative. Since it would be irrational to sell so large a quantity of any product as to reduce total revenue (i.e, where MR is negative), output Q3 of both products is produced, but only Q2 of product 1 should be sold at price P4. The rest of product 1 (Q3-Q2) should be withheld from the market and possibly destroyed or "dumped" in another market (dumping is then a special case of price discrimination). All of product 2 produced, Q3, should be sold at price P3.
Plant managers typically have little discretion in varying the product mix in the short run. To alter the output mix usually requires a long-run adjustment to plant, equipment, and technology to be effected through capital investment. Without perfect prior knowledge of the costs and revenues of alternative product-mix combinations, the company's manager, acting in an entrepreneurial capacity, can only proceed iteratively to try an alternative combination when the next occasion for capital reinvestment arises. If the new product mix increases profitability (a successful entrepreneurial decision), the manager can assume that an adjustment in the proper direction has been made.
The long-run decision to vary the proportions in which joint products are produced can be illustrated with an isorevenue map superimposed over an isocost map, similar to the isoquant-isocost analysis of production elaborated in Appendix 9A. We choose not to elaborate the theoretical isocost-isorevenue model in the text of this chapter because the ability to estimate the equations of surfaces from which isocost curves can be extracted requires near-perfect prior knowledge of the company's multiple-product production possibilities. This is typically far more information than can be mustered in most real decision settings. Readers who wish to examine such a theoretical model are directed to Appendix 17B.
Increasing Size and Complexity
To this point we have assumed the convenient fiction that the management of the company consists of the single person, the "manager," who makes decisions in pursuit of the profit objective. The owner-entrepreneur of a small-scale single proprietorship fits this description nicely, and there are throughout the world tens of thousands of such one-person companies in existence, many of them well-managed, successful enterprises.But as other companies, organized as partnerships and corporations, have become much larger than could ever have been accommodated under the proprietorship form of organization, a wide variety of approaches have emerged for dealing with the resulting problems of coordination and control. As noted in Chapter 13, these problems usually show up as decreasing returns to scale in the production function, and as diseconomies of scale in the long-run cost function. Virtually all of the attempted remedies have been means of specializing and dividing the labor of decision making among a multiplicity of managers. They include:
(b) the functional specialization of line managers to ever narrower realms of discretion and responsibility;
(c) the establishment of multiple tiers of managerial responsibility organized along hierarchical lines of authority; and
(d) divisionalization of the company's operations.
We shall leave the further elaboration of the first three of these approaches to texts in organizational theory. The purpose of divisionalization is to create several smaller decision units to replace (or in lieu of) a single, large, unwieldy administrative unit. Divisionalization may be along horizontal or vertical lines. The horizontal divisionalization of the company may be organized along geographic or product lines. Each such horizontal division may be construed as a near-autonomous entity over which the appointed management staff is given the responsibility to be profitable (or to meet some other specified company goals), and the decision-making discretion and authority to pursue this end (hence they may be designated "profit centers"). The horizontal divisions may have been created by dividing a previously unified organization. More likely, a horizontal divisional structure is the outcome of one or more acquisitions or mergers where complete integration of the combined companies has not been achieved, and may not even by intended by the acquiring owners. In many cases, the fellow divisions are expected to compete with each other as well as with other companies. In any case, they must vie with each other for access to the parent company's financial resources.
Since there is often no particular economic reason for the horizontal divisions to be parts of the same company (unless the objective is merger to avoid competition), the justification for their common ownership lies in the "deeper financial pockets" of the larger company. We leave further examination of this angle to the auspices of corporate finance. In most cases of horizontal divisionalization, the models that we have already elaborated should be adequate to the analysis of both short- and long-run decision criteria.
Transfer Pricing
To this point we have assumed each company to be perfectly vertically integrated, i.e., to perform all operations in proper sequence to convert a batch of raw materials into a final product. This fiction (or reality in a few, rare cases) allowed us to discuss the construction of a single production function, implicitly encompassing all sequential operations without reference to any particular operations. It also permitted us the luxury of imagining the specification of a single cost function encompassing all of those separate operations. Without making it explicit, we have assumed that the intermediate product was simply "work in process" to be passed from one processing stage to the next without having to be "costed" or "priced." Any profit (normal or supernormal) that resulted would accrue to the company as a whole without any necessity of distributing or attributing it to the various productive operations.The alternative to vertical integration is vertical segmentation (or disintegration) where each identifiable productive operation is performed by a separate company. Each company in performing its operation adds value to the intermediate product. The partially-processed product is then sold to another company that adds more value by performing the next operation in sequence, and so on until the state of "final product" is attained. If a production process were perfectly vertically segmented, each of the companies in the vertical sequence would maximize profits by finding the price and quantity for which marginal revenue is equal to marginal cost. The price that each company would charge would be equal to its marginal revenue if market conditions were purely competitive, but price would exceed marginal revenue in imperfectly competitive markets. In a vertically-segmented production process, each company's price would become part of the next company's per-unit costs.
From a social perspective, the application of marginal decision criteria in a competitive market would lead to an efficient allocation of resources among the successive operations and profits among the separate companies. From the company perspective, efficiency (and hence, profitability) is served by applying the marginal decision criteria among its vertically related divisions. Virtually all manufacturing companies are to some extent vertically integrated in that they perform more than one identifiable operation in the sequence necessary for the production of the final product. No additional modeling or analysis is required if the vertically integrated company is organized as a single unit for which one production function and one cost function may be estimated.
However, the vertically integrated company may be organized into separate, semiautonomous divisions within which managers are given discretion for determining output and responsibility for controlling costs and earning profits. It then becomes necessary to determine the prices of the intermediate goods as they are transferred from each division to the division that will undertake the next stage of processing. Realistic transfer prices are as important to the allocation of resources between divisions within the vertically integrated company as realistic intermediate goods prices are to the allocation of resources between companies in a vertically segmented production process. A too-low transfer price will result in a sub-normal profitability of the division (profit center), and resources will tend to be underallocated to the division as division output is decreased. Since the too-low transfer price becomes a too-low per-unit cost to the next division, profits there will be supernormal, and resources will tend to be over-allocated to that division.
Transfer pricing among divisions is an especially critical matter if executive or employee compensation across the divisions is based upon the profitability of the divisions. Profitability differentials among the divisions that are due to errors or deliberate distortions in transfer pricing will inevitably lead to a deterioration of executive or employee morale.
Parent companies with subsidiaries in other countries may devise a transfer pricing strategy to shift cash from one country to another. For example, if the parent company sets prices well above costs on inventory shipped to a foreign subsidiary, cash is shifted to the parent company. Vice-versa, if inventory shipped from the subsidiary to the parent is overpriced relative to costs, cash is shifted from the parent to the subsidiary.
The matter of realistic transfer pricing is even more critical if the division manager is also allowed the discretion to sell some of the output to buyers outside of the company as an alternative to transferring all of the intermediate good to the next processing division within the company. If the in-house transfer price is set too low, the company may find it more profitable to sell to outsiders at market prices than to transfer intermediate product to the next in-house division, in which case vertical disintegration will occur as the company becomes less vertically integrated. The company may instruct one division to price-discriminate in favor of a fellow division and against an outside buyer, but this may lead to interdivisional differentials of profitability, and it is likely to attract the attention of the antitrust authorities. For example, consider the implications if the Saginaw Division of General Motors were to sell power steering units to the Buick Motor Division of General Motors at a more favorable price than to Chrysler for installation in Jeep vehicles.
Suppose that a division manager is given the authority to source intermediate goods requirements from outside the company even though a fellow division produces the intermediate good. A too-high transfer price for the intermediate good will lead to vertical disintegration as the division manager shifts to the externally-sourced supply of the intermediate good at lower market prices.
Figure 17-3 can be used to illustrate the determination of the transfer price at any stage of production when the manager of the division is given no discretion to source the intermediate product from the market or sell product to the market after the division's processing of it. The product demand and marginal revenue curves are represented as D and MR. The product is assumed to go through j stages of processing where each stage is accomplished in a semi-autonomous division of the company. The marginal cost curve after the final, or jth, stage of processing is MCj. The company will maximize profits at output level Q1, the output level at which MR is equal to MCj.
Figure 17-3. Transfer Pricing with no External Market for the Output.
As processing ensues through the stages of production from the first to the jth, the marginal cost curves (as well as the average variable and average total cost curves) for the respective stages can be imagined to step upward, approaching MCj as the limiting and final-product position. The rationale for the upward stepping of the MC curves is that the transfer price set in any stage becomes the per-unit cost of the intermediate product at the next stage, to which the marginal costs at the next stage are added to find the next transfer price. Thus the transfer price at each stage is higher than the transfer price at the previous stage of processing. On analogy, if the unit prices of the materials inputs in any production process were to increase, the whole set of per unit cost curves (average variable, average total, and marginal cost) would shift upward. In the divisionalized, vertically integrated company, the price of the intermediate product rises as more value is added to it at each stage of processing.
Given that the executive decision has been made to produce Q1 units of output to be sold at the P1 price, and assuming that the required cost functions can be specified and statistically estimated at each stage of production (i.e., by each division), the transfer price for the ith division can be found at the intersection of the vertical from Q1 with the division's marginal cost curve, MCi. In a competitive industry, this marginal cost curve above its AVC minimum would constitute the ith division's intermediate product supply curve.
The demand by division i+1 for the output of division i is in effect perfectly elastic at the marginal cost of producing the value added by processing at the ith stage of production, but only up to output level Q1. Beyond Q1, division i+1 has no demand at all (nor does anyone else) for the output of the ith division. Hence, since MRi = Di when demand is perfectly elastic, MRi is equal to MCi at output Q1, and the appropriate transfer price for the ith division is Pi, which is just equal to the marginal cost of the value added to the intermediate product by processing it in the ith division. Whether division i is functioning profitably at transfer price Pi then depends on the level of its average variable costs, the magnitude of the overhead costs, and how the overhead costs are allocated to the various divisions.
Suppose that division i+1 can purchase an equivalent intermediate product from a competitive external market at a market price below Pi. In this case, disintegration is likely to ensue since none of the output of the intermediate product should be purchased by division i+1 from division i. All of the required intermediate product should be purchased from the external market, and the company should dispose of division i. We can imagine that the intermediate product after processing by division i-1 might be sold to another company to perform the ith stage of value-added processing, then be purchased by division i+1 for further processing, thereby completely skipping the ith stage of processing within in company. This phenomenon occurs in effect when a company contracts with another company to perform a certain stage of processing, then proceeds with further processing in-house. An executive decision might be made to mandate the purchase of the intermediate product by division i+1 from division i even at a transfer cost above the external market price. In this case, other divisions of the company subsidize the higher-cost division. The likely consequence is distortion of both the allocation of resources within the company and the attribution of returns among the divisions.
Suppose that division i finds that it can sell the intermediate product after its processing on a competitive external market at a price above Pi, say Pt in Figure 17-4. The manager of division i should take the demand and marginal revenue curves to be Dt and MRt, respectively, and will find incentive to push his division's output to Q2. With this larger output being produced, Q1 will be transferred to division i+1, while quantity (Q2- Q1) can be sold on the external market. However, since the marginal cost of producing the larger quantity is higher, the transfer price to division i+1 will be the higher price Pt rather than Pi. This will have the effect of shifting upward all of the marginal cost curves of the subsequent processing divisions, including that of the final product, MCj. This will likely reduce the maximum profit output for the firm below Q1. This can be imagined to set in motion a series of iterative readjustments by processing divisions all along the vertical sequence until a new equilibrium solution is found.
Figure 17-4. Transfer Pricing with an External Market for the Output.
What's Ahead
This chapter has explored a number of possibilities for adding realism to the simple models elaborated in Chapters 13 through 16. These possibilities are not intended to be exhaustive, but only suggestive of the directions in which model elaboration might be taken. In Chapter 18 we examine a number of challenges to the theory of the firm that is based on the assumption of single-minded orientation of the management toward profit maximization.BACK TO CONTENTS
APPENDIX 17A. A MATHEMATICAL MODEL OF PRICE DISCRIMINATION
In this appendix we show the mathematical steps necessary to compute the profit-maximizing prices and quantities for a company considering price discrimination in the sale of one item in two separable markets. Suppose that the company has, via regression analysis, estimated its demand functions for markets 1 and 2 as
= 20 - 4 Q1 - 4 Q2 + .5 Q12 + Q1Q2 + .5 Q22.
9 - Q1 - 5/3 Q2 = 0
Q1 = 3 and 2/7 or 3.28571 units of 1 million
Q2 = 3 and 3/7 or 3.42857 units of 1 million.
The prices to be charged in each market can be computed by inserting the solved values for Q1 and Q2 into the respective demand curve equations and solving for P1 and P2.
P2 = 5 - .3333 Q2 = $3.86.
The total revenue, total cost, and total profit may be computed from their respective functions:
TC = 20 - 4 Q + .5 Q2 = 20 - 26.857 + 22.541 = $15.684
TN = 10 Q1 + 9 Q2 - Q12 - 5/6 Q2 - Q1Q2 - 20 = $11.857
The elasticities may be computed for each price-quantity combination:
Without price discrimination, the total demand across the two markets can be computed as
= 47/5 Q - 7/10 Q2 - 20,
7 Q = 47
Q = 6 5/7 units of 100,000 each.
= 142/35
= $4.057.
= $11.557 million (without price discrimination).
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APPENDIX 17B. JOINT PRODUCTS PRODUCED IN VARIABLE PROPORTIONS
The problem of joint products produced in varying proportions can be illustrated with a graphic model. Assuming a three-dimensional cost function where the dependent variable, TC, is a function of two outputs, Qa and Qb, for products A and B, the cost surface has the appearance of that in Figure 17B-1. The equation for such a cost function might take the following form that is cubic in both independent variables:
Other equation forms are possible. A joint-products cost equation could be of different orders in the included variables, and there may be more than two jointly-produced products to be encompassed in the cost function equation. The analyst, in attempting to estimate such a function might try including higher-ordered terms than may be relevant, then inspecting the inference statistics for the statistical significance of the terms.
Figure 17B-1. A Total Cost Surface for Two Products.
The TC surface could be sliced vertically, parallel to either floor axis for particular quantities of the item represented on the other floor axis, thereby generating the conventional two-dimensional TC curves that we have analyzed in Chapter 8. However, Figure 17B-1 illustrates horizontal slices taken at successively higher altitudes (i.e., cost levels or amounts budgeted for expenditure on production of the two items). The projections of the slices through the cost surface into the floor generate a set of concentric isocost curves, which, when looked at from above, have the appearance of the isocost map llustrated in Figure 17B-2. Along any single isocost, e.g., TC3, are points the coordinates of which represent the combinations of quantities of A and B that can be produced at the same level of expenditure on production, TC3. The isocost curves in Figure 17B-2 appear to get closer together to the northeast because the surface rises more steeply in this range.
Figure 17B-2. An Isocost Map Derived from the Total Cost Surface.
A three-dimensional total revenue function where TR depends on the prices of A and B and the quantities of each sold,
or
can be represented as in Figure 17B-3, assuming pure competition in both product markets (the reader might speculate on how the shape of the surface would be changed in any form of imperfect competition). When this TR surface is sliced at different altitudes (i.e., levels of revenue), and the slices are projected down into the floor, this gives the appearance when viewed from above of the isorevenue map illustrated in Figure 17B-4.
Figure 17B-3. A Total Revenue Surface for Two Products.
Figure 17B-4. An Isorevenue Map Derived from the Total Revenue Surface.
Given the equation of the total revenue function,
it may be solved for Qa,
which is in the slope-intercept form of a straight line with slope, -Pb/Pa. All of the isorevenue curves have the same slopes, determined by the prices of items A and B. The isorevenue map may be superimposed over the isocost map as depicted in Figure 17B-5 (or in three-dimensions the revenue surface may be shown cutting the cost surface). Because the isorevenue map is dense (i.e., the revenue surface can be sliced at any and all altitudes), isorevenue curves of the same slope re drawn where needed tangent to the isocost curves. The profit can be computed at the tangency of each isocost curve with an isorevenue curve by subtracting the total cost from he total revenue. The largest profit, in this case profit = 100, occurs at the tangency of TC200 with TR300, and the coordinates of the point of tangency represent the quantities of A and B that will maximize the profits from the jointly-produced products. No point along an isocost that is not at a tangency with an isorevenue curve can yield as much profit as that realized at a tangency point.
Figure 17B-5. Superimposed Isocost and Isorevenue Maps.
What decision criteria can be extracted from the isorevenue-isocost analysis of jointly-produced goods? Suppose that the company is currently producing at point R, the coordinates of which represent the quantities of items A and B being produced. Although the company can reallocate its production in any direction from point R, let us suppose that it limits its changes to moving along either an isorevenue curve or an isocost curve. If the company moves downward along the isorevenue curve toward point T, its revenues will remain the same as it produces more of item A and less of item B, but its costs will fall (it reaches ever-lower isocost curves). If the company moves downward along the isocost curve, its costs will remain the same while again it produces more of item A and less of item B, but its revenues will increase (it reaches higher isorevenue curves). In either case, profits will increase. We leave it to the reader to deduce what would happen to profits if the company should move upward along either the isocost or the isorevenue curve from point R.
The slope of the isorevenue curve, Pb/Pa, measures the rate at which item A can be substituted for item B within the company's product mix while remaining at the same level of revenue. This rate will be referred to as the marginal rate of revenue substitution (MRRS) of A for B.
The slope of the isocost curve, DQb/DQa, measures the rate at which item A can be substituted for item B within the company's product mix while remaining at the same level of cost. This rate will be referred to as the marginal rate of cost substitution (MRCS) of A for B. The MRCS can further be understood by breaking the movement from R to S down into two component parts, the movement from R to U, and the movement from U to S. The movement from R to U results in a decrease of production cost, -DTCb, consequent upon a decreased output of B, -DQb the ratio of which measure the marginal cost of item B (assuming a smallest-possible DQb):
Likewise, the movement from U to S results in an increase in production costs, D TCa, as the production of item A is increased. And the ratio of the two measures the marginal cost of item A:
which we have already identified as the slope of the isocost, MRCS. To reiterate the significant point, the ratio of the marginal costs (MCa/MCb) measures the marginal rate of cost substitution.
