SMtext
Simulation Modeling
the Business Environment
Richard A. Stanford
Copyright 2011 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. INTRODUCTION
Chapter 1. The Role of Modeling in Economic Analysis
PART B. THEORETICAL FOUNDATIONS
Chapter 2. Consumer Behavior
Chapter 3. Demand and Revenue
Chapter 4. Production
Chapter 5. Costs
PART C. THEORIES OF THE FIRM
Chapter 6. The Competitive Environment
Chapter 7. Pure Monopoly
Chapter 8. Monopolistic Competition
Chapter 9. Oligopolistic Competition
Chapter 10. Extending the Model of the Firm
PART D. CONCLUSION
Chapter 11. Realism, Accuracy, and Specificity in Models
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PREFACE
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.
In the microeconomic analysis the theory of the firm, the operations of a business firm are elaborated with mathematical models that for classroom illustration purposes are rendered both algebraically and graphically. This book employs a Java applet, SIMMOD, that can be implemented on the web to illustrate many of the features of the theory of the firm.
The chapters in Part A of this book introduce economic method and describe the process of modeling a business firm.
The chapters in Part B lay out the theoretical foundations of the theory of the firm: consumer behavior, demand, production, and cost.
Part C elaborates the competitive environment ranging from pure competition through monopolistic and oligopolistic competition to pure monopoly.
Part D offers conclusions in regard to realism and accuracy in modeling.
Richard A. Stanford
Summer, 2011
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PART A. INTRODUCTION
CHAPTER 1. 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.
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? Perhaps only a chuckle. 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 modeling are presented.
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.
Modeling Procedures Used in Economic Analysis
The modeling procedures commonly used in economic analysis begin as 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. 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.
Simulation Modeling
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.SIMMOD, a Java applet, employs an nth-order (up to 4th order) polynomial equation to simulate various economic mechanisms, including demand-supply, production functions, production possibilities, revenue and cost functions, and profit maximization relationships. The general form of an nth order equation is as follows:
SIMMOD data-entry text boxes for two functions (revenue and cost in this example) are displayed in Figure 2-1. Once the graphic model is displayed, the user may change any parameter value by highlighting the values to be changed in any of the text boxes and typing in new values. When all parameter values are as desired, the model display may be invoked by clicking on the "Plot Functions" button. This process may be repeated time after time to cause the displayed graphic plots to shift.
Figure 1-1.
How can the SIMMOD simulation applet be put to good use? The author employed it to discover the parameter values of "well behaved" functions to be used in illustrations for this book. Students of economics and management might use it to explore the implications of varying parameter values in functions that they are studying. One of the most effective uses of such a simulation model is for managers to examine the effects of shifts in any of their relevant revenue, production, or cost functions before having to make decisions that impact their operations. It is this potential that we illustrate in the following chapters.
PART B. THEORETICAL FOUNDATIONS
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CHAPTER 2. CONSUMER BEHAVIOR
Chapter 4 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.
Chapter 3 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. In this chapter we begin with a consideration of the principles of consumer behavior.
Consumer Behavior
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. 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.
Utility
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 pre-acquisition 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 2-1.
Figure 2-1 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 (or assuming constant) all other factors. The graph of the TU function can be perceived to be a two-dimensional section through a three-dimensional utility surface. As it is illustrated in panel (a) of Figure 2-1, 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 marginal utility (MU) curve derived from the TU curve illustrates the rate of change of total utility as the quantity consumed of the good increases (marginal utility may be computed as the first derivative of the total utility function). 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 2-1, curve MD (marginal disutility) represents the marginal cost of acquiring additional units of the commodity (constant as illustrated). The consumer should push consumption 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 2-1 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.
Simulation Modeling of Consumer Behavior
In Chapter 1 we introduced the SIMMOD Java applet computer program as a model simulation system. Our purpose is this section is to elaborate its potential usefulness in the analysis of utility theory.Suppose that a consumer's initial utility function for a product is given by the equation,
Figure 2-2. The initial loci of the total, average, and marginal utility functions.