Now a decision criterion can be specified. If the MRRS is greater than the MRCS, i.e.,
the company can increase its profits by producing more of item A and less of item B. Graphically, if the slope of the isorevenue curve (the MRRS) is steeper than the slope of the isocost curve (the MRCS), the company should produce more A and less B to increase profits (both the isocost and isorevenue curves have negative signs). The sense of this is that if the rate at which costs can be reduced while revenue remains constant (i.e., by moving along the isorevenue curve) is greater than the rate at which revenue can be increased while costs remain constant (i.e., by moving along the isocost curve), profits can be increased by producing more of item A and less of item B. The reader is encouraged to reread this paragraph, making appropriate alterations on the assumption of a reversal in the direction of the inequality, and starting from some point such as V in Figure 17B-5. These rates are not directly observable. But, with sufficient knowledge of the markets for items A and B (i.e., the prices at which they can be sold) and the joint-production total cost function, all of the ingredients are available or can be computed to establish practically useable decision criteria. The marginal costs of items A and B can be found by computing the partial derivatives of the TC function, i.e.,
a maximum-profit combination has been found, but it may be at any point along the expansion path CDEFG in Figure 17B-5. The manager of the company may still have to experiment with scales of operations to find the absolute maximum profit that can be realized.
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CHAPTER 18. CHALLENGES TO THE THEORY OF THE FIRM
All of the models surveyed and elaborated in previous chapters have been based upon the premise that the manager of the company will apply marginal decision criteria in the single-minded effort to maximize the company's profits. But personal experience, casual observation, and a mounting volume of empirical evidence suggests that real-world business managers often do not use marginal decision criteria. In response to survey questionnaires they typically indicate that profit is only one among several goals that command their attention. And even when profit is the dominant goal, they usually specify their objective as seeking a satisfactory return on invested capital rather than the maximum sum that it is possible to achieve. These considerations have led in some cases to doubt and skepticism about the conventional models, and in other cases to alternative approaches.
Multiple Goals
As we noted in Chapter 2, the multiple goals pursued by the managers of companies may include, in addition to profit, personal compensation, the enjoyment of perquisites ("perks"), professional and social recognition, the exertion of authority and control over human and physical resources, and the pursuit of commercial growth. The latter may be indicated by any of a wide range of quantities, including numbers of employees, invested capital, sales volume, and share of the market. A rational way to deal with multiple goals is to select one for primary pursuit, so that others can be regarded as subordinate goals. Kenneth Boulding has written about the extreme difficulty of the subordination of subordinate goals (Management Science, Volume 12, Number 6, February, 1966, pp. B-161 - B-169). The subordinate goals can be construed as constraints upon the pursuit of the primary goal. This is the process of optimization, or constrained maximization, to which the calculus and the Lagrange multiplier may be applied (as described in Chapter 5).William Baumol has developed a constrained sales maximization model that may be illustrated by the diagrams in Figure 18-1. The total profit function, TN, can be derived as the vertical difference between the total revenue, TR, and the total cost, TC, curves. Suppose that the manager treats profit as subordinate to the primary objective of maximizing sales volume. Here, a minimum satisfactory amount of profit specified by the manager can be represented by the altitude of the horizontal dashed line drawn across the total profit function. It is now possible to identify several pertinent output levels. Outputs Q1 and Q2 are the break-even levels; outputs below Q1 and above Q2 will incur losses, while any output level between these extremes will yield a positive profit. Output Q3 is the profit-maximizing output level where the slope of the TC curve is just equal to the slope of the TR curve (i.e., marginal cost is equal to marginal revenue), and the slope of the TN curve is zero. The intersection of the horizontal dashed line with the TN curve finds the output level, Q4, which is the maximum output that can be produced and sold before profit falls below the minimum acceptable level. Using this criterion, the company can maximize sales volume subject to a minimum-profit constraint. But, suppose that the company is under the scrutiny of antitrust authority and needs to maintain a low profile. Output Q5 is the lowest output level that is consistent with the minimum profit requirement.
Figure 18-1. Baumol's Constrained Sales Maximization Model.
Suppose that the manager is so obsessed with increasing sales volume that a loss may be tolerated, but that the maximum loss that is acceptable is represented by the depth of the dot-and-dashed horizontal line drawn below the horizontal axis. Now it is possible to recognize Q6 as the maximum output that can be produced and sold before the incurred loss exceeds the maximum acceptable loss. And in case the low profile strategy is in effect, Q7 is the least output that can be produced before the loss becomes unacceptably large.
The Baumol model can also be handled algebraically if the equation of the profit function is known or can be derived from known revenue and cost functions. In order to find Q4 and Q5 in Figure 18-1, the profit function is solved simultaneously with the minimum profit constraint expressed as an equation (alternatively, the minimum profit constraint can be substituted into the profit function to allow solving for Q). But while "the answers" can be found using either a graphic or an algebraic approach, neither yields decision criteria that can be used to decide whether to increase or decrease output and raise or lower price (remember, if profit maximization is the objective, such a decision can be based on a comparison of marginal revenue and marginal cost). All that the manager can do is to proceed iteratively, i.e., to try one output-price combination, then another, in search of the acceptable profit or loss level.
Non-Marginal Decision Criteria
Real-world business managers rarely use the economist's ideal decision criteria, marginal revenue and marginal cost. Aside from the possibility that they may not be acquainted with the correct decision criteria, such criteria employ information that is not directly observable. Although marginal revenue and marginal cost may be inferred, estimated, or computed from observable information, the process of capturing an adequate amount of such information and generating the required decision criteria becomes progressively more difficult the more complex is the decision setting. For example, a wholesale distributor of hardware (tools, nails, screws, pipe fittings, hinges, locks, etc.) may carry 20,000 or more different items in the warehouse. It would be an heroic task to gather the required data for estimation of demand and cost functions for each and every one of the warehoused items so that marginal revenues and marginal costs could be computed.Business managers usually respond in questionnaires that they employ an alternative pricing procedure to determine price, then sell as much of each item as they can at the set price. The alternative procedure is a rule-of-thumb approach variously known as cost-plus (variable cost plus an overhead cost/profit contribution), mark-up (from manufacturer's price), mark-down (from a "suggested retail" price), add-on, or full-cost pricing. The usual procedure is to
(b) estimate the per-unit direct (or variable) cost of producing the item at that production rate (for a distributor, it is the price from the manufacturer plus shipping expense); and
(c) add a standard markup-up as a "profit contribution" that will cover overhead expense and allow for a net return.
A variant of this approach that is more appropriate to manufacturing than to wholesale or retail distribution is "full-cost" pricing. The objective here is to fully allocate all overhead costs to the various items in production. This is no problem in the single-product firm: all overhead (i.e., fixed) costs go to the single product, and are then "spread" across all of the units produced. However, in a multiproduct company, since there is no objective way to allocate overhead expenses among the company's product lines, the allocation process becomes highly arbitrary. A typical approach is to use as allocation shares the percentage of the company's gross revenues accounted for by each item.
To illustrate how full-cost pricing is accomplished, suppose that the direct production cost for a particular item is $4.17 per unit, and that the item's share of overhead expense (however arbitrarily allocated) divided by the number of units of the item produced (the method of "spreading the overhead") is $6.37. The sum of the per-unit direct and overhead expenses is thus $10.54. Then, an additional mark-up to allow for profit, say 25 percent or $2.63, is added to establish the final price of $13.17. The manager then may "psychologically price" the item at $12.99 or $13.49.
An extension of this mark-up pricing approach may illustrate the satisficing hypothesis advanced by Herbert Simon ("Theories of Decision Making in Economics and Behavioral Science," American Economic Review, volume 49, number 3, June 1959, pp. 253-80). According to Simon, many business managers don't attempt to maximize profit in any absolute sense. Rather, they try only to realize a satisfactory level of profit, usually expressed as a target rate of return (TROR) on invested capital. In the previous example, the 25 percent mark-up to allow for profit was stipulated only arbitrarily. Suppose that the company has $1 million dollars invested in its plant and equipment for producing the item, and expects to produce 50,000 units of the item per year at 75 percent of capacity. If the company targets a 10 percent return on investment, then it must realize a profit of $100,000 per annum, which when divided by the 50,000 units means that the mark-up allowance for profit should be $2 per unit. The price that will satisfice with respect to the TROR requirement is $12.54.
An Assessment of Non-Marginal Pricing Practices
From the perspective of the economist, any sort of mark-up or full-cost pricing technique is inappropriate to the goal of profit maximization. The reason is that it is based exclusively upon costs. The demand side of the relationship is completely ignored. No elasticity conditions or competitive pressures are recognized by such procedures. The danger in employing such one-sided pricing techniques can be illustrated in Figure 18-2. Here the manager first selects a normal output, say Q1, as the 75 percent of plant capacity, then sums the per-unit direct and overhead costs, and finally adds a profit-contribution mark-up to arrive at a target price. Suppose that the full-cost price is P1, such that the coordinates (Q1, P1) find point A. Since no consideration has been given to demand conditions, represented by the demand curve D, it would be purely coincidental for point A to lie on the demand curve.
Figure 18-2. Pricing without Regard to Demand Conditions.
As illustrated in Figure 18-2, point A lies above the demand curve. If the company insists on trying to sell the Q1 output at full-cost price P1, it will suffer an inventory accumulation of Q1- Q2. Alternately, if the full-cost price happens to be P2, the coordinates (Q1, P2) find point E which lies below the demand curve. If the company insists on trying to sell output Q1 at price P2, an inventory depletion of Q3- Q1 will result if indeed the company has that much of the item in inventory. If not, then an opportunity-loss occurs due to the lost sales. In either case, the manager will have to abandon the full-cost price in order to relieve the ensuing inventory problem. Or, if the company is competing in an industry characterized by price followership, it may have to abandon the full-cost price if another company prefers a lower price.
Mark-up competition often emerges as the primary vehicle for recognizing competitive pressures. Sale prices and discounts become the means for recognizing price elasticity differentials among products or between geographic markets. Phenomena such as these lead many economists to conclude that non-marginal pricing techniques eventually result in the same (or nearly the same) prices that would have been established had the marginal pricing criteria been employed. This conclusion is most pertinent to successful companies, i.e., those that have survived over the "long-haul." The rule-of-thumb approaches, though clearly suboptimal in a theoretical sense, are lower-cost means of getting to the same conclusion that could have been reached only at the greater expense of modeling and statistical estimation.
Should we throw out the theoretical models based on marginal decision criteria in pursuit of profit maximization? Not if Professor Friedman is correct: what matters is that managers behave as if they utilize the marginal decision criteria.
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PART E. THE MACROECONOMIC SETTING
CHAPTER 19. THE FIRM IN SOCIETY
As noted in Chapter 9, the central function of the business enterprise, or "firm" as we have called it, is production. We construe the term "production" broadly to include all of the functions associated with extraction, processing, assembly, packaging, and distribution; it also encompasses the provision of services. The business firm is a creation of members of society to improve the efficiency of production by enabling specialization and division of labor and management. This statement presupposes that society has organized its economic arrangements as market capitalism and that the extant government at very minimum tolerates the existence and activities of such business firms.
However, even if the society in question has adopted some authoritarian form of economic organization (e.g., fascism or socialism) rather than capitalism, efficiency in its productive relationships is still be served by organizing production in units that enable specialization and division of labor and management. For example, in a Soviet-style planned economy, such production units exist and often are referred to as "enterprises." They are distinguished from firms in capitalism in that they are owned by the state while the latter are privately owned by members of the society. Another distinction is that their managements are required to respond to dictates of the planning authority, whereas managements of firms in market capitalism are free to respond to market incentives.
Our further examination of the firm's situation in its societal relationships presupposes a setting of market capitalism, but the tone suggested in the first two paragraphs of this chapter belie alternatives that managers should keep in mind: the society, or its government, may cease to be so tolerant of the existence or activities of privately owned and managed business firms. Alternatives include governmental efforts to modify or constrain the management and operations of the privately owned enterprise, or to take over the enterprise and run it as an organ of the state.
The Firm's Roles in Society
Business firms in market capitalism make a great many contributions to the societies that host them. First and foremost is the provision of the goods and services demanded by the society. It is indeed a high and noble activity to perceive human needs and function successfully to fulfill them. The private enterprises of Western market economies have demonstrated to the world their great capacities both to provide a flood of high quality goods and services, and to generate tremendous wealth in the process.Second, in a social context where the principle avenue to consumption is by productive employment to earn spendable income, business firms are the chief providers of jobs. Western market economies have demonstrated abilities to provide productive employments to well over ninety percent of their growing labor forces. The production of goods and services thereby serves to generate incomes that are distributed to both the owners and the employees of the firms. During the twentieth century in western market economies, the proportion of the generated income that has been distributed as wages and salaries has gradually risen from around two-thirds towards four-fifths.
Third, business firms are tax payers, and thereby constitute important sources of revenue to governments at all levels. Business-related revenue sources have included property taxes on the firms' assets, floor taxes on their inventories, value-added taxes, sales and excise taxes, import tariffs, export licenses, payroll taxes, business licenses and associated fees, and corporate income taxes. It is not unusual for business-related taxes to account for forty percent or more of governments' revenues in western market economies.
Finally, business firms themselves are citizens of their societies. Firms organized as corporations are also legal persons. Whether corporate persons or not, citizen firms have presences in their communities. Their offices, plants, and warehouses have significant impacts upon the appearances of the communities within which they are situated. Their employees are active in the schools and churches of their communities. Many firms make valuable monetary and in-kind contributions to their communities.
This brief discussion has not exhausted the many contributions made by business firms to their communities. As firms contribute to their communities, they also incur responsibilities in their communities. While the roles mentioned above reveal the significance of business firms to society, each is also fraught with the potential for misbehavior by firms. It is such misbehavior that may lead the society to become less tolerant of the continued unfettered operation of firms in the private sector.
The Firm's Societal Contacts
Business firms in market economies come into contact with a great many different types of people as they conduct their productive activities. Their raison d'etre is to serve their customers by providing the goods and services demanded by them. Many business firms take only a passive role in attempting to discover demands that they may undertake to fill, but some firms aggressively attempt to create or manipulate such demands. The term consumer sovereignty describes the former case, whereas a firm that succeeds in first determining what it will produce and then creating a demand for it has exercised producer sovereignty. The host society may tolerate a significant amount of such producer sovereignty, but if it is perceived to become troublesome the government of the society may exercise state sovereignty to nationalize the firm and operate it as a state enterprise. The managerial implications of this prospect should be clear although it is much less likely to occur in the democracies of North America and Europe than in some countries of Africa, Latin America, and Asia.As we noted in Chapter 2, managers of private sector business firms often feel that they must answer to a number of constituencies in addition to their customers. With the process of separation of ownership and management during the nineteenth and twentieth centuries, the owners became another significant constituency of the firms being managed. As long as the owners maintain effective control of their firms, the managers must meet the owners' expectations of returns or other goals, and this may be a matter of satisficing rather than maximizing. But as we also noted in Chapter 2, the widespread dispersion of the ownership of corporate stock may enable the management of a corporation to so gain control over its own destiny that it can pursue its own private goals without fear of owner interference. The account of the take-over of RJR-Nabisco in the book Barbarians at the Gate by Bryan Burrough and John Helyar (Harper Collins Publishers, 1990) is illustrative of this point.
The firm's employees are another constituency that may constantly tug at the managers of the modern business firm. The principal employee concerns are wages, working conditions, amenities, and such benefits as health insurance and pension fund contributions. In a growing economy that experiences inflation, the interest of employees is in advancing wages at a rate fast enough to offset the effect of inflation that would decrease the purchasing power of their incomes, and to further capture as large a share of the fruits of growth as possible. The resulting tug-of-war is about the division of the growing "income pie" between the interests of labor and capital.
In theoretical terms, each productive resource employed by the firm seeks to receive an income that is at least as large as its marginal revenue product; if it fails to do so, it becomes the subject of exploitation. A potential problem for management is that labor often can muster significant political influence over elected or appointed government officials to make them believe that labor is being exploited (whether it truly is or not), and that government should use its state sovereignty to curb the power of capital or redistribute income in the interest of labor. It is significant that in most Western democracies during the twentieth century, the pro-portion of national income going to wages and salaries has trended upward from sixty toward eighty percent.
The firm's suppliers may sometimes become a vocal constituency whose voices must be heard by the managers of the firm. In competitive resource markets, suppliers are always seeking to gain the attention of the firm's purchasing agents, and thereby to gain supply contracts at the expense of competitor suppliers. If suppliers gain monopolistic advantage in the control of unique resources, they may be able to exercise their monopoly powers to raise resource prices above competitive levels, and thereby capture a larger share of the "income pie" at the expense of the firm. Such circumstances often encourage firms to extend their degrees of vertical integration by attempting to acquire their suppliers and thereby gain monopolistic position in regard to unique resources. If a firm can gain a monopsony position (monopoly as a buyer) in a resource market, it may be able to dictate price and delivery schedule conditions to its suppliers. But the attainment of monopoly or monopsony position may attract the attention of governmental authorities and invite unwanted responses.
As we have noted in Chapter 16, in oligopolistic markets (which may in fact encompass most real-world commercial and industrial activity) the firm's competitors certainly constitute one of its most important constituencies. Because of the relatively small number of firms in each geographic and product market, each firm must be concerned not only with what each of its competitors may do, but also with how competitors may respond to any action taken by the firm. The potential for inducing undesirable competitive response may be so great that the firm's management finds itself in a mould of decision rigidity. But even if this extreme condition does not result, the firm's managers must assess the competitive response risks attendant upon any strategy that they are contemplating.
The process of dispersion of stock ownership also opens the door to responsiveness to yet other constituencies as managers begin to feel some sense of social responsibility to "third parties," i.e., innocent bystanders to the actions and activities of the firm. Sometimes the externalities or so-called "spillover effects" are benefits that are conferred upon neighbors due to simple proximity to the business firm. Examples include better roads and street lighting. But there are also possibilities of negative externalities such as the various forms of environmental pollution and congestion associated with the firm's activities. Positive spillovers may be rewarded with plaques given at meetings of civic organizations, but complaints about negative spillovers often attract the attention of society at large and its elected or appointed government officials who tend to become ever less tolerant of the unconstrained operations of the firm.
These and other constituencies continually pull at the managements of modern business firms. As we suggested in Chapter 2, it is unrealistic for the managers to try pursue multiple goals simultaneously. Practically speaking, what usually happens is that the "squeaky wheel gets the grease," i.e., the most vocal constituency at the moment captures the attention of the firm's management. That constituency's interest becomes the goal selected for primary pursuit, and all other constituencies' interests function as constraints upon the pursuit of the primary goal. Once the constituency's concerns have been adequately addressed, some other constituency's complaint will rise to the surface to dominate the attention of the firm's management. But if the management cannot or will not satisfactorily address the voiced concerns of its constituencies, it can expect intervention by some governmental authority.
The Workings of Economic Mechanisms
The economics of public choice is the study of how societies decide whether economic decisions are to be made in the private or the public sectors. A brief examination of the workings of the market economy will bring us to a fundamental principle of public choice decision making. In the market economy organized as pure capitalism (a hypothetical situation with no real-world examples), all productive assets are privately owned and all decisions concerning their use are made by their private owners. Resource owners are presumed to be motivated by prospects of personal gain or profit. Information about changing economic conditions is disseminated throughout the market economy by prices that change in response to shifts of market demands and supplies. Competition among participants in the market economy serves to enforce compliance with the dictates of the market changes, i.e., the prospect of profit or loss invites appropriate adjustment, but competition insures that appropriate adjustment ensues. Those who perceive the emerging opportunities and act upon their perceptions are rewarded with profits and survival; those who either do not perceive the opportunities or simply ignore them are penalized with losses and failure. The perceptive, responsive, and efficient survive and prosper. The imperceptive, unresponsive, and inefficient suffer losses and fail.Societies that favor dispersed and participatory modes of social determination are generally pleased to leave economic decision making to the members of society unless there emerges widespread belief that private decision making yields results that are detrimental to the general welfare of the society. When such perception emerges, the government of the society has two fundamental alternatives: to try to make the private decision mechanism work to the satisfaction of society, or to substitute public decision making in place of the private discretion. This is the fundamental issue of public choice. And it was consequent upon the emergence of this issue that the distinction between the private sector and the public sector was born.
The principal means for improving the functioning of private sector decision mechanisms are to reduce or eliminate market imperfections, and to curb the unbridled desires of decision makers to accumulate wealth or to gain exclusive control over their situations. These motives may lead private sector decision makers to indulge in unethical or even criminal behaviors. Market imperfections include restrictions upon the availability of information and the ability of market participants to adjust. They also encompass the achievement of monopolistic position in a product or geographic market. The relief of market imperfections may come via technological advances that improve information flows or reduce the costs and time requirements of resource mobility. But these same technological advances may also serve as bases for the achievement of monopoly position.
In Western democratic societies it often seems easier to replace the errant market mechanism with an authoritarian decision making structure than to devise means of making the market mechanism function more satisfactorily. More often than not, when a private sector decision mechanism is perceived to work unsatisfactorily, some substitute for private decision making is sought. The obvious substitute for private decision making is public or authoritarian decision making, perhaps in the form of a regulatory commission to determine such things as prices or distribution and quality of services.
An irony of this issue may be seen in societies that historically have opted for authoritarian decision mechanisms. For example, from 1818 forward in the Soviet Union, socialism became the predominant form of economic organization. In the purest form of socialism (of which there are also no real-world examples), all of the society's productive assets are owned by the state, and all decisions in regard to their use are made by administrative fiat. When shortcomings are perceived in regard to the exercise of such governmental authority, some substitute for the authoritarian mechanism is sought. The obvious substitute for authoritarian decision making is individual discretion exercised by private decision makers in market mechanisms. The Soviets upon numerous occasions found themselves falling back upon market mechanisms when authoritarian decision making resulted in shortages or other problems.
There are no real-world examples of either pure capitalism or pure socialism. All economies are "mixed" in the sense that they incorporate varying degrees of private discretion and authoritarian decision making. The U.S. economy is appropriately described as mixed capitalism to indicate that market mechanisms are the primary economic decision making vehicles, but that there is also a significant role for government to play in the economy. Before its demise, the Soviet Union could be described as mixed socialism in which authoritarian decision making in the form of central planning and direction was the primary decision vehicle. Economies of other nations may be described as varying mixtures of private and authoritarian decision making.
Opportunities and Threats to the Firm
The discussion to this point is intended to support the central thesis of this chapter, i.e., that the firm's situation within its host society provides innumerable opportunities that it may exploit, but also poses a variety of threats to the manager's decision making discretion, and possibly to the very existence of the firm as an organization independent of the society's governing authority.
Societies through their governments may intervene in their economies in a variety of ways including:
b. providing a stable money supply that can grow along with the economy;
c. providing for law and order, i.e., an environment conducive to enterprise;
d. establishing the security of private property, the conditions under which title to it may be transferred, and the means to arbitrate disputes over the ownership of it; e. maintaining competitive conditions;
f. stabilizing the macroeconomy;
g. redistributing income and wealth; and
h. reallocating resources.
The opportunities and threats to private business firms lie in how extensively the government intervenes in the economy and how effectively it succeeds in achieving the goals of its interventions. For example, if the values of weights and measures are not certain, or if the purchasing power of the unit of money is volatile, there will be mostly threats to the success and survival of private-sector firms. If the private ownership of property is not adequately secured, firms will be threatened by declining investment in their assets. A redistribution of income will provide opportunities for firms servicing customers who receive additional income, but pose threats to firms whose clients suffer income losses. The enactment of antitrust legislation and its vigorous enforcement will constitute threats to firms bent upon achieving monopoly positions, but will enable opportunities for firms that are attempting to achieve entry into profitable markets. As noted in Chapter 18, governmental efforts to stabilize the macroeconomy are also a mixed bag of opportunities and threats to private-sector firms, especially since it is not at all clear that deliberate efforts at stabilization accomplish their ends without further destabilizing the macroeconomy.
The private sector of any economy will yield a certain allocation of resources that can be construed as efficient if there are few externalities and little exercise of monopoly power. It is efficient in the sense that under competitive conditions, output of each good will be adjusted until its marginal cost (society's valuation of the resources used to produce the good instead of some other goods) is just equal to its marginal revenue (or price, society's valuation of having one more unit of the good rather than some other goods).
But even if the allocation of resources is efficient, it still may not be satisfactory to the society, primarily because of two reasons: public goods are not produced in response to market incentives, and markets tend to over- or underproduce social goods, i.e., those resulting in externalities. It may then be said that in regard to society's preferences that resources are misallocated, and that there is a justification for government to act to reallocate resources. Chapter 21 is devoted to the issue of governmental reallocation of resources.
Ethics and the Business Community
It is sometimes suggested that people in the business community are more likely to behave in illegal or unethical manners than are people in other occupations. There is no evidence that people who become managers of business enterprises are by race, ethnicity, religion, education, training, cultural conditioning, or heredity significantly different from people who enter other walks of life. Unethical people may become teachers, ministers, plumbers, doctors, politicians, or managers of business enterprises; by the same token, ethical people may likewise enter any of these occupations.People "in business" have the same responsibilities of citizenship as do people in other fields. It may be true that business men and women, because they are trustees of corporate assets and exercise decision-making authority over other people, are subjected to temptations to engage in questionable behavior that are commensurate with their positions of authority. Does this mean that they should be held to higher standards of honesty and integrity than people in other occupations? These are certainly foundation blocks for a workable market economy. Market capitalism would cease to function efficiently, and might cease to function at all, in the absence of honor and trust in business dealings.
All people, irrespective of their occupations or positions, should be expected to behave according to the same high moral and ethical standards. To this point we have described the roles that business decision makers play in their societies, and implicitly the responsibilities that they incur to their societies to provide goods and services, employment, tax revenues, and good citizenship behavior. But societies have a collateral responsibility to members of their business communities and indeed to all of their citizens, irrespective of occupation or position, to inculcate into them the virtues of honesty and integrity.
Business per se is neither ethical nor unethical, moral nor immoral. But positions of business leadership and authority may be filled with honest or dishonest people, just as can pulpits, classrooms, operating rooms, and legislatures. Society should expect no less (but also no more) of its business leaders than of its preachers, teachers, doctors, electricians, or legislators.
What's Ahead
In our survey of the relationships between the firm and society we have noted points at which governmental roles might be needed. Chapters 21, 22, and 23 examine these possibilities.BACK TO CONTENTS
CHAPTER 20. ETHICAL DIMENSIONS OF MANAGERIAL DECISIONS
Ethics in Management
Ethical dimensions of managerial decision making were not much discussed prior to the late twentieth century, perhaps because discussion of them might betray the existence of problems. There are now both management textbooks and management courses with titles containing the term "ethics." Of course, there really is no such thing as a particular variety of ethics peculiar to the managerial decision setting. The discussion should be about ethics in the generic sense, but as applied to managerial decision settings.Managerial decision making involves complex interactions between producers and consumers, employers and employees, managers and owners, business executives and members of the communities in which their firms operate. While these relationships are essentially economic in nature, they also have ethical dimensions. Some of these dimensions include the work environment, the effects of pollution and depletion of natural resources, and the safety of consumers.
Managerial decision making, whether in the profit, not-for-profit, or public sectors, must be based upon moral foundations if relationships are to be reliable and predictable. Nonetheless, we hear and read of a variety of practices in both public and private sectors that most people would judge to be unethical, among them bribery, embezzlement, breaking contracts, price fixing, collusion, deceptive advertising, falsification of expense accounts, underreporting of income or padding of expenses on tax reports, use of substandard materials, producing and selling products that fail to function as advertised, failing to divulge to consumers possible product dangers, and so on. Any of these behaviors may erode the moral foundation of commerce and make business activity both unreliable and unpredictable.
In the private sector, the pursuit of profit has traditionally been viewed as the chief motivation to engage in productive activity. The pursuit of profit cannot be regarded as a morally neutral activity because the receipt of profit income may lead to inequality in the distribution of income between those who are entrepreneurially successful and those who are not or who do not choose to behave in an entrepreneurial fashion.
A challenge to the legitimacy and authority of privately owned and managed business enterprise has emerged in the United States during the second half of the twentieth century. The challenge focuses upon the legitimacy of business, its right to exist, and the right of people to own and use business property to their own private benefit. Statistical evidence in support of this contention is implicit in numerous surveys and polls that indicate that many Americans believe that the ethical standards of business are lower than those of American society as a whole.
A Framework for Thinking About Ethics
In order to provide a framework for thinking about ethics in managerial decision contexts, it will be convenient to employ a classification scheme provided by W. Michael Hoffman and Jennifer Mills Moore in Business Ethics: Readings and Cases in Corporate Morality (McGraw-Hill, Inc., New York, 1990).In simplest terms, morality may be defined as what is good or right for human beings. Ethics involves choices in regard to moral precepts. A choice may be ethical or unethical depending upon whether behavioral rules are obeyed, or whether the choice yields good or right outcomes for those who are parties to the decision, and perhaps also for "innocent third parties." Hoffman and Moore identify three ethical orientations that cover most of the positions that can be taken by business decision makers.
2. Ethical absolutismAt the opposite end of the ethical spectrum from ethical relativism is ethical absolutism. Ethical absolutists believe in the existence of universal standards of ethical behavior. For Immanuel Kant (1724-1804), ethical criteria were "categorical imperatives" in the sense that they are absolute and unconditional, irrespective of the consequences. Examples of Judeo-Christian scriptural dictums that may serve as categorical imperatives include those found in the Ten Commandments (e.g., prohibitions against stealing and lying), scriptures relating to oppression, the Golden Rule ("Do unto others as you would have them do unto you"), and Jesus' command to love one's neighbor as oneself (Matthew 19:19, 22:39; Mark 12:31, 33; Luke 10:27). Religious fundamentalists of the late twentieth century, whether Moslem, Jew, or Christian, would perhaps be most comfortable with categorical imperatives in the form of scriptural dictums to guide their behavior.
3. Consequentialism. The intermediate range of the ethical spectrum is occupied by a variety of positions that focus upon the outcomes of behavior. Consequentialism is the belief that the consequences of an action are the sole bases for judging whether an action is right or wrong. For a consequentialist there is no universal standard of ethical behavior; any action that yields a desirable outcome can be rationalized as ethical. For a consequentialist the end justifies the means as ethical, or if it is an undesirable end, the end indicts the means as unethical. Consequentialism dichotomizes into ethical egoism and utilitarianism.
B. Utilitarianism. In contrast to ethical egoism, utilitarianism holds that people ought to act so as to promote the greatest total balance of good over evil, or the greatest good for the greatest number. A rule utilitarian would obey those rules that experience has shown generally promote social welfare, even when doing so does not always lead to good consequences. An act utilitarian may hold that one ought to act so as to maximize total good even if doing so violates rules that usually promote social welfare.
Milton Friedman in Essays in Positive Economics (The University of Chicago Press, Chicago, 1953) raises an interesting question in regard to means and ends: If the end does not justify the means, then what does? He goes on to suggest that if a person is serious in raising this question, for him the means are actually a more important end than the end that had been contemplated. We may infer that such a person is less likely to be an act utilitarian than a rule utilitarian or a categorical imperativist.
We may infer that some variety of consequentialism must underlie the rationale of any dictator who assumes absolute political authority. A society that finds itself with a dictator can only hope him or her to be a benevolent act utilitarian rather than an autocrat who is an ethical egoist. Likewise, societies with democratic polities should attempt to elect act utilitarians rather than ethical egoists. Act utilitarianism is perhaps the ethical orientation most consistent with the pragmatism of late-twentieth century American social and political liberalism. Late twentieth-century Christians who are religious liberals might tend toward rule utilitarianism, whereas Christian fundamentalists are more likely to be categorical imperativists.
While numerous scriptural references imply care for other members of society, there do not appear to be any explicit scriptural dictums that are congruent with act utilitarianism. Although Cain's question in Genesis 4:9 ("Am I my brother's keeper?") went unanswered, an affirmative answer often is adduced to it. A liberal translation of "brother" to refer to all of humanity would seem to suggest an act utilitarian orientation. In Luke 10:29, a lawyer asks Jesus, "And who is my neighbor?" Jesus replies with the story of the Good Samaritan that concludes that the neighbor is the one who showed mercy to the injured man. Although never stated explicitly, the implication is that "neighbor" refers to anyone encountered, and in the limit all of humanity. The latter interpretation implies an act utilitarian ethical orientation.
In 1776, Adam Smith (who trained as a moral philosopher) tied ethical egoism and utilitarianism together when he asserted (in The Wealth of Nations) that pursuit of self-interest by each member of society may contribute more to the common weal (welfare) than the individual either knows or intends.
The Role of Justice in Ethics
The concept of justice plays an important role in ethical considerations in American society.Procedural justice is achieved when appropriate procedures are employed, as for example when universal rules are obeyed. However, the use of just procedures may not yield desirable results. The Golden Rule, "Do unto others as you would have them do unto you," is an example of a categorical imperative that would achieve procedural justice, but which may not result in desirable consequences if others choose not to reciprocate.
Distributive justice is achieved when benefits and burdens of economic activity are distributed fairly, but this begs a question of what constitutes fairness. The egalitarian notion of distributive justice is an equal (or as nearly equal as possible) distribution of benefit and burden. Non-egalitarians may hold that fairness is achieved when the benefits and burdens are distributed on the basis of some specific criterion, such as need, merit, effort, hard work, or contribution to society.
The principle of justice underlying American capitalism has tended to emphasize contribution to society recognized by market demand as the criterion for judging the fairness and hence the justice of distribution. Americans typically have not expected everyone to end up with an equal share of benefits and burdens; rather, those who receive more do so because of their greater contribution.
Ethical Orientations of Managerial Decision Makers
It can be argued that managerial decision makers must behave relatively more ethically than less so in order to ensure continuance and reliability of commercial relationships. Are managerial decision makers, by training, social conditioning, or innate character (among those who select themselves into commercial occupations), inclined to be ethical relativists, ethical egoists, utilitarians, or categorical imperativists? We are likely to find some of each kind in any walk of life, including commerce. A pure speculation is that the for-profit sector has a natural attraction for ethical egoists. Those who are intimately engaged in international business operations probably become drawn to ethical relativism. Managers who are professing Christians are more likely to be rule utilitarians or categorical imperativists. Social liberals who are act utilitarians are likely to be drawn into public sector managerial settings or politics.Although American business interests may be characterized by egoism as a predominant guiding principle of their ethics, Adam Smith's premise that there often is a convergence of private interest with the public weal goes a long way toward explaining why some may engage in actions that serve their own self interests while at the same time engaging in rhetoric to the effect that they are also contributing to the public welfare. Whether there is reality beyond the rhetoric is subject to scrutiny and debate. This issue is made more obscure because some in the non-business public take self-righteous positions in criticizing the apparently self-serving actions of American business decision makers.
Social Responsibility
In the last few decades, the American business community has given the appearance of becoming more socially aware and responsible. This may be a manifestation of the quest for legitimacy in the face of the challenge to the power and authority wielded by business executives. Many businesses have created and displayed business ethics statements. Some have gone to great lengths to indoctrinate their employees to act upon the tenants of their company ethics statements. For others such statements may be little more than marketing ploys. To the extent that business executives take their corporate ethics statements seriously and back them up with civic generosity and ethical behavior, this suggests that they are becoming less egoistic and more utilitarian in ethical orientation.
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CHAPTER 21. THE ROLE OF THE GOVERNMENT
We have made numerous allusions in previous chapters to the interrelations between the firm and the government. Our purpose in this chapter is to delve into these relationships, but our task is made all the more interesting and challenging by the recent events transpiring in Eastern Europe, the former Soviet Union, China, and other parts of the world where socialism has been the predominant form of economic organization for a half century or more.
Forms of Economic Systems
The nature of the relationship between the microeconomic productive unit (i.e., the "firm" in our previous discussions) and the state depends critically upon the form of economic system in place in the society. Although it is possible to identify a wide range of economic system types (including communalism, tribalism, feudalism, and traditionalism), we shall limit consideration to the three that seem to be most pertinent to circumstances of the modern world: socialism, capitalism, and fascism.In the extreme form of authoritarian socialism, the microeconomic productive unit may be little more than an appendage of the state. Indeed, there is little point in making distinctions among micromanagement (i.e., the management of the productive unit), industrial organization and policy, and the macromanagement (i.e., the implementation of macropolicy) of the entire economy. They are all tied up together. For all intents and purposes, there is virtually no freedom of enterprise in authoritarian socialism.
Efforts at centralized and authoritarian direction of the economy seem to have revealed inefficiencies almost everywhere they have been tried. However, societies employing such forms of economic organization seem to be backing away from them in favor of capitalism. Capitalism is distinguished by private ownership of productive resources that are organized by markets. Rather than being highly centralized, decision making in capitalism is widely dispersed to the managements of a myriad of microeconomic productive units, i.e., individuals and the firms or enterprises that compose the economy.
In most forms of capitalism there is a cleavage between the microeconomic productive units and the state that functions as government. In the purest form of capitalism, the state owns no productive resources and engages in no productive activity. Its role is closely circumscribed to providing a legal and social environment that is hospitable to the functioning of the private economy. By the same token, the privately-owned productive units have no significant governing responsibility or authority, but they enjoy a maximum of freedom of enterprise. It is these entities that have been the focus of managerial economic analysis thus-far in this text.
Between the extremes of authoritarian socialism and pure capitalism is possible a wide range of governmental productive activity as well as the use of market mechanisms in conjunction with central planning. The terms "mixed capitalism" and "mixed socialism" are used to described these intermediate forms of economic organization. The exercise of decision-making authority by the managers of enterprises depends critically upon the nature of the relationship between their organizations and the government.