SIMMOD enables the user to change any of the parameters of the utility model. Suppose that in response to a consumer's changing taste for the product, the coefficient of the linear term (Q) changes from 8 to 10. The revised equation becomes
Figure 2-3. The initial (1) and subsequent (2) loci of the total, average, and marginal utility functions.
What are the circumstances under which such information about the implications of a parameter change might be useful? A consumer's preferences are normally subject to the buffeting of market forces and changing personal preferences and perceptions that may cause his or her total utility curve to shift, and the total average and marginal utility curves to shift accordingly.
As we shall note in Chapter 3, if the firm can achieve any degree of control over market demand, it may be able by engaging in well-designed marketing strategies to change its customers' utility functions in order to shift the market demand curve for its product. Or, it may be able to prevent the leftward shift of its product demand curve in the face of aggressive marketing drives by competitors to improve prospective customers' perceptions of their products.
CHAPTER 3. DEMAND AND REVENUE
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 proposition 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 as described in Chapter 2. 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 a good or service falls, the consumer can purchase more of that item itself, more of other items that he or she normally consumes, or retain unspent purchasing power. The decrease in the price of the item then results in an implicit increase of his or her 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 or she normally purchases, or spend more than he or she 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
Figure 3-1.
We have drawn the demand curve in Figure 3-1 as a straight line with a negative slope. The equation for such a linear demand curve can be given in slope-intercept form as
If the demand curve illustrated in Figure 3-1 is a realistic representation of a 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
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 3-1, 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
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 3-2. 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 3-2.
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,
Figure 3-3.
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 3-4.
The three-dimensional perspective enables another important observation. In Figure 3-3, 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 3-5. 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
Figure 3-5.
The three-dimensional surface represented in Figure 3-3 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 Figure 3-5 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 steak 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 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
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
(10) Q = 20 + (-4)P.
We have omitted the subscript "d" in equation (1) 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 = P x Q, we may derive the total revenue equation (12) by multiplying equation (11) through by Q,
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,
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 3-6; 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 3-6 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 at 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 3-6.
Figure 3-7 is a reproduction of Figure 3-6, 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 3-7, prices successively lower than P3 yield revenue rectangles of progressively smaller area. The graphic approach illustrated in Figure 3-7 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 3-7.
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.
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
Equation (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 3-8 is a reproduction of Figure 6-7, but with the MR curve drawn in. The most important observation to make in regard to Figure 3-8 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 maximum reaches its maximum value.
Figure 3-8.
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 6 through 9 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.
Simulation Modeling Demand and Revenue
In Chapter 2 we introduced the SIMMOD Java applet computer program as a model simulation system. Our purpose is this section is to elaborate its potential usefulness in the analysis of demand and revenue relationships. Suppose that an initial total revenue function for a product is given by the equation,
Figure 3-9. The initial loci of the total, average, and marginal revenue functions.
SIMMOD enables the user to change any of the parameters of the revenue model. Suppose that in response to a successful marketing effort, the coefficient of the linear term (Q) is changed from 60 to 62. The revised equation becomes
Figure 3-10. The initial (1) and subsequent (2) loci of the total, average, and marginal revenue functions.
What are the circumstances under which such information about the implications of a parameter change might be useful? The business firm's product demands are normally subject to the buffeting of market forces that cause the demand curve to shift left or right, and the total revenue function to shift accordingly. As we shall note in Chapters 7 through 11, if the firm can achieve any degree of monopoly power, it can exert some control over its price. It may also be able by engaging in appropriate marketing strategies to shift its demand curve to the right to capture a larger market share. Or, it may be able to prevent the leftward shift of its demand curve in the face of aggressive marketing drives by its competitors.