Fascism is a curious combination of the characteristics of socialism and capitalism. Resources remain privately owned as in capitalism, but the state (often in the form of a dictatorship) exercises centralized authority to impose production quotas to be met by the privately-owned enterprises. In fascism, freedom of enterprise is severely restricted. Although fascism has an infamous twentieth-century history, the most prominent examples of it have been eliminated from the world scene. But there almost certainly are examples of functional fascism in today's "third world." And some Western societies are experimenting with a softer variant, statism, that involves increasing willingness to rely upon the powers of the state to treat social, political, and economic problems.
The Applicability of Managerial Decision Criteria
The managerial economic principles and decision criteria elaborated in earlier chapters have been postulated for the context of privately-owned, profit-motivated business enterprises operating within market capitalism. It is not clear that these principles and criteria are also applicable to microeconomic production units in a centrally planned and directed economy. Nor is it clear that they can apply to governmental departments and their subdivisions and agencies, or to organizations in the not-for-profit sector of a market economy (churches, charitable organizations, educational institutions, health-care organizations, etc.). These are similar in that while each is oriented toward pursuit of some mission, that mission is not to realize the maximum possible amount of net income. It therefore appears that decision criteria that are postulated for profit-oriented firms may not be applicable to not-for-profit organizations.One problem is that in both the government agency and the not-for-profit sector, the financial requirement is simply to remain within budget (i.e., a budgetary non-negativity constraint), rather than to maximize profit (net revenue). A similar constraint usually is imposed upon a factory in a centrally-planned economy. However, this is not unlike satisficing, i.e., the pursuit of a target return on invested capital, in the for-profit sector of a market economy as originally hypothesized by Herbert Simon (discussed in Chapter 2). In the government agency and the not-for-profit organization, the target return is simply zero rather than some positive net amount. If for-profit business firm managers can target some (any) positive amount of net income (rather than try to realize the maximum possible), it should be feasible for the managers of not-for-profit organizations to employ the same decision criteria in pursuit of a zero or non-negative return. Zero should be as good a target as some positive amount.
In Chapter 5 we examined the thesis that managers of some for-profit business firms may attempt to optimize rather than maximize with respect to profit. Optimization means maximization of a primary goal subject to one or more constraints that are imposed by the existence of subsidiary goals. William Baumol hypothesized that many managers, instead of attempting to achieve the maximum possible profit, actually pursue some non-profit goal, e.g., sales volume or share of market, subject to a minimum acceptable profit constraint (e.g., a target return on invested capital). The Baumol model is elaborated in Chapter D6.
In the not-for-profit sector, the organization always has some mission to accomplish or some goal to pursue. Often the mission or goal can be expressed in some quantifiable but non-pecuniary form. For example, in a charitable organization such as the Salvation Army, the mission may be to provide the most welfare services (meals, shelter, etc.) to constituents while not overexpending the budget. The manager of a (former) Soviet factory may be required to meet an output quota imposed by the central plan while remaining within the factory's budget. These are fairly straight-forward applications of the Baumol thesis taking the minimum acceptable amount of profit as zero (i.e., no loss or negative profit).
Production units in centrally planned economies and not-for-profit organizations in market economies are notorious for inefficient operation in the sense that costs tend to be excessive and goal achievement seems to be deficient in comparison to comparable for-profit enterprises. A significant problem in these situations is that it is very difficult to provide the manager with performance incentives. It is also difficult to link the process of mission pursuit to any factor that constitutes a performance incentive for the manager. This linkage often is achieved in the for-profit sector of the market economy by letting the manager share in the net income of the enterprise (bonuses, stock options). But this is a problem of linkage, not a problem of the applicability of managerial decision criteria.
A final problem that we shall note is that of organizational bureaucracy. Typically there are several levels of management in any complex organization. The managerial decision criteria that we have described in earlier chapters are most appropriately employed at the highest level of managerial policy making where the managers can take a view that oversees the whole enterprise. These principles may be of lesser applicability at any intermediate level within the bureaucracy where the department or division-level manager (bureaucrat) can see and exercise control over only the few variables associated with the department. But bureaucracy is no less a problem for the corporation in the for-profit sector than for a charitable organization in the not-for-profit sector or the factory in a centrally planned economy.
The conclusion to which we have been moving is that the managerial decision criteria elaborated in earlier chapters should be applicable to decision making in not-for-profit organizations and government agencies, but there are other problems of performance-incentive linkage and bureaucracy that must be dealt with.
Benefit-Cost Analysis
If the principal objective of a not-for-profit organization is to maximize some aspect of its non-pecuniary mission, the marginal comparison criteria applied in the for-profit sector to revenues and costs should be equally applicable in the not-for-profit sector to the quantifiable characteristics of the mission being pursued. "Benefit-cost" analysis may provide decision criteria for the organization manager in the government and not-for-profit sectors. The sum of all benefits (non-pecuniary as well as revenue) resulting from mission pursuit constitutes the numerator, B, of the benefit-cost ratio. Its denominator, C, consists of the sum of all costs (non-pecuniary as well as pecuniary) incurred in pursuing the mission. If the value of the ratio is a number greater than unity (i.e., B/C > 1), then the activity under analysis is justifiable; any benefit-cost ratio less than unity (i.e., B/C < 1) suggests that the activity is unwarranted.Simple benefit-cost analysis has been extended to the concept of marginal benefit-cost analysis. This version is applicable to situations where the question is whether to do more or less of the activity that is already in progress. The numerator of the marginal benefit-cost ratio includes only the additional benefits that are expected to flow from some increment of the activity; the denominator sums only the increased costs incurred by the activity increment. The same decision criterion holds for the marginal as for the simple benefit-cost ratio: a value greater than unity warrants the activity increment while a value less than unity indicates that the activity increment should not be undertaken. While marginal benefit-cost analysis has been used most often as a decision criterion in the not-for-profit sector, it is apparent that the for-profit criteria of marginal revenue and marginal costs are special cases of marginal benefits and costs where the benefits and costs are pecuniary values (or equivalents).
Both simple and marginal benefit-cost analyses are subject to bias and fraught with the potential for abuse. The bias follows from the requirement to include all benefits (psychic and other non-pecuniary benefits as well as any revenues resulting from the activity) and all relevant costs (non-pecuniary psychic and opportunity costs as well as explicit money costs). The problem is that a decision maker who is has a predisposition favoring a proposed activity tends to exhaustively identify all possible benefits and also tends to overestimate their money value equivalents. A decision maker with such a predisposition also tends to be more casual about identifying the relevant costs, and may also be inclined to underestimate their money value equivalents. By the same token, a decision maker with a predisposition against an activity tends to do the opposite, i.e., to casually overlook some benefits and underestimate the values of those identified, while exhaustively finding all relevant costs and carefully estimating their full money-value equivalents. Because of the subjectivity involved, it is entirely possible for two decision makers, confronted by precisely the same prospects and with the same information, to estimate widely divergent benefit-cost ratios and reach opposite decisions about whether to proceed with the activity.
Points of Contact between the Firm and the Government
Because capitalism (or market economy) is the form of economic organization to which the world seems to be drawn, we shall presume its general characteristics in subsequent discussion of the role of government. Given this presumption, there are six principal points of contact between firms and the government.
(2) Firms pay taxes to the government. The taxes may be related to the firms' profits, their sales, their inventories or other assets, or the wages that they pay to their employees. Tax-related record keeping and reporting often become burdensome to business firms, and tax liabilities and rates are subject to change at the dictatorial or parliamentary whims of the state.
(3) Depending upon the government's particular political, social, and military programs, various firms in the economy may become objects of support by the government. Such support may take the forms of subsidies, approval of licenses, preferential contracts, or other encouragements. The government may attempt to structure such activity as a coherent industrial policy for the promotion of international competitiveness of domestic companies.
(4) In pursuit of its agenda, government's interests in firms may extend beyond support to efforts to control the activities of firms. Objects of governmental controls may include directions of research and development efforts, determination of product mixes and item specifications, selection of capital investment alternatives, eligibilities for import or export licenses, and employment practices. These activities may become elements in a more comprehensive industrial policy.
(5) The private sector may become an object of regulation by the government in the interest of employees, consumers, or other interests in the economy. Such regulation almost always imposes additional costs upon business firms, and consequently squeezes profits or results in higher market prices.
(6) And finally, the private sector may become the object of efforts either to promote and encourage competition, or to stifle or prevent competition. In the former case, "antitrust" or "antimonopolies" laws may be enacted and enforced; in the latter case the government may become the prime mover in the effort to "rationalize" or cartelize industry (also a possible component of industrial policy).
In their extreme manifestations, points (1) and (4) above may devolve to the characteristics of fascism. We may also note that the government can effect a ready transformation to the characteristics of socialism simply by nationalizing private-sector firms so that they become government-owned and directed enterprises. Our purpose in making these observations and otherwise identifying the various points of contact between firms and the government is to note that the operation of government in a capitalistic economy may pose threats to private sector firms as well as provide opportunities that they may attempt to exploit.
Rationales for Governmental Involvement in the Market Economy
The most fundamental role for government to play in the market economy is the maintenance of an environment that is hospitable to the functioning of market economy and the exercise of entrepreneurship. At very minimum this means establishing the rules for holding, transferring, and arbitrating disputes over the possession of private property, determining weights and measures, providing a stable money supply, insuring the sanctity of contracts, and otherwise maintaining law and order. John Stuart Mill during the nineteenth century referred to these minimal roles for government as the "night-watchman" functions.Beyond the night-watchman functions are four other significant rationales for governmental involvement in the market economy: to maintain competition, to reallocate resources, to redistribute incomes, and to stabilize the economy. Each of these rationales is founded upon some fault, shortcoming, or failure in the functioning of the market.
From this perspective it may be noted that any problem in the functioning of a market may invite some response from government to address the perceived problem. And if market mechanisms exhibit traumatic failure or become fundamentally distrusted by the political leadership of the society, these constitute the rationales for shifting to fascism by conferring product-mix decision making upon a central authority, or to socialism by nationalizing privately-owned productive resources and imposing central planning and direction. By the same token, failure of authoritarian socialism constitutes the rationale for shifting from authoritarian control to some form of market economy. It appears that this latter phenomenon is being widely experienced in the Eastern Europe even as some economies of the West experiment with more statist orientations.
The Maintenance of Competitive Conditions
Viable competition among business firms in each market is the sine qua non of market capitalism. It is competition that ensures that firms efficiently produce only those goods and services demanded by the consumers of the society. But there is an inherent divergence of interest between the firms in an industry and their customers. Although customers surely benefit from adequate competition (lower prices, higher quality merchandise, greater product variety), firms might achieve greater profits in cooperation with each other or as sole monopolists of their respective markets.Firm managements find incentive to attempt to achieve monopoly by internal growth, acquisition of competitors, or engaging in practices to destroy the abilities of competitors to effectively compete. If the achievement of monopoly is blocked by public policy (e.g., antitrust law and its effective enforcement), they may attempt to cartelize the industry. If cartelization is prevented, firms may attempt to collude with competitors to set prices or allocate sources of materials or markets. If all of these avenues are blocked, the firms in an industry may engage in price leadership-followership behavior. Each of these behavior patterns is discussed in Chapter 11.
Governments of democratic societies then find rationale to undertake the promotion and preservation of competitive conditions in their economies. This is usually done by enacting legislation that declares the existence of monopoly to be unlawful (in the U.S. this is accomplished by Section 1 of the Sherman Antitrust Act) and the perpetrator of monopoly to be guilty of an unlawful act (Sherman, Section 2), or that enumerates specific acts or activities which diminish competition and which are thus unlawful (the Clayton, Robinson-Patman, and Wheeler-Lea acts). But the enactment of legislation alone is not enough. The government must further establish an enforcement authority (in the U.S., the Federal Trade Commission and the Antitrust Division of the Department of Justice) and resolve to make effective the enforcement of the relevant legislation. This resolve may differ significantly according to the political party in office and the particular agenda that it is attempting to implement.
The managerial implications of the determined enforcement of laws that are intended to preserve and maintain competition are that managers of business firms must make themselves knowledgeable of the pertinent laws, and they must make calculated judgments as to whether to risk violating such laws in any of their sourcing, producing, or marketing activities. It may also be worthwhile to note that in a society governed by law (as is the U.S.), innocence is presumed until guilt has been established. The significance of this is that no act undertaken by the management of a business firm is necessarily in violation of the law until it has been tested in the courts.
In a legal environment of presumed innocence, even though a law may declare a certain act unlawful and other firms engaging in the act have been indicted and successfully prosecuted, the act may be repeated by yet another firm. In order for the firm to be penalized under the law, the act must be detected, indicted by an appropriate legal authority, and successfully prosecuted in court. Because failure may occur at any of these stages, the management of a firm may behave rationally to assess the probability of detection, the probability of indictment if detected, the probability of successful prosecution if indicted, and the magnitude of the penalty if found guilty under the law. Then if the "expected value" of the penalty (i.e., the conditional probabilities multiplied by the likely penalty) is judged small enough, the management may deliberately assume the risks of detection and prosecution by engaging in the act. Indeed, it is not uncommon for business firms to maintain legal staffs or contingency funds to cover legal fees and any penalties that are actually assessed.
Two cautionary notes are appropriate at this point. First, even though the behavior described in the paragraph above may be rational, the reader should not take this acknowledgement as an advocacy of the assumption of risk in knowingly breaking the law. And second, although the liability of corporate shareholders is limited to their investment in the firm, corporate managers should beware of the possibility of both criminal prosecution and civil liability suits when their firms have been found guilty of violation of the law.
Rationales for Reallocation and Redistribution
We shall devote Chapter 21 to the governmental rationale for reallocating resources in the economy. Suffice it to say at this point that the rationale is based upon the conclusion that the particular allocation of resources resulting from the normal functioning of the market economy is not satisfactory and needs adjustment. This conclusion may emerge if there are so-called "public goods" desired by society but not producible in response to market incentives, or if there are positive or negative externalities (or "spillovers") resulting from the market production of goods or services. The managerial implication of this rationale is that declining profits or losses will likely emerge in industries from which resources are diverted, but profitable opportunities should be found in industries toward which resources are reallocated.The income redistribution rationale follows from a social and political judgment that incomes are being inequitably distributed across the population of the society by the normal functioning of the market economy. There is little doubt that any market economy distributes incomes unequally because of the fundamental reward mechanism of capitalism: to each according to his or her contribution to the process of production of demanded goods and services. Since members of any population possess differential abilities and experience varying intensities of drive and motivation, there will occur different contributions to the production process, and as a consequence an unequal distribution of income.
Social action becomes warranted only when it is judged that the inequality of distribution is also inequitable. The governmental vehicles for redistribution include progressivity of income and profits taxation, the taxation of capital appreciation, and any of a wide range of possible transfer payments. One managerial implication of governmental redistribution is that business net incomes, assets, and wages paid are likely to be objects of taxation to raise revenue for redistribution to lower-income members of society. Another is that businesses catering to transfer recipient clienteles may benefit from the redistributions. However, there may be little hope for managements of business firms to exert significant control or influence upon the political process that determines how incomes are to be redistributed.
The Government's Potential for Stabilizing the Economy
The rationale for bringing the offices of government to bear upon the stability of the economy is based upon the view that market economies are naturally unstable, that the degree of instability is intolerable, and that some force must be applied to counteract the natural instability of the market economy. Of course, the only entity in the economy that can possibly bring enough force to bear upon the problem of instability is the government.
What's Next
The next two chapters explore the role of the government in reallocating the resources of a market economy and in attempting to stabilize the macroeconomy.BACK TO CONTENTS
CHAPTER 22. REALLOCATION OF RESOURCES BY GOVERNMENT
As we noted toward the end of Chapter 20, the private sector of any economy will yield a certain allocation of resources that can be construed as efficient if there are few externalities and little exercise of monopoly power. It is efficient in the sense that under competitive conditions, output of each good will be adjusted until its marginal cost (society's valuation of the resources used to produce the good instead of some other goods) is just equal to its marginal revenue (or price, society's valuation of having one more unit of the good rather than some other goods).
But even if the allocation of resources is efficient, it still may not be satisfactory to the society, primarily because of two reasons: public goods are not produced in response to market incentives, and markets tend to over- or underproduce social goods, i.e., those resulting in externalities. It may then be said that in regard to society's preferences that resources are misallocated, and that there is a justification for government to act to reallocate resources. The remainder of this chapter is devoted to the issue of governmental reallocation of resources.
Public vs. Private Goods
In the ensuing discussion we use the term "goods" to refer to both goods and services. Private goods are those that are provided by firms in the private sector in response to profit incentives. Private goods involve expense outlays that can be handled by individual members of society. Because there are clear correspondences between the benefits that the purchaser might receive and the costs that must be paid, it is possible for the purchaser to reach a rational decision to buy the private good. Private goods are subject to the so-called "exclusion principle," i.e., the private purchaser can exclude other members of society from enjoying the benefits of the good.A competitive market economy can be expected to yield an efficient allocation of resources to the production of private goods that involve no externalities. Except for providing an environment conducive to their production and maintaining competition, there is very little other role for government to play in regard to private goods. We note below that there may occur special cases of private goods where too little or too much of them is produced, and that this may warrant a role for government.
In contrast to private goods, public goods are not produced by the private sector in response to profit incentives. This is because they tend to be large and "lumpy" in the sense that they involve larger outlays than can be undertaken by most single members of society, and they must be purchased "in toto" rather than in small pieces. Public goods may yield benefits to society at large, but it is often difficult for individual members of society to identify any particular benefit that accrues to them personally. With such a lack of clear correspondence between outlay and benefit, it is usually not possible for the individual to reach a rational decision to purchase a public good, or even his or her small share of one. Also, public goods typically are not subject to the exclusion effect, i.e., it is not possible for the purchaser(s) to prevent other members of society from enjoying benefits flowing from the public good. A corollary of this feature of the public good is the so-called "free-rider" effect, i.e., that other members of society tend to "ride free" because they can enjoy the benefits without paying the cost of acquisition.
Examples of public goods include national defense, local police services, fire departments, parks, and a variety of infrastructure facilities such as highways and streets, water, sewer, and refuse collection systems, and in some places electricity and gas generation and transmission systems. As soon as we have identified possible examples of public goods, readers may begin to think of possible exceptions... private amusement parks, toll roads, private security services, etc. But the principle still holds as a general phenomenon, even if we can think of possible exceptions.
The salient point for our purposes is that a market economy will not of its own volition allocate resources to the production of public goods. It usually takes a social decision reached by some governmental body in order for a public good to be produced, and for resources to be reallocated to the production of the public good. However, in Western democratic societies that organize their economies around markets, public goods are not produced in the public sector. Rather, they are provided by the public sector in the sense that a social decision is reached to commission their production and public funds are budgeted to pay for them. Their actual production occurs in the private sector as public agencies contract with private firms to build the public goods. The incentive for a private sector business firm to contract to produce such a public good is that the contracted price is expected to more than cover the estimated expenses in order to allow a "profit." However, this is not the basis for a conclusion that public goods are produced in the private sector in response to profit incentives.
Now we come to the important point: the social decision to commission and fund the construction of a public good provides opportunities for private sector firms. The usual procedure is for the commissioning authority to make public announcement that competitive bids will be entertained from private sector firms. The criteria for "letting a contract" to one of the bidding firms include the bid price, the estimated completion date, and a variety of possible design or performance conditions. Often the "low bidder" gets the contract, but this does not always occur.
Threats to private sector firms may be contingent upon the bidding process if firms conspire to "rig bids" so that one of them gets the particular job while others anticipate getting other jobs in the future. Also, the firm that wins the contract to construct the public good may suffer a threat of law suit if it fails to meet any of the contracted conditions, including the bid price, the completion date, or any of the design or performance conditions.
There are yet other threats to private sector firms in that the societal decision to commission the production of a public good has the effect of reallocating resources away from the production of private goods. The problem is less critical in an economy suffering significant unemployment, but in a nearly fully-employed economy, the prices of resources tend to rise as they are bid away from the production of private goods. This will have the effect of increasing production costs and narrowing profit margins for private goods producers that use the same resources. If this process results in rising market prices for the private goods, less of them will be sold (their demand curves slope upward from right to left) at the same time that more of the public good is produced. Private goods producers who can no longer earn at least normal returns can be expected to exit their respective industries.
Social Goods Yielding Positive Spillovers
Social goods are special cases of private goods. They are private goods because some quantities of them will be produced in the private sector in response to profit incentives. They are special cases in that while their private-intentions market demand curves recognize the explicit demands for them at going market prices, they fail to recognize any positive or negative spillover effects (or externalities) resulting from either their production or their consumption.Examples of positive spillovers include the satisfactions enjoyed by passers-by because a firm has beautified its buildings or grounds, and the fact that health services tend to benefit many people other than those who directly receive them. Also, while education or training benefits the recipient by increasing the income-earning potential, other members of society also are made better off when the recipient becomes productive. The sense in which markets misallocate resources in the production of goods yielding spillover benefits is that they are produced in inadequate quantities.
Figure 22-1 illustrates this point. A normal market supply is represented as S. The demand curve labeled Dp represents the private intentions market demand curve, i.e., the quantities of the good that would be purchased at each possible price by those who benefit directly from the consumption of the good. Suppose that the good yields spillover benefits to other members of society who did not directly demand the good. Their implicit demand for the good can be represented by an addition to the private intentions demand that shifts the demand curve outward to a new locus, Dt, representing the "total" demand for the good.
Figure 22-1.
The problem for society is that the locus of Dt is virtual rather than actual. The relevant market demand curve that interacts with the market supply curve is Dp. This market interaction will result in the production of only Q1 which is sold at market price P1. But if the market could in some way be made to recognize in an explicit sense the spillover benefits included in the virtual demand curve Dt, a larger quantity, Q2, would be transacted at a higher price, P2. Because the market produces only the smaller quantity, Q1, it may be said that resources are under-allocated to the production of the good. But it would be desirable from a social perspective for the larger quantity, Q2, to be produced and consumed. Recognition of this desirability constitutes the basis for some action by society to try to reallocate resources toward the production of more of the good that yields spillover benefits.
How can government attempt to correct this misallocation of resources? It could attempt to adjust the locus of the market demand curve, but this is a very difficult thing to do. The government could mount an advertising campaign that encourages people to consume more of the good ("Take flu shots....They are good for you and others as well!" "Stay in school....You will benefit and the rest of society will as well!"), and this might have some effect in shifting the market demand curve to the right toward Dt in Figure 22-1. However, such admonitions are unlikely to have the desired social impact.
Governments have found it to be much more effective to manipulate the locus of the supply curve than the locus of the demand curve. The principle means of doing this is to provide a subsidy that shifts the market supply curve far enough to intersect the market demand curve at the desired quantity. In Figure 22-2, S' lies below (and to the right of) market supply curve S by enough to allow it to intersect the market demand curve, Dp, at the quantity Q2. This is the quantity that would be transacted in the market if the market demand curve reflected the spillover as well as the direct benefits. The vertical distance between S' and S is the per-unit amount of the subsidy.
Figure 22-2.
The subsidy, if provided to the consumer, has the effect of reducing the purchase price of the good so that a larger quantity, Q2, is bought at the lower price, P3. If the subsidy is paid to the producer, it serves as an off-set to the cost of production, thereby shifting the supply curve downward. In a competitive market the reduced production costs can be expected to be passed through to consumers in the form of lower market prices. But in any imperfectly competitive market, the exercise of monopoly power may result in the subsidy being internalized to allow a wider profit margin.
A practical problem from the perspective of public policy is recognizing the effect that the spillover benefit should have on the locus of the demand curve, i.e., the true locus of the virtual demand curve, Dt. If the responsible government officials overestimate the effect of the spillover benefit, the subsidy may be set at too large an amount with the effect of inducing an overallocation of resources to the production of the good. On the other hand, if the government officials underestimate the effect of the spillover benefit, the subsidy will be too small, which will leave resources underallocated to production of the good. It is almost heroic to think that government officials (or anyone else) are perceptive and astute enough to estimate just the right magnitude of a required subsidy so as to achieve a correct allocation of resources to the production of the spillover benefit good.
This problem aside, what are the opportunity and threat potentials for firms in the private sector? Producers of goods for which subsidies are provided may find market opportunities to expand both production and profit margins. These opportunities will be greater to the extent that government officials tend to overestimate spillover benefits and thus set subsidies at levels that are too large, and vice versa if they underestimate the spillover benefits. This is a persisting problem for officials at state universities that receive subsidies from state government treasuries. Since the subsidies have the effect of allowing the state universities to price their products below their per unit costs of production, the quantity demanded of higher education is typically larger than would be the case in the absence of such subsidies. The relevant question is how much additional higher education should be provided to the society to recognize the spillover benefits. Similar questions arise in regard to subsidy and pricing of health services. We shall not attempt to address questions in either area.
There are also threats consequent upon the provision of subsidies to the production of goods yielding spillover benefits. If the subsidies have the effect of reallocating resources toward the production of the spillover benefit good, they also have the effect of reallocating resources away from other private goods. This will be to the detriment of the other private goods producers, and the effect will be the greater if the responsible government officials tend to overestimate the spillover benefits.
Spillover Costs
Private goods may result in negative spillovers, or spillover costs, although such goods are not customarily referred to as "social goods." Spillover costs are the negative effects that descend upon innocent bystanders to the activities of the firm. Examples of spillover costs include the unsightliness of "rust-belt" manufacturing plants, the noise and odors resulting from some manufacturing processes, the entire variety of industrial effluents ejected into the atmosphere and waterways, and congestion on the highways attributable to concentrated industrial or commercial activity.The analysis of spillover costs starts with a normal market demand curve, D, as illustrated in Figure 22-3. Superimposed over it is a private-intentions market supply curve, Sp, showing the quantities of the good that producers would offer on the market at possible alternative prices. The market can be expected to adjust to an equilibrium at quantity Q4 which is sold at price P4. The market supply curve is a summation of the individual supply curves of all of the firms producing the good. Each of their supply curves reflects all of the costs that are relevant to the production process, whether they are explicit or implicit costs. The relevant-cost supply curves include none of the costs that are irrelevant to current decision making. This means that the market supply curve excludes all spillover costs because such costs descend upon members of society other than those who make production decisions within the producing firms.
Figure 22-3.
If such spillover costs could be incorporated into the market supply curve for the good in question, it might lie at locus St, above Sp by an amount that reflects the magnitude of the spillover costs. Supply curve St represents the total of the costs of production, including relevant and spillover costs. St is only a virtual supply curve, but if it were the actual market supply curve, a smaller quantity, Q5, would be transacted in the market at a higher market price, P5.
Because quantity Q4 (which does not recognize the spillover costs) is larger than quantity Q5 (which would recognize the spillovers), it may be said from a social perspective that too much of the good is being produced and sold, and thus that resources are over-allocated to the good that yields spillover costs. This then constitutes a justification for society to act through its government to deal with the spillovers.
There is a variety of ways in which government might attempt to address the spillover cost problem. We shall examine the managerial implications of four possibilities:
2. Government permits the process causing the social cost to continue but requires the offending firms to compensate those who are harmed.
3. Government auctions pollution rights to the highest-bidding firms.
4. Government imposes a punitive tax in the form of an excise on each unit of the good sold.
A governmental edict that a social cost must cease will be ineffective unless backed by a further provision in the law that makes the action a criminal offense with serious penalties, or makes the innocent third parties harmed by the social cost eligible to collect civil damages. In either case, the expense of legal defense, court costs, and penalties or damages will become explicit costs to the firm or to its managers personally, and will thus become costs that are relevant to operating conditions. The higher explicit costs will narrow profit margins and thereby discourage production and further entry into the market. Or if the costs can be passed along to consumers in the form of higher prices, consumers will purchase less of the good yielding the spillover cost. In either case, the social objective of reallocating resources away from production of the good will be accomplished.
If government permits the socially offending activity to continue but requires compensation of all who are harmed, the compensation outlays will likewise become explicit costs of operation and hence relevant to decision making. The same resource reallocation effects will follow.
A popularly-discussed approach to dealing with spillover costs is for government to auction rights to continue the process. The outlays paid by the highest bidders will also become explicit costs of production that are relevant to production decision making, and again the desired resource reallocation effects will follow. A further possibility is that if the prices bid for the pollution rights are higher than the costs of abating the spillover costs (e.g., by making capital expenditures to filter, scrub, dampen, or otherwise diminish the air, water, or noise pollution), some firms will incur the expense of abatement rather than bid on the pollution rights. Such expenses will also become explicit and hence relevant costs to the production processes.
Finally, a responsible government authority might opt for a punitive excise tax that would shift the market supply curve upward to the position of St in Figure 22-3. The per-unit amount of the excise tax is represented by the vertical distance between Sp and St. The market price would be expected to rise to P5 and quantity transacted to fall to Q5 (because consumers purchase less at higher prices). The declining production is accompanied by the desired reallocation of resources away from production of the offending good.
Just as in the case of spillover benefits, there is also the practical problem of whether the responsible government official can accurately estimate the magnitude of the spillover cost so as to determine just the right level of excise tax. If the spillover cost is overestimated, the excise tax will be too large, and a further misallocation of resources will occur as output of the good decreases below Q5. If the spillover cost is underestimated, the amount of the excise tax will be too small, and the existing misallocation of resources will persist.
These four alternatives have all assumed deliberate action on the part of government to bring about the socially desired resource reallocation. The same end might be accomplished with no government action at all if managers of firms causing spillover costs become aware of the problem (possibly because of complaints by one or more of their constituencies), and with a twinge of conscience become more "socially responsible." Irrespective of whether the adjustment ensues as a matter of social conscience or in response to governmental action, the spillover costs that formerly were not relevant to managerial decision making have become explicit costs of production that are relevant. One moral of the story, as first noted in Chapter 9, is that costs which are presently irrelevant to managerial decision making always have the potential to become relevant, and thus should never be completely ignored.
Thus far our discussion has focused upon threats to society and to firms that are producing goods involving spillover costs. Are there any opportunities to be exploited in regard to spillover costs? Resources that are reallocated away from production of goods involving spillovers are released for use in producing other goods. Firms using such resources may enjoy falling input prices that expand profit margins and encourage increased production. There are also opportunities in industries that produce the equipment that accomplishes abatement or clean-up of the effects of the cost spillovers.
What's Next
The next chapter examines the potential for government to stabilize the macroeconomy within which firms operate.BACK TO CONTENTS
CHAPTER 23. GOVERNMENT AND MACROECONOMIC INSTABILITY
Macroeconomic Instability
There's no way around it. Any economy organized around markets experiences macroeconomic swings in the form of expansion and contraction of output, falling and rising unemployment levels, greater or lesser rates of inflation, and variations of interest rates, more-so for short-term rates than for long-term rates. Macroeconomic instability creates uncertainty that constrains enterprise freedom. And instability that diminishes welfare more on the downswings than it increases welfare on the upswings has the potential to limit consumer sovereignty and religious liberty.
Marxians and other critics of capitalism (including Postmodernists and Liberation Theologians) have advocated the replacement of the capitalist form of economic organization with authoritarian socialism, both as a means for achieving distributional equity and as a way of ending macroeconomic instability. However, neither of these goals was accomplished and other problems with authoritarian economic organization during the twentieth century resulted in the failure of central planning experiments. Following these failures there has been a wholesale return to market economy, even with all of its "wrinkles, scars, and warts". Postmodernists have begrudgingly accepted that “the end of history” will involve market capitalism rather than Marxian socialism.
After the Great Depression and World War II, the British and American
governments were the first to assume responsibilities for trying to stabilize their predominantly market economies by maintaining high-enough levels of employment, i.e., low-enough levels of unemployment. Over the next half-century, these governments gradually took on responsibilities for other dimensions of macroeconomic stability, particularly the control of the price level in order to avert excessive inflation. Soon after the turn of the third millennium, the prospect of deflation became a serious concern. Governments of other countries also began to assume macroeconomic stability responsibilities.
Fiscal Policy
Possibilities for exercising macroeconomic policy lie in two broad realms, fiscal policy and monetary policy. Fiscal policy entails manipulation of the government's own budget to counterbalance swings of spending in the private sector, i.e., in the business and consumer sectors. The idea, first proposed by John Maynard Keynes in The General Theory of Employment, Interest, and Money (1936), is to deliberately cause the government's budget to go into deficit (disbursements exceeding revenues) as the macroeconomy contracts. This may be accomplished by reducing taxes, increasing purchases or transfer payments, or some combination of the two. Tax cuts leave more purchasing power in the hands of taxpayers to spend, and increased government purchases and transfer payments actually inject more purchasing power into the economy. If such fiscal policy actions work as expected, the economic contraction will come to an end and the economy will begin to expand, returning production, employment, and income generation to more normal conditions.
Sometimes the turn-around from macroeconomic contraction goes too far,
and the expanding economy begins to "overheat" as it approaches and exceeds its normal operating capacity. Or, quite apart from any action by government to bring about recovery from a recent downswing, the private sector of the macroeconomy may expand of its own volition (as may have happened in the US economy during the 1990s). Excessive inflationary pressures, lower than usual rates of unemployment, and plant operation above normal capacities are evidences of macroeconomic overexpansion. When this happens, Keynesian economists advocate that the government should deliberately take its budget into surplus by increasing taxes and decreasing purchases and transfer payments. These actions are intended to siphon purchasing power out of the economy so as to curb excessive spending, alleviate inflationary pressures, and bring the macroeconomy to more normal conditions of production, employment, and inflation. Of course, there is always the risk of overdoing the fiscal dampening to precipitate undesirable economic contraction.
Monetary Policy
The same risk of overdoing policy also applies to monetary policy. Monetary policy is the effort by a government’s monetary authority to determine and control the quantity money in circulation and the interest rate (the “price of money”). In most countries monetary policy is the province of a central bank, and lately there has been a growing global consensus that a nation's central bank should be as independent as possible of the political process in order to avert pressures for inflationary money supply increases as governments run budgetary deficits that have to be financed.
Monetary policy may be implemented primarily in two ways: by manipulating the interest rate, or by changing the nation's money supply. Without doubt, a central bank can change its own interest rate, i.e., the one that it charges to commercial banks when they borrow from the central bank, but it is not at all clear that the central bank's changing its own lending rate causes market-determined interest rates to change. A central bank interest rate change might precipitate market interest rate changes in the same direction if banks and other lenders have been holding their lending rates constant in anticipation of a central bank rate change.
It's much more likely that market interest rates can be manipulated indirectly by the central bank with actions to change the quantity of money in circulation. The Federal Reserve Bank is the name of the central bank of the United States. The "Fed" increases the US money supply when it buys US Treasury bonds from the bond “open market”, paying for them with deposits to the sellers' bank accounts and additions to commercial bank reserves. Bank reserves are highly liquid assets that commercial banks, by legal requirement or banker volition, maintain in order to meet demands by depositors for withdrawals of funds. The bond sellers' increased bank deposits are additions to the money supply. When banks sell bonds, the increases of their reserves enable them to increase lending to customers, and thereby to increase the quantity of money in circulation. The Fed reduces the US money supply as it sells bonds in the open market because non-bank buyers have to pay for the bonds that they purchase by giving up some of their bank deposits, and banks that buy bonds have to give up reserves to pay for the bonds that they purchase.
The enabling condition for the conduct of open market operations by a central bank is the existence of a large mass of public debt and an open market in which that debt is traded. But very few of the other nations' central banks are so fortunate as the US Federal Reserve in its ability to conduct open market operations to manage the US money supply. While many nations' governments chronically have run budgetary, the deficits often have been financed by direct money creation (printing it) rather than issuing bonds, so there is no mass of public debt in the form of bonds and no open market in which it is traded. Some governments have financed their public debts by issuing bonds, but the bonds have been sold and are traded in open markets elsewhere in the world. There is little point in their central banks engaging in open market purchases and sales of bonds (theirs or others) in an ever more global open market because such open market transactions mostly affect money supplies in other countries or the global money supply rather than the local money supply.
Some nations' central banks do not specify legal reserve requirements for their commercial banks to meet, leaving the determination of the amounts of such reserves to the discretion of individual commercial bankers. In these nations, monetary policy is executed by the central bank primarily in manipulating the central bank's lending rate or by engaging in open market operations.
Central banks that enforce reserve requirements but do not have access to the facilities of open markets in their own countries are constrained to executing monetary policy by adjusting the reserve requirement ratio that they impose on their commercial banks. This is something that the US Federal Reserve is empowered by law to do, but the Fed seldom changes reserve requirements because of the potentially large and disruptive effects on the nation's money supply.
The process of globalization with ever more-open economies, instantaneous communications, and round-the-clock bond market trading has rendered the conduct of monetary policy largely ineffectual to all but a very few central banks in the very largest economies, notably the US and the EU. It is heroic to presume that a central bank in a third-world country can significantly affect its own money supply through open market operations, reserve ratio adjustments, or central bank lending rate changes. Smaller countries are looking ever more to the US Federal Reserve or the European Central bank as the global makers of monetary policy.