Assuming that by market research to gather data and regression analysis to estimate parameters the management of the firm has a good idea of the equations of its demand and revenue functions, it can model them with SIMMOD. When market forces cause the demand to shift, the management can then make corresponding changes to the revenue function in SIMMOD to approximate the market shifts, and thereby analyze the likely effects. Or, with adequate monopoly power, the management of the firm may devise possible offensive strategies to shift demand and revenue functions to the right, or defensive strategies to prevent their leftward shifts. In either case, prospective shifts of functions may be simulated in SIMMOD to allow examining the likely implications of the strategies.
CHAPTER 4. PRODUCTION
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.
Managerial Functions in the Production Process
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.
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 inputs 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 the chapters in Part C. 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
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:
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 ).
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 a recipe, i.e., a list of ingredients together with instructions for combining them in the preparation of some quantity of a desired product.
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
Four hypothesized shapes for the three-dimensional production surfaces are illustrated in Figure 4-1. 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.
Figure 4-1. Hypothesized shapes of production surfaces.
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 4-1 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.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.
Slicing the Production Surface
[The so-called "vertical slice" approach discussed in this section 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. Elaboration of a vertical slice approach may be found in the Appendix to Chapter 8 of A Managerial Economics Primer by the author.]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 4-1, panel (d). It is reproduced in an enlarged format in Figure 4-2. 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 4-1. Second, the smooth, continuous surface illustrated in Figure 4-2 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 4-2. A labor-variable section through a production surface.
A short-run production perspective may be analyzed in Figure 4-2 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 4-1.
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 4-2, 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 4-2. 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 4-2 by extracting it from the surface and laying it out on a set of two-dimensional coordinate axes in panel (a) of Figure 4-3. 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 4-3. Total, Average, and Marginal Product Curves.
Employing analytical techniques first noted in Chapter 6, we can now trace out in panel (b) of Figure 4-3 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.,
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 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 4-3. 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 4-3, 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.
The Incremental Product
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 4-3, panel (a), the incremental product of labor over the L2 to L3 input range can be computed as
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 4-4, 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 4-4. A capital-variable (labor-constant) section of the surface.
Simulation Modeling the Production Process
In Chapter 1 we introduced the SIMMOD Java applet computer program as a model simulation system. We have discussed its applicability to consumer behavior in Chapter 2, and to revenue and demand in Chapter 3. Our purpose is this section is to further elaborate its potential usefulness 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,
Figure 4-5.
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 4-6.
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. 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 a firm 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 employ SIMMOD to model the equations of its total, average, and marginal product functions. When any of these functions change either by deliberate actions of the management or due to matters beyond the control of the management, it may analyze the effects of such changes in SIMMOD by making appropriate changes to the respective functions as illustrated above.
CHAPTER 5. COSTS
Variable and Fixed Costs
Economists distinguish between direct costs and overhead costs, or to use the 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 4, 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.
The Cost-Production Nexus
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 4. 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 4 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.
In order to begin our graphic analysis of costs we make three simplifying assumptions, which 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 6 and 7 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 4-3 and reproduced with only minor modification in Figure 5-1. 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 5-2, this has the effect of reversing the concavities of the TP curve, but there are as yet no other significant changes.
Figure 5-1. Total, Average, and Marginal Product Curves.
Figure 5-2. 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 5-3, so that the total variable cost, TVC, is the (vertical) sum of the TLVC and TMVC. As is apparent in Figure 5-3, 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 5-3. 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.
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 5-4, 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 5-4. 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 5-4 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 5-4 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 5-4, may be derived from the TVC curve in the same fashion that the MP curve was derived from the TP curve in Chapter 4. Marginal cost may be computed as
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 5-4. 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 5-4 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 5-4 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 5-4).
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 5-4.
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 5-4). 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 5-4). 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 14 and 15).
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 12 and 13 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 6-3 and 5-4.
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 6 and 7. 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 intact, can be illustrated in panel (a) of Figure 5-5 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 5-5. 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 5-4 and reproduced in panel (b) in Figure 5-5, serves both the TC and TVC curves.
Figure 5-5. 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
_________
1It 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.
_________
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 5-5 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 5-5, 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.
Simulation Modeling of Costs
In Chapter 3 we introduced the SIMMOD Java applet computer program as a model simulation system. We have discussed its applicability to revenue and demand in Chapter 7, and its usefulness to the analysis of production in Chapter 9. Our purpose is this section is to further elaborate its potential usefulness in the analysis of cost relationships.Suppose that empirical research and regression analysis has yielded parameters for a third-order total cost function (TC) with equation
Figure 5-6.
As illustrated in Figure 5-7, the constant value has been changed from its initial value of 120 to the larger value, 180. The revised TC equation is
Figure 5-7.
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, SIMMOD could be employed to model the equations of the 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 in SIMMOD by making appropriate changes to the respective functions as illustrated above.
The criteria for appropriate pricing and output decisions are developed in Chapters 6 through 9. 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.
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PART C. THEORIES OF THE FIRM
CHAPTER 6. 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.
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 8 and 9 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.
(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 6-1 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. Because all firms in a purely competitive 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).
Figure 6-1. A Firm in a Purely Competitive Industry.
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 3 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.
The appropriate output 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.
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 6-1 at any output for which AR < AVC, or in panel (c) at any output for which TR < TVC. 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. 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.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 5, 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 6-2 for which AR < ATC, which also corresponds in panel (c) to any output for which TR < TC.
Figure 6-2. Purely Competitive Adjustment in the Long Run.
Short-Run Industry Adjustment of the Competitive Industry
Figure 6-2 is an extension of Figure 6-1 to include the TC curve in panel (c) and the ATC curve in panel (b). We may recall 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 6-2. 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.
Discussion of the issues associated with long-run adjustments in a competitive industry may be found in Chapter 12 of A Managerial Economics Primer by the author.
Simulation Modeling the Competitive Environment
In Chapter 1 we introduced a graphic model simulation system. We have discussed its applicability to revenue and demand analysis in Chapter 3, and its usefulness to the analysis of costs in Chapter 5. Our purpose in this section is to bring together the revenue and cost functions for a firm in a competitive market and examine the applicability of the graphic simulation model to the analysis of the marginal criteria for selection of the competitive firm's profit-maximizing price and output in the short run. We assume that the competitive firm has no pricing discretion so that it simply accepts the market price as a "given," i.e., it is a "price taker." This implies that its demand (average revenue) and marginal revenue curves are horizontal and coincident.With modifications, the revenue and cost functions that were first introduced in Chapters 3 and 5 can serve this purpose. The initial total revenue function was given by the linear equation,
Figure 6-3.
Figure 6-5 illustrates the graphic display for a simultaneous solution of the two marginal equations. The profit-maximizing value for Q is between 24.9 and 25.0 units. The quantity 25.0 entered into the demand and marginal revenue equations yields average revenue (price) of $20.0 and marginal revenue of $20.0. The average total cost of $17.3 may be determined by entering the value of Q into the average total cost equation; marginal cost for this value of Q is $20.0. The difference between the price and average cost at quantity 25.0 units is the per-unit profit contribution of $2.7.
Suppose that the coefficient of Q in the total revenue equation is decreased from 20 to 15. The new total revenue function equation is
Figure 6-4 shows the results of decreasing the coefficient of Q in the total revenue equation from 20 to 15. A comparison of the two graphic displays reveals that the total revenue function rotated downward consequent upon the decrease in the coefficient of Q; the average and marginal revenue curves (coincident) are also shifted downward. The marginals now intersect between 22.8 and 22.9 units of output. Using the value of 22.9 for Q in the AR, MR, ATC, AVC, and MC equations, we find that the profit-maximizing price is now $15.00 and marginal revenue is also $15.00; average total cost is $17.29 and marginal cost is $15.07. At a quantity of 22.9 units, the difference between price and average cost is now a per-unit loss of $2.29. Since price of $15.00 is still greater than average variable cost of $12.05, the firm should keep operating, covering all of its operating costs (i.e., average variable cost) and making a contribution of $2.95 per unit of product sold to covering overhead (fixed) costs.