To an ever-increasing extent, the money supplies of most countries are affected more by the respective government's budgetary policies and how it finances its deficits than by its central bank. Lack of fiscal discipline resulting in chronic budgetary deficits that are monetized directly by treasury departments (or indirectly by central banks under the domination of treasury departments) causes inflation--too much money chasing too few goods. This has become such a serious problem worldwide that governments of a growing number of nations are "dollarizing" or "euroizing" their currencies (or at least considering doing so). This means that they are adopting the dollar or the euro as the local currency and proceeding to replace their local currencies with dollars or euros as international trade and financial conditions permit. What they gain in dollarizing or euroizing their currencies is the monetary discipline that the US Fed or the European Central Bank exercise in restraining the growth of dollars and euros. What they lose is local control of their domestic money supplies, but it may be an illusion that they actually ever had effective control over their domestic money supplies.
Problems with Government’s Efforts to Address Macroeconomic Instability
At the middle of the twentieth century, macroeconomists thought that by engaging in fiscal and monetary policies they could fine tune a market economy to avert both cyclical swings and oscillating pressures of inflation and deflation. But experience has demonstrated in both developed and less-developed economies that government budgets are much more attuned to the requisites of program finance than to the needs of macroeconomic stability. Especially in democratic polities, legislative assemblies often perceive the need or the desire to mount new programs or enhance existing programs. But each expanded program or newly enacted program has to be financed. If financing provision is not made by way of increasing some tax, new or expanded programs contribute to growing deficits. The deficits result in inflationary pressures if they are financed with direct money creation or if the central bank feels compelled to expand the money supply to prevent interest rates from rising. Program-oriented budget finance thus has an inherent inflationary bias.
Even if a government does attempt to manage its budget in the interest of economic stability, a growing number of economists have come to believe that deliberate fiscal actions by the government may elicit counterproductive changes in the private sector that tend to neutralize the deliberate fiscal stimulus. For example, increases of government spending to alleviate recession may increase the budget deficit, causing interest rates to rise, thus crowding out private sector borrowing to finance investment or interest-sensitive consumer spending. Or, decreases of government spending during a period of contraction may so lower market interest rates as to elicit crowding in of private sector borrowing to finance more investment or consumer spending. Both crowding-out and crowding-in effects in the private sector tend to neutralize the deliberate fiscal policy actions taken in the public sector.
During the late-twentieth century and early in the twenty-first century, governments in a number of Western countries attempted to use monetary and fiscal policies in efforts to stabilize their economies. Experience with these efforts has convinced many economists that deliberate policy activism often involves policy overreactions due to time lags in recognizing changing conditions, initiating policy actions, and the completion of adjustments. Today, economists are not so sure that deliberate manipulation of the government's budget in efforts to diminish macroeconomic instability doesn't inject more instability into the economy than would be present if the government simply left the macroeconomy to manage itself.
Similar statements can be made with respect to monetary policy actions by the central bank that are intended to stabilize the economy, but which, because of various time lags, may tend to destabilize the economy. The financial turbulence and recession of 2008-2010, together with the efforts by the US and other governments to stem the recession tide, may provide an interesting test case of this proposition.
When unemployment or inflation have “reared their ugly heads”, politicians usually have felt compelled to follow the admonition, “Don’t just sit there, do something!” Because discretionary policy overreactions may tend to destabilize a macroeconomy rather than stabilize it, a growing number of macroeconomists have become discretionary policy skeptics. But politicians have difficulty following the reverse admonition: “Don’t just do something, sit there!” The ability to wait patiently is simply not in the genes of political animals. Political inaction may be worse for a politician’s career than policy overreaction.
Discretionary policy skeptics have more faith in the automatic self-correcting features that are inherent to any well-functioning market economy than in the ability of government officials to exert stabilizing macropolicies. Policy skeptics have come to favor so-called automatic stabilizers such as a progressive tax rate system. During a period of economic expansion as more people gain employment, wages and salaries increase due to rising wage rates and overtime work, and bonuses increase. Because people's incomes reach ever-higher tax brackets, the increase of tax payments to the government has the effect of siphoning purchasing power out of the economy to dampen the expansion. The process also works in reverse to leave more purchasing power in the economy during an economic contraction.
An unemployment compensation system also can act as an automatic stabilizer. During an economic contraction, ever more people lose employment and become eligible for unemployment compensation (UC). The UC benefits serve as an injection of purchasing power into the economy that replaces some of the earned income that was lost due to unemployment. The system also works in reverse to diminish the injection of purchasing power into the economy when it expands and people go back to work.
But UC is not necessarily the automatic stabilizer panacea that many have hoped for. Some economists argue that UC benefits that are “too rich” (i.e., an amount that is too large as a proportion of the previously earned income) can have a job-search disincentive effect if they make staying of work too comfortable. A matter of continuing debate during the protracted 2008-2010 recession is whether extending the duration of unemployment benefits from twelve months to 99 weeks will have the effect of prolonging unemployment. The rationale of this argument is that UC benefit recipients have little incentive to seek work until their benefits are about to run out.
It may be possible to moderate macroeconomic instability with successful implementation of monetary and fiscal policies, but there is an emerging view among a growing number of macroeconomists that imperfect governmental efforts to moderate instability may actually have the effect of amplifying the instability, thereby threatening consumer sovereignty, enterprise freedom, and religious liberty.
Managerial Implications of Economic Instability
While market economies contain within themselves automatic adjustment and self-stabilizing features, both external and internal shocks can be time consuming and cause unexpected macroeconomic swings that disrupt normal business activities and pose risks for business firms operating in the economies. And well-intended efforts by governments to avert or ameliorate the disruptions may have the perverse effects of actually aggravating the impacts of the shocks.Economic instability, whether cyclical or episodic, is such an extremely complex phenomenon that it is very difficult to draw significant managerial implications in regard to it. However, we may note two important implications with respect to long-run change that unfolds gradually. First, since there is a tendency for maverick views to become orthodoxies with cumulative adoption, the business firm manager should monitor closely both the real phenomena as he or she perceives them, and the emergence of views expressed in the media. The manager should be prepared to adjust business policies when it appears that the views are widely enough accepted that people are beginning to predicate their economic decisions upon them. Second, the manager can rely only to a point upon the prognostications of others. Ultimately the manager must become his or her own economic analyst and forecaster. The effectiveness of this role can develop only with experience and sharpened perceptiveness of changing phenomena in the economy.
Managerial reaction to economic shocks is another matter. Shocks are phenomena that are unpredictable and which often unfold in a very short periods of time. Economic shocks constitute disasters for some and opportunities for others. They induce both inventory and price effects soon after their impacts. Those most directly affected by the shocks will have to respond as seems appropriate at the moment. As we have seen from the simulation exercises, the macroeconomy will be better off if business decision makers do not respond to shocks by changing rates of production or inventory management policies. The vast majority of firms, assuming that the shock impact will be short-lived, will probably also be better off to adjust prices and let inventories change to absorb the shock, but not alter production rates or employment levels. Only if it appears that the effects of a shock will unfold over a longer period of time should the manager give consideration to adjusting output and employment rates.
Finally, we note that the exigencies of macroeconomic instability will almost certainly provide occasions for entry into or exit from industries. A growing economy, or one enjoying cyclical expansion, will involve buoyant market conditions that may encourage entrepreneurial interests to undertake new ventures and enter expanding industries. Such conditions will also be propitiated if the economy possesses newly-recognized or developed comparative advantages vis-a-vis the rest of the world. But a stagnating or contracting economy will likely be accompanied by depressed market conditions that will result in declining sales and falling profits in many industries, especially those for which the economy no longer has international comparative advantages. In such a business climate, the weaker competitors in the various markets are more likely to fail. While this phenomenon will certainly be painful for former owners and employees of failed firms, it may have cathartic effects for the economy as a whole as weaker firms fail but financially viable firms survive. And there are entrepreneurial opportunities even in a contracting economy. Technological advances that enable decreased costs are especially appropriate to the declining economy, and market demands may actually increase in cases of goods with low or negative income elasticities of demand.
Wise business firm managers should monitor both natural and political phenomena. The usual risk-management procedures apply:
2. Diversify operations, geographically and in terms of the product mix and supply and distribution chains so that the effects of disruptions in one locale or affecting one product line will have minimal effects on operations in other locales or product lines.
3. Design inventory management systems with automatic adjustment features to respond quickly to supply disruptions.
4. Identify possible catastrophes and purchase catastrophic insurance policies if premiums are deemed favorable relative to the potential for losses attributable to possible disruptions.
5. Access futures markets (commodities, currency) to hedge against adverse price and exchange rate changes.
6. Prepare to shift operations regionally or withdraw from locales within which physical or political disruptions become untenable.
7. All else failing, the manager may simply have to "bite the bullet" and assume the risk, i.e., the ultimate entrepreneurial response to risk.
What's Next
The next chapter explores the potential for firms to engage in international commerce in the global economy.BACK TO CONTENTS
CHAPTER 24. INTERNATIONAL COMMERCE
We open this chapter with a half-serious apology for including a chapter that focuses upon the international dimension of business. The reason for the apology is that in much of the rest of the world outside of the United States of America, there is little significant distinction between international and domestic business operations. If one is in business at all, he or she automatically engages in international business operations. Managers of such firms hardly give second thoughts to the requisites for sourcing supplies, selling products, or locating production in countries other than that within which the firm's home office is located.
The apology is only half serious because many people in various countries, and notably the United States of America, are somewhat intimidated by the international dimension. It is a mixed blessing to the United States that it has a rich endowment of natural resources and a huge internal economy. Domestic firms have been able to rely upon the internal economy for both sources of supply and markets for their domestically-produced products. Because they have been able to look inward for over two centuries, managers of American firms have tended to regard the outside world as marginal or peripheral to their activities. Many view the international sector as possessing some mystique that requires special capabilities to penetrate. This perception is enhanced by the fact that Americans are for the most part monolingual. Although English is the only language spoken and understood by the majority of Americans, Spanish may yet overtake English as the American lingua franca.
If much of American business has seemed intimidated by international involvements, post-war American consumers have carried on a love affair with foreign-made goods and services. During much of the post World War II era, U.S. balance of payments deficits have been the rule rather than the exception. Concerns about on-going trade deficits and mounting international debt to foreigners have led various U.S. governmental agencies to devise programs to promote exports and discourage imports. American experience with protecting domestic industries from foreign commercial incursions spans more than two centuries.
On-going trade and payments deficits and official concern about them have aroused the interest of the American academic community in international commercial relations. Some graduate programs have specialized in international commerce; examples include the American Graduate School of International Management (the "Thunderbird School") in Phoenix, Arizona, and the Masters of International Business Studies (MIBS) offered by the Business School of the University of South Carolina. Beginning in the 1970s, a deliberate effort was mounted by business studies programs to internationalize their curricula.
By the early 1980s the principal business studies accrediting organization, the American Assembly of Collegiate Schools of Business (AACSB), had established a standard requiring any program seeking accreditation or reaccreditation to achieve a satisfactory internationalization of its curriculum. The most commonly used models for such internationalization have been to employ foreign faculty and recruit foreign students, to introduce new courses focusing upon international business problems and procedures (e.g., international marketing, international finance, international management), and to infuse international concepts into existing courses as appropriate. The latter two models have spawned a flock of new textbook titles as well as revisions of existing texts to incorporate references to the international arena.
In a sense, the recent obsession of American commerce and academia with anything international is only a transitional phase. With the passage of time, international commercial activity will become more commonplace; eventually business studies curricula will become sufficiently internationalized that special commentary about the international sector will no longer be warranted. Three phenomena militate in favor of this transition. (1) Technological advances in communications and transportation shorten the time and costs of distance, thereby diminishing market imperfections and facilitating international exchange. (2) English, the language spoken by the majority of Americans, seems to have emerged as the global language of commerce as well. (3) Efforts underway in various regions of the world to achieve both economic and political integration (the European Union, a "single market" by 1993, currency union by 1999, and a "United States of Europe" by some point in the twenty-first century) tend to render concepts of the international ever less significant. But until such transformation is completed (if ever), we shall be compelled to include chapters such as this in our texts.
Bases for Interregional Commerce
John Donne has said that "No man is an island, entire of itself..." (Devotions upon Emergent Occasions, Meditation 17). It is surely true that no nation can be an island completely unto itself either. Some have tried. After both its Revolutionary War and World War I, the United States seemed to withdraw into isolationism in order to avoid further international entanglements, both political and commercial. After its establishment in 1918, the Union of Soviet Socialist Republics (U.S.S.R.) pursued a de facto strategy of autarky, i.e., internal self-sufficiency. Of all of the nations in the world, these two might have come closest to functional autarky because of the immense richness of their natural resource endowments. But neither of these nor any other nation in the world has been able to achieve absolute autarky. There are several fundamental reasons why they have found it either necessary or beneficial to engage in international commercial relations. There is a very significant difference between international and interregional commerce, but we shall defer consideration of it until a later section. For the moment we shall focus attention upon bases for interregional commerce.It is a fact of physical nature that resources are unequally distributed across the earth's geographic space. Some resources approach ubiquity (found everywhere); others are concentrated by regions. Resources that are found in only one or two places on earth may be referred to as geographic uniquities. Examples include rare elements or precious gems or metals, agricultural commodities that grow only under very special conditions, and natural tourist attractions. Populations of regions possessing such uniquities are fortunate in having access to such resources that they are able to exploit; populations elsewhere are correspondingly unfortunate. Populations of regions devoid of such uniquities may acquire them (or things produced using them) by engaging in interregional trade or military aggression to capture them.
There are few perfect ubiquities or uniquities among productive resources. Most resources are found in many places across the globe, although in greater or lesser geographic concentrations. Goods and services requiring those resources as inputs may be produced more cheaply in regions where they are found in abundance than in other regions where they are scarce.
The Principle of Comparative Advantage
Economists have enunciated the principle of comparative advantage to explain regional specialization in the production of goods and services. According to this principle, people in each region should specialize in producing those goods and services that can be produced most efficiently in their region compared to other regions. "Most efficiently" means at least opportunity cost (in terms of other goods and services foregone) compared to the other regions. Since the production of goods becomes geographically specialized, people in different regions must trade their specialties for the specialties of people in other regions.Generalization in consumption is enabled everywhere through trade even though there is regional specialization in production. It can be shown with theoretical exercises as well as empirical information that those who specialize their production according to the principle of comparative advantage and trade with one another enjoy higher welfare than they would under conditions of autarky.
It is sometimes suggested that there are regions of the world that are essentially devoid of productive advantages, whereas other regions seem to possess all of the advantages (veritable "Gardens of Eden"). We can resolve this problem by further refining the definition of comparative advantage. A region's absolute advantages include all of those things that it can produce at lower opportunity costs than can be achieved in other regions. A region's absolute disadvantage is anything that can be produced elsewhere at lower costs in terms of other goods and services that must be foregone.
It may well be that opportunity costs of most things are lower in one region relative to all others, but this does not mean that the region should generalize in production. Its comparative advantages lie in those things for which it has greatest absolute advantage(s), while the comparative advantages of other regions lie in the things for which they have least absolute disadvantages. They should still specialize in production, but the one in its greatest absolute advantage and all the rest in their least absolute disadvantages. It follows logically from this definition of comparative advantage that it is not possible for a region to have no comparative advantage(s). Furthermore, it can be shown that all of the regions of the world, the sparsely-endowed as well as the abundantly endowed, will enjoy higher welfare with specialization according to the principle of comparative advantage and trade with one another unencumbered by politically imposed constraints.
Modern elaborations of the theory of comparative advantage recognize at least five bases for regional comparative advantages: resource endowments, cultural preferences, known technologies, scale economies, and company-specific knowledge. The first three are endogenous to locale; the last two technically are independent of geography, but may become location specific at the discretion of production decision makers. For purpose of illustration, it is usual in trade theory to hypothesize a two-resource, two-commodity, two-region world. Suppose one of the regions, A, is abundantly endowed with capital resources but has only enough labor to operate its capital stock, and that the other region, B, is abundantly endowed with labor but has a small amount of capital that serves as minimal tools for the labor. The two regions produce two commodities, X which under technologies known in both regions requires a great deal of labor but not much capital, and Y which uses substantial amounts of capital but only a little labor. If the two regions employ identical technologies for producing the two goods and further have identical preference functions, region A should specialize in producing good Y, whereas region B should produce more of good X. Each should trade some of its specialty to the other in exchange for some of the other's specialty.
Suppose that the two regions have identical resource endowments and know the same productive technologies. While people in both regions consume both goods, suppose that people in region A have a stronger preference for X, the labor intensive good, while people in region B like Y, the capital intensive good. In this case, it would be appropriate for region A to specialize in producing X and region B in producing Y. Each should trade some of its output to the other in order to achieve consumption generalization in both regions. In this case, the basis for comparative advantage is differential preferences rather than resource endowments.
As a third possibility, suppose that the two regions possess identical resource endowments and share a common preference system, but that scientists and engineers in region A have advanced technology with respect to the production of X so as to economize on labor, whereas common technology continues to be used in the production of Y, the capital intensive good, in both countries. Again, intuition suggests that region A should specialize in the production of X leaving region B to specialize in production of Y. They should trade some of their respective specialties to each other. The basis of comparative advantage here is differential technologies rather than resource endowments or preferences. Scale economies and company-specific knowledge may also serve as bases for regional comparative advantage.
It would be highly unlikely in any of these cases that perfect specialization (i.e., only X is produced in A and only Y is produced in B) would result. Both goods would continue to be produced in both regions, but in each region more of the comparative advantage good would be produced, and less of the comparative disadvantaged good(s). Also, the real world is composed of many regions, some of which are similar to others in respect to resource endowments, preferences, or technologies, and different from the other regions in various respects. The basis for comparative advantage of each may lie in one of these areas or a combination of them. Empirical evidence suggests that a larger volume of the world's trade is conducted among regions that are similar in income levels and preferences, than among regions that are widely divergent in any of these areas.
Qualifications to the Principle of Comparative Advantage
As noted in previous chapters, managerial opportunities and threats are to be found in almost any circumstances, including those of interregional trade. Certain qualifications to the argument presented to this point should be noted. One is that comparative advantages, whether attributable to resource endowments, preferences, or technologies, are not "struck in stone," i.e., they are changeable. Circumstances of resource depletion can terminate a former comparative advantage based on the richness of a resource endowment. The discovery of a new deposit or pool of a natural resource can confer a comparative advantage. Population growth or immigration may confer a comparative advantage in producing labor intensive goods where one formerly did not exist. By the same token, emigration may result in depletion of a former comparative advantage based on labor abundance. Natural disasters such as a volcanic eruption, a hurricane, or a freeze that destroys a crop stock may bring to an end some historic comparative advantage. Changing preferences away from "old" goods and toward newly developed ones may shift comparative advantage from regions specializing in the "old" and toward regions specializing in the "new."The forms of comparative advantage transition noted above follow from natural or market phenomena that are not under the control of the firm. One of the most significant forms of change in comparative advantages comes about through technological advances that develop new items or new processes that economize on scarce resources. Another significant phenomenon that may change comparative advantage is capital investment. Regions that formerly were capital scarce may become capital abundant, as for example the newly industrialized countries ("NICs") of South Asia. The reason that these two forms of comparative advantage transition are significant to managerial decision making is that they are implemented at the discretion of managers of firms. It is by mounting an effort at research and development (R&D) or by capital investment that managerial decision makers may seize entrepreneurial opportunities and deliberately change the competitiveness of their firms and the comparative advantages of their regions.
The International Dimension
To this point we have been discussing interregional trade; in the so-called "pure theory of trade" there is no distinction between interregional and international trade. The emergence of national identity and the nation state over the past four centuries have enabled two additional factors that provide for regional differentiation: nationalism and the operations of government.The interests of governments in international commerce have necessitated another qualification to the comparative advantage theory. The government may attempt to protect an old domestic industry in order to preserve a comparative advantage that is fleeing to foreign regions. An example is the cotton textile industry as it moves from the South of the United States to East and South Asia. Such protection may take the forms of subsidies to the domestic industry or quotas or tariffs imposed on imported merchandise. Or the government may promote the development of what is believed to be a latent comparative advantage of the region by subsidizing a so-called "infant industry." A recent example of this may be the developing electronics industries in India and Singapore.
Government may attempt to neutralize another region's comparative advantage by imposing an import tariff that is intended to eliminate a foreign cost advantage ("leveling the playing field"). The government may impose an import quota as a means of limiting the damage resulting from importation of an item that can be produced at lower cost elsewhere. Or the government may take "compensatory" action in any of these areas to offset some policy being implemented by the government of another region. In any of these cases of protection, the effect will be to diminish any potential for gain by comparative advantage specialization.
National identity leads to nationalism, a sort of emotional cement that binds together people of the same cultural background. They may share a common history and heritage; they may be more-or-less homogeneous with respect to race and ethnicity; typically they subscribe to the same religion or various sects or denominations of a common religion; the vast majority of them speak the same language; and, most importantly, they share a common vision about what it means to be a citizen of the nation. The term is often used to describe a "nation of people" or simply "a people" in the biblical sense (the "Children of Israel" in the Bible are an example of a nation in this sense). The emotional cement of nationalism may reveal itself in the form of patriotism, i.e., love of homeland, its cultural and political heritage, its flag.
Other terms such as provincialism or regionalism may attain almost the same sense of nationalism, but with respect to the attitudes of people in more restricted geographic locales. Belgians typically are much more nationalistic with respect to being Flemish or Walonian than they are about being Belgian. It is more important to some in the United States to be Texans or Southerners than it is to be American. The European Union is attempting to establish a sort of super-national regionalism so that citizens of the fifteen member states will begin to feel a sense of European nationalism that eventually may displace nation-state nationalism. Although there is no good term to describe it, a similar emotional cement often exists among the students and alumni of an American state university, especially when in athletic competition with a rival state university.
Nation states are political entities defined by boundaries encompassing areas that may coincide closely with that populated by a "nation of people" in the biblical sense. Sometimes a nation state encompasses two or more nations of peoples. American Indian tribes have often been referred to as "nations;" there were many nationalities in the former Soviet Union; modern India encompasses numerous tribal peoples. In the early 1990s, the various nationalities contained by both the Soviet Union and Yugoslavia began to pull apart.
Occasionally political boundaries separating nation states divide peoples of the same nationality. The post-war political division of Europe left the German people separated by "walls" as well as borders. In South Asia, the Bengali tribal people are split by the India-Bangladesh border. The Pakistan-Afghanistan border divides the Baluchi people, while the Pakistan-India border separates Punjabi tribal people. Separatist movements in these and other areas may have as their goal the reunification of peoples of the same nationality that have been separated by political boundaries.
Nation states also may not coincide with economic regions that are characterized by the possession of natural resources. Both the United States of America and the Russian Republic include numerous uniquely definable economic regions. Sometimes national boundaries split a common resource endowment region. Europeans have often redrawn national boundaries across the rich coal and iron deposits of the Alsace-Lorraine region.
The essential characteristic of the nation state is its possession and exercise of national sovereignty by the government of the nation state. "National sovereignty" means that the government of the state has the authority and the power to do anything it wishes with respect to the peoples and resources contained within its political boundaries. This power includes the ability to determine the form of economic organization of the economy of the state (until recently, the government of the former U.S.S.R. mandated socialism), and to impose protectionist measures with respect to the industries within the economy (the government of the U.S.A. has a long history of protectionism). It includes the right to insist upon the use of a national currency within the realm and to exclude the currencies preferred by others. Sometimes this authority and power leads to human rights abuses to which people and authorities in other nation states raise objections. Such exercise of discretion by the state is constrained only by the tolerance of its citizens and by attitudes and military prowess of other nation states.
Currency Diversity
One of the most critical factors that sets international trade apart from interregional trade is a consequence of the exercise of national sovereignty: the use of different currencies in different nation states. Because the dollar in used in the U.S. economy while the pound sterling is accepted exclusively in the United Kingdom, the balance of payments between the U.S. and the U.K. is important to economic and political considerations in both countries. The dollar-sterling exchange rate is critical to the volume of goods and services entering into international commerce between the two countries at any point in time.Where the same currency is used throughout a region, these matters become irrelevant. In the United States, who is concerned about the balance of payments between South Carolina and New York? And what about the exchange rate between the currency used in South Carolina and that accepted in New York (both use the U.S. dollar)? In the European Union the British still insist upon the pound sterling while the French use francs and the Germans use marks. The U.K.-French and U.K.-German balances of payments continue as hot issues, as do the pound-franc and pound-mark exchange rates. This is true especially since governments in some of these countries (Germany, in particular) insist upon stabilizing the exchange rates while governments of others (notably the U.K.) are inclined to use currency devaluation or exchange rate fluctuation as means of correcting balance of payments disequilibria. The Maastricht Treaty of 1992 provides for the establishment of a common currency in Europe by 1999 once certain entry conditions are met, but it appears that nationalism within Europe may prevent the attainment of currency union.
Currency matters spill over upon the commercial sectors of the international trading partners. We venture a guess that these issues will become irrelevant in Europe only when Europeans can adopt and accept a common currency such as the Euro or one of the constituent currencies. But there will still be problems in the balance of payments between the U.S. and Europe and with the dollar-Euro exchange rate until such time that Americans and Europeans can agree to use a common currency.
The Cultural Dimension
The analysis of nationalism would be much simpler if every nation state were associated exclusively with a certain nation of people. But as we have already noted, this is not the case. Whether we are speaking of the nation state or a particular nation of people who share a common heritage, the principal implication of nationalism is that there are significant differences among populations that yield important consequences for trade and the location of economic activity. These differences may spring from natural phenomena such as heritage, customs, language, etc., or they may be artificially imposed by the behavior of the governments of the nation states.Even if political relationships are not involved, differences of national heritages and languages lead to suspicions about the customs and intentions of "foreigners," and in extreme cases to xenophobia, i.e., fear and hatred of foreigners. An extreme economic consequence of xenophobia is the attempt to achieve autarky. The important point is that nationalism, whether emanating from cultural differences or state sovereignty, tends to diminish the potential for gains from interregional and international specialization and trade. In the extreme, nationalism can completely eliminate such potential gains if sovereign national governments pursue strategies of extreme political isolation and economic autarky.
Because of nationalism, it is necessary to recognize that comparative advantage may be based upon preferences that differ by regions that are defined by national boundaries as well as by cultural heritage. It is also necessary to note that natural comparative advantages may be enhanced or neutralized by the discretionary actions of government officials.
The managerial implications of nationalism, whether based in cultural differences or the exercise of state sovereignty, is that business decision makers wishing to buy, sell, or produce in other countries must come to an understanding of the cultural characteristics and governmental practices of the other countries. It is these differences that make foreign dealings appear to be mysterious, difficult, and risky. The antidotes are acquaintance and familiarity with the foreign environments within which the firm expects to operate. Acquaintance and familiarity can be achieved through study, travel, and interaction with nationals from the target markets. The study should include examination of cross-cultural differences that lead to appreciation of customs and practices different from one's own.
One of the best ways to achieve such appreciation is to learn the languages of the peoples who live in the regions where the firm wishes to operate. Competence in the languages of the target markets may also be crucial to successful business dealings. Peoples in most countries of the world are multilingual; in some few countries (notably the United States) the norm seems to be monolinguality. A business negotiator who is knowledgeable of the trading partner's language as well as his or her own will likely have the upper hand over a negotiator who speaks only one language. Also, if one is not familiar with the trading partner's language, the partner will be able to lapse into his or her own language when speaking with associates. Finally, we may note that most people in other lands have greater appreciation of their trading partners if they can at least attempt to speak the local language.
What's Ahead
In this chapter we have explored the possibilities of engaging in international commerce, i.e., exporting to or importing from other regions of the world. But it is also feasible and potentially profitable to engage in direct foreign investment, i.e., to locate production in other regions of the world than the home country, and to engage in direct foreign investment to establish the foreign domiciled production facilities. Chapter 25 is devoted to the multinationalization of enterprise.BACK TO CONTENTS
CHAPTER 25. THE MULTINATIONALIZATION OF ENTERPRISE
We finished Chapter 24 with a notation that while regions of the world may have macro level comparative advantages, the operatives who have to discover and exploit those comparative advantages are micro level people who function as decision making agents of business firms. We should also note that business decision makers can attempt to change a region's comparative advantages through implementing technological change and capital investment. The acts of discovering, exploiting, and changing comparative advantages are essentially entrepreneurial in nature.
Macro level comparative advantages are region (or country) specific. The microecononmic vehicles for discovering, exploiting, and changing comparative advantages are competitive advantages that are company specific. Another way to say this is that no latent comparative advantages can be discovered or developed unless managers of business enterprises can establish and exploit competitive advantages over actual or potential rivals. The entrepreneurial motivations to do so are profitability, growth potential, and control over markets and production processes. How are these decision-making goals pursued?
The Location of Economic Activity
Some economic activity, by its very nature, must take place in close proximity to the markets that it serves. The restaurant and real estate businesses come readily to mind. In fact, most services must be rendered at the site of consumption (financial and insurance services may constitute exceptions). Other economic activity is more appropriately located nearer to sources of supply of the raw materials that are required as inputs in the final products. The over-riding principle is that under sufficiently competitive market conditions, commercial activity tends to locate relative to markets and input supplies where it can operate most profitably. Inappropriately located productive sites will yield lower returns or losses, and ultimately may result in failure and exit from the market.Two further locational principles can be identified. In order to minimize the combination of production and shipping costs, products that lose weight in the manufacturing process tend to be produced closer to sources of supplies of the inputs of greatest weight per unit cost. Products that gain weight in the production process tend to be produced nearer to their final markets. Examples of weight-losing manufacturing processes are found in the refinement of ores to produce metals of high purity. Any product that is assembled in stages from materials or components may serve as an example of a weight-gaining process.
Economic activity may relocate for a variety of reasons. One is simply that producers realize that their former sites are uneconomic relative to other sites. This realization may be brought upon them by the subnormal returns or outright losses that they suffer compared to those realized by producers in other locales. One of the most potent forms of industry relocation is the failure of productive ventures in one region at the same time that new ventures producing the same goods or services are started in another region. Capital is withdrawn and labor displaced at the former site, and new capital is invested and employees are recruited at the new site, but rarely by the same people.
One of the principal vehicles for industry relocation is changing comparative advantage. As we have already noted, comparative advantages are not "struck in stone." When comparative advantages change, either for natural reasons or because of human intervention, industry tends to relocate away from the former locus of the comparative advantage, and toward its new locus. Whether the comparative advantage has shifted regionally or from one country to others, locales where the advantage is departing may resist as strongly as possible their loss of advantage, and may solicit the offices of the governments of their countries to prevent the flight.
When a region's comparative advantages change, what business decision makers see are changing competitive advantages, not macro level comparative advantages. The entrepreneurially perceptive firm managers will see competitive opportunities in other industries or other locales sooner; the less perceptive and more risk averse will remain too long in their current industries or locales and ride their firms into decline and failure.
Economists can with confidence argue that specialization according to comparative advantage will maximize world welfare. One of the great ironies of the principle of comparative advantage is that the adjustment to a shift of comparative advantage can be extremely painful in regions that lose it, even while the gainers enjoy the ebullience associated with expanding output, employment, and profits. Usually all of the pains are suffered in one region, while all of the benefits are enjoyed in another. A loss of comparative advantage will be manifested to business firms by operating losses, business failures, distress sales of plant and equipment, a declining tax base, and disemployment. It is these conditions, especially when they result in threats of political instability, that command the attention of government officials. But if international economic realities truly have changed, any governmental action to "stem the tide" of a fleeing comparative advantage can only distort the international allocation of resources and lower efficiency and welfare, both at home and abroad.
Some productive resources tend to be more mobile than do others. It is often thought that labor is the most mobile resource while capital and natural resources are less mobile. There have been historical instances of human migrations for economic reasons. From the sixteenth century forward, people have left Western Europe for North and South America, South Africa, and Australia in search of greater opportunity, i.e., richer endowments of natural resources. The nineteenth century in the United States saw a great westward migration for similar reasons. Today, people are fleeing certain Eastern European countries for both political and economic reasons.
It is also possible to extract and ship natural resources to remote locations for processing, as it is possible to take the processing to the site of the extraction. A footloose industry is one in which both materials and capital are more mobile than the labor necessary to produce the output. A footloose industry need not locate near to either sources of raw materials or to markets for the product. The cotton textile industry may be an example of a footloose industry because it seems to move continually across the earth's geographic space in search of the lowest cost labor. This seems to be a case of "the mountain going to Muhammad," i.e., the industry going to the labor. Cultural heritage tends to militate against the mobility of labor across national boundaries. Technological advances in communications and transportation tend to render all industries ever more footloose because the declining costs of shipping materials and capital resources make them ever more mobile relative to labor.
Opportunities in an Open Economy World
Our discussion is intended to be suggestive of the many opportunities as well as threats to business enterprises in a world characterized by open economies. The term "open economy" refers to a situation where neither cultural nor governmental hindrances to enterprise prevent international trade, requirements sourcing, the location of production, or immigration. In a closed economy, the business decision maker has only to decide where within the economy to locate the enterprise, from whom to source materials requirements, and in which domestic markets to offer the produced goods and services. An economy becomes closed either because its people are so xenophobic and isolationist that they will not interact with foreigners, or because the government acts to diminish or prohibit foreign commerce. Even if an economy is not entirely closed by xenophobic attitudes or governmental hindrances to trade, the presence of such forces tend to constrain international commerce and diminish the potential benefits.When an economy is more-or-less open to international commerce, the range of decision options available to the business decision maker extend to considerations of
(b) whether to source materials requirements abroad;
(c) whether to locate production in other countries;
(d) whether to raise financial capital abroad; and
(e) whether to recruit employees and managerial personnel internationally.
As we noted at the beginning of Chapter 24, business decision makers in many countries do not make serious distinctions between domestic and international commerce. But for business decision makers in a large, inward looking country such as the United States, it may take a special orientation for a decision maker even to perceive the "foreign" opportunities, and an even more special attitude toward risk to be willing to delve into the unknown or mysterious facets of foreign commerce. This is what renders international operating decisions essentially entrepreneurial in nature.
The same decision criteria may be employed by the entrepreneurial decision maker irrespective of whether domestic or international operations are at issue. If the anticipated benefits of undertaking a new international operation exceed the estimated costs, the operation is economically justifiable. In case of an anticipated expansion of an on-going activity in the international arena, an excess of marginal benefits over marginal costs warrants the expansion. Similar criteria can be specified for contracting or terminating any international operation. The additional difficulty for international considerations is identifying all of the relevant benefits and costs. Because of the uncertainty and variability associated with the international arena, risk factors may be more significant than in known domestic markets.
It is a classification of convenience to identify four types of enterprises on the basis of their engagement in international commerce:
(2) A foreign firm is one that, with respect to a particular nation state, is organized or incorporated in a second nation state, but which is doing business by way of buying or selling in the domestic economy of the first nation state.
(3) An international firm is one that maintains principal office and productive facilities in one nation state and conducts buying and selling activity in that and other nation states.
(4) a multinational firm is one that maintains offices and productive facilities in multiple nation states and determines executive policy without preference or prejudice with respect to national origin or location.
The more risk averse is the management of a firm, the more likely it is to remain a purely domestic firm. Venturing into the realms of international and multinational operations requires willingness to assume risk. Needless to say, the vast majority of business firms in the world are either domestic or international firms; some of the latter are in the process of becoming true multinationals; there are indeed only a few firms in the world that have achieved true multinationality.
All firms engaged in international operations facilitate the mobility of resources and goods, and thereby contribute to allocative efficiency across national boundaries. International importers and exporters do so in response to international market incentives. Franklin R. Root (International Trade and Investment, South-Western Publishing Company, Sixth Edition, 1991) characterizes the multinational enterprise as an international transfer agent. Although it responds to external market forces, the multinational enterprise employs managerial discretion rather than market incentives to direct the flows of resources, capital, product, technology, and managerial expertise within itself and among its affiliates in other countries. In so doing it surmounts both market imperfections and political hindrances to market-initiated flows. The multinational enterprise thereby achieves greater allocative efficiency through the exercise of managerial discretion than can be achieved purely through international market transactions, especially if market transactions involve externalities.
The international opportunities open to a purely domestic firm are limited exclusively to the unsolicited interaction with foreign nationals who happen into the firm's place of business. The broader horizons of the international firm include possibilities of both importing and exporting as well as licensing and participating in joint ventures. The international firm may import final products to be marketed to customers within its economy, or to be re-exported to customers in other countries. It may also import raw materials, partially processed goods, or components to which it adds value in further processing, assembly, and packaging. These goods may then be marketed domestically or re-exported for sale or further processing in other countries. Even if the international firm has not imported materials or finished goods, it may export its domestically produced goods and services.
The impetus to export domestically produced goods is the perception of market opportunities in other countries that appear more profitable (or no less so) than domestic distribution. The impetus to import materials or components is the discovery of cost advantages in international sourcing compared to domestic sourcing. The impetus to import finished goods for domestic distribution may be either foreign cost advantage, the perception of domestic markets for uniquely foreign merchandise, or both. In fact, the strength of domestic demand for a foreign-made item may be great enough to outweigh its cost disadvantage; many American consumers appear willing to pay higher prices for certain foreign-made automobiles (e.g., Mercedes Benz, BMW, Jaguar) than for comparable domestically assembled vehicles (Cadillac, Lincoln).