Figure 6-4.
In this example we have illustrated the ability, using a graphic simulation model, to analyze the effects upon the profitability of a firm in a competitive market of a change in one (or more) of the parameters of its revenue and cost functions. The reader may similarly analyze the likely effects of changes in the revenue and cost functions for any firm or product line if the functions can be known or estimated from historical data via regression analysis.
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CHAPTER 7. 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, but the monopolist is still subject to the discipline of market demand
(4) Supernormal profits and control over its situation are the two prominent benefits that monopoly position confers upon a firm.
Short-Run Adjustments by the Monopolist
Figure 7-1 illustrates the short-run revenue and cost curves for a pure monopolist. The reader is invited to compare these with those in Figure 7-1 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 6-1 are apparently missing from Figure 7-1. They are in fact present in Figure 7-1, 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 7-1. Cost and Revenue Curves for a Pure Monopolist.
The second obvious difference between Figures 6-1 and 7-1 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 3, diverges from the demand curve and lies below it when the total revenue curve is a parabola.
The cost curves illustrated for the pure monopolist in Figure 7-1 have essentially the same appearances as those illustrated for the pure competitor in Figure 7-1.
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 (MR > MC) 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 7-1. If marginal cost is greater than marginal revenue (MC > MR), 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.
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 can lead the monopolist toward the profit maximizing price and output levels, P3 and Q3 in Figure 7-1. 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 that 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.
A pure monopolist 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 7-1 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.
Simulation Modeling of a Monopoly Firm
In Chapter 1 we introduced a graphic model simulation system. We have discussed its applicability to revenue and demand analysis in Chapter 3, and its usefulness to the analysis of costs in Chapter 5 and a competitive firm in Chapter 6. Our purpose in this section is to bring the revenue and cost functions for a firm together and examine the applicability of the graphic simulation model to the analysis of the marginal criteria for selection of a monopoly firm's profit-maximizing price and output. We assume that the firm has a significant degree of monopoly power so that its demand curve slopes downward from left to right when plotted in price-quantity coordinate space.The revenue and cost functions that were first introduced in Chapters 3 and 5 can serve this purpose. The initial total revenue function was given by the second-order equation,
Figure 7-2.
Figure 7-2 illustrates the graphic display for a simultaneous solution of the two marginal equations. The profit-maximizing value for Q is between 17.5 and 17.6 units. The quantity 17.6 entered into the demand and marginal revenue equations yields average revenue (price) of $33.6 and marginal revenue of $7.2. The average total cost of $19.29 may be determined by entering the value of Q into the average total cost equation; marginal cost for this value of Q is $7.33. The difference between the price and average cost at quantity 17.6 units is the per-unit profit contribution of $14.31.
Suppose that the coefficient of Q in the total revenue equation is increased from 60 to 65. The new total revenue function equation is
Figure 7-3 shows the results of increasing the coefficient of Q in the total revenue equation. A comparison of the two graphic displays reveals that the total revenue function shifted upward and outward consequent upon the increase in the coefficient of Q; the average and marginal revenue curves are also shifted to the right. The marginals now intersect between 18.8 and 18.9 units. Using the value of 18.9 for Q in the AR, MR, ATC, AVC, and MC equations, we find that the profit-maximizing price is now $36.65, marginal revenue is $8.30; average total cost is $18.51 and marginal cost is $8.61. At a quantity of 18.9 units, the difference between price and average cost is now a per-unit profit contribution of $18.14, which exceeds the original per-unit profit contribution of $14.31. The new revenue function is obviously an improvement over the original revenue function.
Figure 7-3.
In this example we have illustrated the ability, using a graphic simulation model, to analyze the effects upon the profitability of a firm of a change in one (or more) of the parameters of its revenue and cost functions. The reader may similarly analyze the likely effects of changes in the revenue and cost functions for any firm or product line if the functions can be known or estimated from historical data via regression analysis.
CHAPTER 8. MONOPOLISTIC COMPETITION
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.
(g) Because of the ease of entry into the monopolistically-competitive market, there is a tendency toward convergence upon a common 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.
(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 6, 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 8-1 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 8-1 differ from those for a representative purely competitive firm illustrated in Figure 6-1 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 8-1 curves are actually quite similar to those for the pure monopolist as illustrated in Figure 7-1 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 8-1. Revenue and Cost Curves for a Monopolistically Competitive Firm.
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 8-1 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 be competed away just as in pure competition.
Analysis of demand in monopolistic competition requires two demand curves, similar to those depicted in Figure 8-2, to explain the market adjustment process. The demand curve of Figure 8-1 is reproduced in Figure 8-2, and was intentionally labeled with a lower-case letter "d" so that the other demand curve could be introduced and labeled with the capital "D" in Figure 8-2. Demand curve d is referred to 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 is referred to as the "genus" demand curve because it is generic to the market group.
Figure 8-2. 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.
The firm's generic demand curve shifts to the left consequent upon the entry into the market, and carries with it the firm's species demand curve as we have illustrated it in Figure 8-2. 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 8-3. This state may be described as market (or group) equilibrium.
Figure 8-3. A Monopolistically-Competitive Firm in Market 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, 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.
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 genus 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 is whether the increased demand for the product will generate enough additional revenues to cover the costs of differentiation and promotion. Figure 8-4 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 8-4.
Figure 8-4. 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 in Chapter 9.
Simulation Modeling a Firm in Monopolistic Competition
In Chapter 1 we introduced a graphic model simulation system. We have discussed its applicability to revenue and demand analysis in Chapter 3, and its usefulness to the analysis of costs in Chapter 5. Our purpose in this section is to bring together the revenue and cost functions for a firm in a monopolistically competitive market and examine the applicability of the graphic simulation model to the analysis of the marginal criteria for selection of the monopolistically competitive firm's profit-maximizing price and output in the short run. We assume that the competitive firm has only a slight modicum of pricing discretion so that its demand curve has only a slight downward slope and its marginal revenue curve diverges only slightly from the demand curve.With modifications, the revenue and cost functions that were first introduced in Chapters 3 and 5 can serve this purpose. The initial total revenue function is given by the equation,
Figure 8-5.
Figure 8-5 illustrates the graphic display for a simultaneous solution of the two marginal equations. The profit-maximizing value for Q is between 24.1 and 24.2 units. The quantity 24.2 entered into the demand and marginal revenue equations yields average revenue (price) of $21.37 and marginal revenue of $17.74. The average total cost of $17.24 may be determined by entering the value of Q into the average total cost equation; marginal cost for this value of Q is $180.0. The difference between the price and average total cost at quantity 24.2 units is the per-unit profit contribution of $4.13.
Suppose that the coefficient of Q in the total revenue equation is decreased from 25 to 20.71. The new total revenue function equation is
Figure 8-6 shows the results of decreasing the coefficient of Q in the total revenue equation from 25 to 20.71. This may have come about due to entry into the monopolistically competitive industry in the effort to capture some of the profits being realized by firms already in the industry. A comparison of the two graphic displays reveals that the total revenue function rotated downward consequent upon the decrease in the coefficient of Q; the average and marginal revenue curves are also shifted downward. The marginals now intersect between 22.3 and 22.4 units of output. Using the value of 22.4 for Q in the AR, MR, ATC, AVC, and MC equations, we find that the profit-maximizing price (average revenue) is now $17.35 and marginal revenue is $13.99; average total cost is $17.35 and marginal cost is $14.05. At a quantity of 22.4 units, the difference between price and average total cost now is zero, but all resources used by the firm are receiving "normal returns" at their opportunity costs.