Drives to Multinationalization
The multinational enterprise is subject to all of these drives plus others that lead it to establish or acquire productive facilities in countries other than that where its principal office is located. The establishment of such productive subsidiaries or affiliates requires foreign direct investment that is distinguished from portfolio investment. The former involves the construction or acquisition of facilities over which the firm exercises exclusive control while the latter involves only the acquisition of a small-enough share of outstanding stock that control is not intended or possible. The motivation to foreign portfolio investment is usually found in the anticipation that foreign rates of return are higher than domestic rates of return after allowing for risk differentials. However, there is little evidence to the effect that differences in expected rates of return alone can account for foreign direct investment by multinational enterprises.There is an extensive literature focusing upon the motives to undertake direct foreign investment. We shall here attempt only to examine the prominent theories and summarize the conclusions. Virtually all multinational enterprises are large concerns (in terms of invested capital, sales volumes, number of employees, etc.) that operate in oligopolistic markets. They therefore possess varying amounts of monopoly power in the sense of being able to exercise pricing discretion. Their monopoly power is based upon either scale economies or superior knowledge that confer firm-specific competitive advantages. Such competitive advantage may be applied anywhere in the world, and thus can serve as the basis of a region-specific comparative advantage only at those sites where management chooses to establish operations.
If the benefits of scale economies or knowledge assets are sufficient to outweigh the costs of distance, cultural differences, and dealings with foreign governments, the management of the multinational enterprise may expect greater income from operating in the foreign market than local firms can expect. To realize the larger incomes, the local firms would have to achieve comparable size (to exploit the economies of scale) or in some way acquire similar knowledge assets (which are costly to acquire). The reason that the multinational enterprise may be able to operate more economically in the foreign market than can local firms is that their knowledge assets were developed for the "home market," and thus are sunk costs; the marginal cost of development of the knowledge assets for the foreign market is therefore zero. But the marginal cost of acquiring such knowledge assets by local firms would be significantly non-zero. The exercise of superior knowledge by the multinational enterprise allows it to produce and sell differentiated products in the foreign market. This enables it to exercise monopoly pricing and capture economic rent for the knowledge assets.
A typical life cycle can be described for a product developed by a multinational enterprise. When the new product is introduced, production is initially retained in the home country (or where an affiliate first developed the new product) to allow close contact with design and production technical expertise. The product is sold in the domestic market and may be exported to foreign markets. However, as the product becomes standardized, the enterprise is able to shift production to affiliates in lower-cost foreign locales, most likely in other industrialized countries with large domestic and export markets so that scale economies can be exploited. A collateral phenomenon is that with standardization of the product, local firms can imitate the product (the competitive advantage of the superior knowledge assets begins to erode) to capture some of the multinational enterprise's export market. Foreign production at lower costs may then be a defensive measure undertaken by the multinational enterprise in order to preserve market share.
In the latter stages of the product's life cycle, production in the multinational enterprise's home market may cease as the product continues to be available only as an import from its foreign affiliates. Continuing developments of new knowledge assets by the multinational enterprise are needed to sustain its home-country operations. It is in the continuing development of knowledge assets that the home country of the multinational enterprise may have its real comparative advantage.
Because the multinational enterprise is likely to be an oligopoly with wide dispersion of ownership shares, its management may be more attuned to growth and share-of-market objectives than to profit per se. The Baumol sales optimization model (described in Chapter 16) may be an appropriate vehicle for analysis of the typical multinational enterprise. The development of differentiated products and their sale in world markets is one means by which the multinational may be able to achieve an increased market share or a continually growing volume of sales. Competitor oligopolists are likely to feel compelled to follow a leader into international production and marketing as defensive measures in order to preserve their market shares. Such oligopolistic bunching of entry into foreign markets by competing multinational enterprises tends to be a common phenomenon.
Multinational enterprises may be more inclined to enter into foreign production of their products rather than exporting from the home country or licensing foreign producers. The reason is that by so doing they can internalize control of their superior knowledge assets and thereby protect them from erosion for a longer time. Because a newly developed superior knowledge tends to become a public good very quickly as others master or imitate it, the developer can capture an economic rent for it only as long as the knowledge is secret or can be held proprietary. Exporting the good from the domestic productive facilities, or licensing the production technology to foreign producers, tends to accelerate the deterioration of the proprietary nature of the knowledge assets. This may be regarded as an externality of market-organized transactions, i.e., the market price after the newly developed knowledge becomes a public good fails to reward the developer for the costs of developing the new knowledge. This market imperfection can be averted by the multinational enterprise by retaining sole proprietary exploitation of its superior knowledge assets within the firm and its foreign affiliates rather than letting the knowledge assets leak to the rest of the world through market transactions.
Threats in an Open Economy
While the open economy provides a whole range of opportunities for the enterprise, it also holds some threats. The principal threat to domestic producers comes from foreign producers, especially if they can achieve lower production costs or produce products that are differentiated by virtue of their foreign manufacture. Foreign producers are often perceived to "dump" their products in domestic markets as a means of driving domestic producers from the market, thereby conferring monopoly power upon the foreign producers.Although lower prices of foreign products may reflect lower direct (variable) production costs, another rationale for such apparent dumping is that overhead costs typically have been fully allocated by the foreign producer to the output produced for its domestic market. In this case the price of output destined for foreign markets needs to cover only the direct (or variable) costs. Hence the price of the output produced for the foreign market (excluding any allowance for overhead costs) can be lower than the domestic price (including full allocation of overhead costs).
Technically, "dumping" means that a foreign producer is selling in a domestic market at a price below the foreign producer's full cost of production (including overhead cost allocation). However, it is virtually never possible for one who charges another with dumping to gain adequate information about the other's costs (direct or overhead) of production. For this reason, the "political" definition of dumping is sale by the foreign producer in the domestic market at a price below the domestic producer's full cost of production (including overhead cost allocation). Sometimes domestic producers claim that the foreign producer is dumping when the price is simply below domestic prices. This is a "political" definition because it usually serves as the basis for an appeal by domestic producers to their governments for protection from the foreign producers who are reputed to be engaged in dumping.
The problem with the political definition of dumping is that it really cannot be distinguished from the phenomenon of competitive pricing. For example, if another domestic producer were selling at a price below our own preferred price, or even at a price below our own per-unit cost of production including overhead cost allocation (ATC), we could hardly charge our domestic competitor with dumping. The most that we could do is complain about competitive pricing that may be predatory in nature. But if a foreign firm engages in exactly the same behavior, domestic producers are quick to charge dumping and appeal to their governments for relief.
Actions by governments are also potential sources of threats as well as opportunities. If domestic producers can enlist the authority of government to protect them by imposing tariffs or quotas, this constitutes an opportunity for domestic producers to sustain or expand production and employment (in spite of a lack of comparative advantage), but it is a threat both to foreign exporters and to domestic importers. By the same token, actions by foreign governments to protect their industries will constitute threats to domestic firms that may have real competitive advantages. As we have already noted, protection also tends to distort the world-wide allocation of resources and diminish the potential for gains from trade.
Governmentally imposed quotas implemented by import or export licensing also constitutes a source of threat for domestic firms. Import licensing is more commonly used as a means of protecting domestic producers, but governments of resource-rich regions (particularly petroleum exporting countries) may use export licensing as a means of capturing income from the foreign sale of the resource. The source of the threat is that uncertainty arises as to which firms can acquire licenses to import or export what quantities of goods. Production and shipping schedules may be significantly disrupted, and earnings from sales of imported materials or goods for export may be jeopardized.
But the greatest threat to domestic producers in any country is an adverse shift of comparative advantage. Such may come about because of a natural disaster that destroys a productive advantage, or it may result simply from depletion of an historic natural resource endowment. In the modern world, an adverse shift of comparative advantage is more likely to have been engineered by foreign competitors who develop superior knowledge assets or engage in such massive capital investment as to create a capital-abundant productive environment. Also, technical advances in communications and transportation may render capital and resources so much more mobile than labor that footloose industries move very easily from one part of the world to another in search of ever lower-cost labor. Such a fleeting comparative advantage will severely threaten the viability of firms where the industry historically has been located.
Finally, we note that in oligopolistic markets (which may characterize most of the markets in the modern world) the competitive actions by any single firm can be expected to threaten the market share and profitability of any other firm in the market. If the others do not rise to the occasion they will certainly suffer declining market shares and operating losses that may culminate in failure. This phenomenon is surely so much more intense in an open-economy world than in protected domestic economies.
Even though the threats in an open economy may appear substantial, the opportunities found in international commerce almost surely outweigh them. The evidence to support this contention lies in the expanding volume of both trade and direct foreign investment throughout the world. But as a revisitation to the opening passages of Chapter 23, we note that these concepts and problems of internationalism will tend to diminish in importance as economies become more open, as their peoples become more comfortable with international commerce, as economic and political integration ensues, and as market imperfections diminish with technological advances in communications and transportation.
As we end this chapter, perhaps it would be helpful to list some of the operational objectives that firms pursue in their quests for global competitive advantage. Firms attempt to establish market presences in other regions of the world in order to:
- increase sales revenue and hence profitability;
- achieve unit sales or revenue growth targets;
- increase share of market;
- achieve enhanced oligopolistic position by preempting competitors;
- preserve oligopolistic position by meeting or neutralizing competitors who have already arrived;
- diminish dependence upon mature or stagnant markets;
- increase demand to allow spreading overhead in existing plants; and
- increasing demand to exploit economies of scale from increasing plant size.
- surmount nationalistic preferences for domestically made goods;
- seek higher rates of return than can be achieved elsewhere or by local competitors;
- internalize control of knowledge assets while exploiting them;
- acquire new knowledge resources; and
- circumvent trade barriers.
What's Ahead
The next chapter extends the international scope into the realm of developing economies. Because trade and development are inextricably intertwined, we shall use the international dimension as the platform for launching our survey of entrepreneurial opportunities in developing economies.BACK TO CONTENTS
CHAPTER 26. OPPORTUNITIES IN DEVELOPING ECONOMIES
Developing Economy Terminology
We choose the term "lesser developed country" (LDC) as perhaps the least problematic of the terms that have been employed in the literature to refer to low-income countries in the so-called "third world". These countries are characterized by primary product production and the use of primitive productive techniques. The "first world" consists of the industrialized market economies of Europe and North America; the "second world" encompasses the socialistic economies of the former Sino-Soviet bloc; the "third world" consists of the low-income and underdeveloped countries of the South and East. The distinction between the "first" and "second" worlds is being made obscure by the transitions from socialism to market economy in the latter, and by experimentations with statism in the former.The concept of "lesser developed" is of course relative. All economies except some in the very most remote and primitive parts of the world have experienced some development, some income growth, some adoption of advanced technologies, some industrialization. And many technologically advanced, financially mature economies surely still are "underdeveloped" relative to their resource endowments and potentials for continued development.
We shall take the term LDC to refer to countries that lag behind the technological conditions and income levels of the typical higher income, more industrialized, more technologically advanced economies of North America, Europe, and the Pacific rim. The term "newly industrialized country" (NIC) signifies countries in an intermediate state that are making progress from conditions of underdevelopment toward development.
Risk Factors
Managerial and entrepreneurial decision making in LDC economies should employ the same benefit-cost criteria as employed in advanced economies when considering either domestic or international operations. The problems of LDC decision making center about even greater market imperfections, even less market information, and ever greater market externalities than are found in more advance economies. This means that risks may be greater in any or all decision settings in the LDC economy. It also means that much of the decision making in regard to business operations in LDC economies should be characterized more as entrepreneurial than managerial.As we noted in Chapter 2, the decision maker must compile a storehouse of experience upon which to base assessments of risk. And as noted in Chapter 24 in discussing prospects for international operations, the best way to do this is to become as familiar as possible with the LDC decision setting. This may prove difficult without direct involvement within the LDC environment.
The Role of Entrepreneurship
A significant reason for underdevelopment in the third world is lack of entrepreneurship. A region may have a rich endowment of various natural resources, but it will not be exploited without entrepreneurs to assume risk in innovation. Another region may be essentially devoid of natural resource endowments, but an entrepreneur may still perceive a productive opportunity and "make it happen."A prerequisite to initiating an on-going development process is to provide conditions conducive to and tolerant of entrepreneurship. Where enterprise is essentially lacking in an LDC, the avenues of international trade and investment may provide just the "jump start" necessary to promote on-going development.
An important comparative advantage of the developed part of the world lies in its endowment of entrepreneurial capacity. The exercise of entrepreneurship may be one of the most valuable contributions of the multinational enterprise to the LDC economies within which they operate. The problem for the LDC then is to indiginize the entrepreneurial process so that it will be taken over by local business interests.
The Cultural Environment
Foreign involvement in the LDC environment begs even greater questions about cross-cultural differences than occur when firms become involved in other economies that are similar to their own. Customs and dress are even more exotic. Business practices are likely to be even more closely tied to cultural heritage than the standards of business dealings that have emerged among European and North American countries. In many third-world countries, women do not enjoy the same acceptance in business dealings as do male managers.Although nineteenth and early-twentieth century colonialism has left a legacy of European language blocs in the third world, a wide variety of national and tribal languages and dialects continue to be spoken. Managers of multinational enterprises attempting to do business in third-world countries should not expect to rely upon their home-country languages or those studied in high school or college even though many people in the LDC may understand it as a second or third language. Expatriate managers often find greater acceptance and facilitation of business dealings when they can speak (even meagerly) the language of the realm and avoid faux pas related to cultural differences.
Infrastructure
One of the crucial problems of the LDC decision setting is the underdeveloped nature of infrastructure facilities that are taken for granted in more advanced economies. Transportation and communications facilities may be primitive; electricity and gas generation and transmission facilities may be lacking; sanitation and health care may be at an entirely different level than in the more advanced economy. The firm may find itself having to provide various of these services or facilities simply to be able to conduct its intended lines of business. Indeed, the scarcity of such infrastructure facilities may constitute rich entrepreneurial opportunities for both domestic and foreign firms.A consequence of infrastructure underdevelopment is that it may not be possible to rely upon the commercial environment of the LDC to provide input supplies, complementary services, maintenance and repair support, or even marketing channels for distribution of outputs. A productive facility in an LDC is much more likely to have to be more vertically integrated, self-contained, and stand-alone than needs to be planned for and achieved in a more advanced economy.
Capital Scarcity
A common problem in many LDC economies is that directly productive capital is scarce and technologies are primitive. The so-called "vicious circle of poverty" turns upon the capital scarcity that ensures low labor productivity. The low productivity enables only meager wages. Incomes that are near (or below) the threshold of subsistence needs limit the capacity of the society to save. Little indigenous saving limits the investment potential of the society. Finally, inadequate investment ensures that capital will remain scarce.But the circle of poverty may be broken at numerous points, any of which may provide entrepreneurial opportunities for interests within or from outside the LDC economy. The capital scarcity itself may pose investment opportunities since interest rates should provide higher returns than available in capital abundant parts of the world. Higher interest rates should attract foreign savings either through portfolio or direct foreign investment, or through international bank lending. Foreign lenders will also insist upon even higher interest rates than warranted by capital scarcity so as to include risk premiums against the unknown and uncertain conditions in the LDC environment. Low wages should attract footloose industries from other parts of the world, but they may be perceived to be attempting to exploit an impoverished population.
Labor and Technology
In an LDC the manager should expect to employ labor of pre- or early-industrial attitudes and conditioning. Such a labor force may be attuned to the agricultural sector during peak planting and harvesting seasons, and may thus be absent from the commercial or industrial work place at those times. Labor in an LDC typically is not (yet) attuned to the discipline of the clock or to required manufacturing tolerances.A critical problem of managerial decision making in the LDC setting is choice of "appropriate technologies." The newest and most advanced technology employed in "the West" is not likely to be appropriate to the LDC, but numerous mistakes have been made in adopting Western technologies in LDC economies. The "appropriateness" of a technology should be judged with respect to the resource endowments of the region.
A region that enjoys an abundance of labor but a scarcity of capital should employ labor-using and capital-saving technologies. Unfortunately for many LDC economies, the technologies employed in the West have been developed in capital abundant settings to conserve upon scarce labor, and thus are not appropriate to the LDC setting without extensive adaptation.
Trade and Development
International trade and foreign direct investment are recognized by development economists to be two of the potentially most effective routes to the further development of an LDC economy. Specialization according to comparative advantage and trade can allow the LDC to develop its latent potentials. Foreign direct investment may help to change comparative advantages by relieving capital scarcity and technological backwardness. It may also help to diversity the LDC economy so that it is not so reliant upon one or a few crops or industries.The operations of international and multinational firms can bring labor skills, managerial expertise, and new technologies to the LDC when the firms function as international transfer agents. Multinational enterprises prefer to establish subsidiaries or affiliates in the foreign environment in order to earn rents form their superior knowledge assets while maintaining control over them. The LDC economy will be the beneficiary of the employment and training provided by the multinational firm, and inevitably knowledge asset transfers to people in the LDC will occur deliberately or by leakage.
The Role of the Government
The government of the LDC may pose additional dimensions in the managerial decision setting that are not significant factors in the Western economy. An enlightened government will welcome both international trade and foreign direct investment by multinational enterprises; some have been willing to provide "tax holidays" as inducements to new foreign investment. However, governments of some LDC economies are suspicious of foreign involvements in their economies to the point of regulating and constraining the operations of foreign firms in their economies. One reason is that a multinational enterprise may generate larger gross revenues from its worldwide operations than the annual gross domestic product of the LDC.It is not unusual for LDC host governments to subsidize domestic "infant industries" in their economies, and to protect them from foreign competition with restrictive import quotas or tariffs. The government of the LDC may limit foreign investors to only minority (less than 50 percent) positions in domestic ventures, and may also impose a "sunset law" requiring the foreign investor to withdraw within a specified time period. Laws may also require the progressive indigenization of the labor force and the management. Affiliates of multinational enterprises may find difficulties in importing materials requirements or needed machinery.
The multinational firm is likely to face high taxes on inventories, sales, and plant and equipment. Tax rates may be unexpectedly increased after local operations are started. The multinational enterprise may also encounter difficulties in repatriating profits earned by its affiliate in the LDC.
Finally, we should note that in some LDCs there are distinct risks of nationalization of foreign-owned facilities, and there is no guarantee that the host government will provide adequate (or any) compensation for the assets nationalized.
Entrepreneurial Opportunities
Our discussion of the LDC setting has of course not been exhaustive; it is intended only to give the reader an overview of some of the problems to be encountered in decision settings in lesser developed countries. But we do not intend with this overview to discourage the manager from considering operations within the LDC. There are great opportunities to be considered in the LDC decision setting. A rational approach to such involvement is to identify all of the relevant benefits and costs emanating from such involvement, carefully assess the attendant risks, make adjustments to estimates of benefits and costs to account for the risks, and proceed if the involvement appears viable after allowing for the risks.
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