Figure 8-6.
In this example we have illustrated the ability, using a graphic simulation model, to analyze the effects upon the profitability of a firm in a competitive market of a change in one (or more) of the parameters of its revenue and cost functions. The reader may similarly analyze the likely effects of changes in the revenue and cost functions for any firm or product line if the functions can be known or estimated from historical data via regression analysis.
CHAPTER 9. OLIGOPOLISTIC COMPETITION
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.
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 or differentiated. 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, organizational structures, and technologies.
(4) Unlike monopolistic competition, firms in an oligopolistic market have differing levels of access to information.
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) 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.
(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.
(f) As in both pure and monopolistic competition, there may tend to be a market-wide convergence upon a common price.
(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.
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 essentially 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.
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 collusion (e.g., by forming a cartel). The monopoly model described in Chapter 7 is adequate to the analysis of the behavior of a cartel.
(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. The monopoly model is adequate to the analysis of the behavior of a trust.
(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. If they are successful in hiding their collusive actions, the monopoly model is adequate to the analysis of their behavior.
(7) And finally, even if none of the above occurs, some type of price leadership/followership is likely to emerge.
Models of Oligopolistic Adjustment
Patterns (1), (4), (5), and (6) may be analyzed with the pure monopoly model described in Chapter 7. 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.Oligopolistic Price Warfare. In Figure 9-1, 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 9-1. 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. 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 9-2.
Figure 9-2. Sweezy's Kinked Demand Curve.
If the demand curve for the oligopolist's product really is kinked at point A in Figure 9-3, then a price increase to P2 will result in a larger percentage decrease of quantity demanded (to Q2) than the percentage increase (to Q3) which 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. 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.
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).
Price-Leadership/Followership. Oligopolistic competition is perhaps the most prevalent form of commercial organization in Western society. The most common pattern of oligopolistic interaction where antitrust laws are vigorously enforced is likely 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.
Figure 9-3. 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 9-4, 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 9-4. 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 loose 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 9-5, 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 9-5. Price Leadership based on Plant Size Differences.
Price Leadership based on Unequal Market Shares. Finally, we suppose in Figure 9-8 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. 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 9-8. 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.
Simulation Modeling Oligopolistic Competition
The conditions of oligopolistic competition are so complex, varied, and specific to particular situations that we have not devised a separate simulation model pertaining to oligopolistic competition. The simulation models for monopoly (Chapter 7) and monopolistic competition (Chapter 8) might be useful with parameter modifications to fit some of the circumstances of a firm in oligopolistic competition, but the reader is cautioned that interactive competitive behavior between the firm being modeled and other firms in the same industry may render simulation conclusions incorrect.
BACK TO CONTENTS
CHAPTER 10. EXTENDING THE MODEL OF THE FIRM
The models that we have examined in Chapters 6 through 9 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. The purpose of this chapter is to survey various 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 3 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 6 through 9, 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 8 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 10-1 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 which 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 firm's 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 16-A of A Managerial Economics Primer by the author.
Figure 10-1. A Graphic 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.
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 10-2, 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 10-2, 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 10-2. Jointly-Produced Products Produced in Fixed Proportions.
If marginal cost should fall to MCB in panel (b) of Figure 10-2, 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.
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. 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 tat 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 10-3 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 10-3. 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 10-4. 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 10-4. Transfer Pricing with an External Market for the Output.
The author's intent in this chapter has been to inform the reader of "real-world" conditions that are far more complex than can be handled easily by the simplistic simulation models illustrated in this book. Users of simulation model system are cautioned to adjust model conclusions to account for the dimensions of complexity not included in the simple models.
BACK TO CONTENTS
PART D. CONCLUISION
CHAPTER 11. REALISM, ACCURACY, AND SPECIFICIY IN MODELS
Simple Models and Complex Realities
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 6 through 9 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.
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