Chapter 2Demand, Technology, and the Theoryof the FirmOne of our goals is to understand the forces that influence firm behav...
2.1 The Short Run and the Long RunBefore discussing demand and technological conditions, we first must be clearabout the ti...
2.2 Consumer Theory and Demand3Consumer preferences are extraordinarily diverse and complex. Most people likeice cream, bu...
depends on these givens or parameters in the utility function and the budget constraint.Specifically,consumer i’sdemand fun...
Notice in (2.1) that quantity is on the left-hand side of the equality and its priceon the right hand-side. The graph of t...
good 2 (e.g., cameras) will reduce demand for good 2 and therefore reduce thedemand for good 1 (batteries).Changes in a co...
To distinguish the individual from the market, we use capital Q to representmarket output and capital D to represent marke...
¼1bpQ¼1ba À bQQ¼abQÀ 1: (2.4)For a linear demand function, the elasticity varies along the demand curve.For the example wh...
Thecross-priceelasticityidentifieswhentwogoodsaresubstitutesorcomplements.The cross-price elasticity is positive for substi...
Note that @AR=@Q is the slope of the AR function. If @AR=@Q  0, thenMR  AR; if @AR=@Q  0 then MR  AR; and if @AR=@Q ¼ 0, t...
¼1bpQ¼1ba À bQQ¼abQÀ 1: (2.15)Notice that a market with these qualities has several interesting features:• Total revenue r...
product based only on its intrinsic characteristics. We extend the model by allowingfor nonfunctional motives of demand. T...
consumers can make mistakes when they operate on “autopilot,” making routinechoices automatically without thinking about t...
parameter, a, which increases with a technological change. Regarding laborproductivity, APL ¼ a · L–1/2· K1/2and MPL ¼ (½)...
Another principle reason for economies of scale is associated with gains fromspecialization. Adam Smith’s (1776) discussio...
replicating what has been done before assures that long-run average costs remainconstant. The minimum level of production ...
where a ¼ 1 (AC1) and the other where a ¼ 2 (AC2). In the limit, as a approachesinfinity, both AC and MC approach horizonta...
Although most of our attention will be devoted to the technologies describedabove, there is another cost structure that wi...
An important motive for multiproduct production is the presence of economiesof scope (Baumol et al. 1982). In our two good...
2.4.1 Firm MotivesIn the simple neoclassical approach, the firm is considered a “black box” orinstitution that transforms i...
$1 received in period 1 is worth 90¢ in period 0. To get the present value of $1received in period 2, we must multiply $1 ...
Incentive compatibility is even more problematic when managers haveuneconomic motivations. Marris (1964) argues that manag...
and Burger King, is called a horizontal merger. Economies of scope provideanother reason for firm growth. In this case, the...
We can summarize the influence of these factors on cost-minimizing firm size bydividing costs into two groups. The first cons...
2.5 Summary1. The production process is generally divided up into two periods, the short runand the long run. In the short...
investment in the hope that it will go up in value. Other non-functional motives arebandwagon, snob, and Veblen effects. B...
have invested in the firm. In a corporation, stockholders risk only the amount ofmoney they have invested in the firm.21. Th...
6. A firm sells two brands of a good, x and y. The firm is considering raising theprice of brand y. The cross-price elastici...
Appendix A: A Review of Present Value and Discounting32In general, people value assets differently when they are received ...
More generally, an asset received t years from now isPV ytð Þ ¼ yt Á Dt¼ yt= 1 þ rð Þt: (A.4)In some problems in finance an...
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New perspectives on industrial organization

  1. 1. Chapter 2Demand, Technology, and the Theoryof the FirmOne of our goals is to understand the forces that influence firm behavior. Theprincipal constraints derive from consumers (demand), nature (technology), andcompetitors.1Demand derives from consumers who strive to maximize their utilityor satisfaction within their budget and other constraints. When tastes are under thefull control of consumers, firms take market demand as given. That is, demand isexogenously determined. This is the basis of consumer sovereignty—consumerpreferences determine what firms produce.With at least some consumers, however, preferences are less insular and moreflexible. Some people care what others think, inducing them to purchase a particularstyle of clothing because it is accepted by their peers. When this becomes a dominantfeature of a market, a firm may invest marketing dollars to manipulate consumerdemand in ways that benefit the firm. In this case, there is a certain amount ofproducer sovereignty—firms influence demand by manipulating consumerpreferences. That is, demand is endogenous to the firm, at least to a certain extent.Similarly, technology has both exogenous and endogenous qualities. The laws ofphysics place limits on technology, which defines the set of feasible productionopportunities and determines the maximum amount of output that can be producedfrom a given quantity of inputs. For instance, there is an upper limit on theefficiency of your gas furnace at creating heat (100%). Although this is a techno-logical bound, a firm may invest in a research effort to improve the efficiency of itsheater from 95 to 97%. Thus, technology is given until someone comes up with abetter way of doing things, which is a technological change.In this chapter, we consider demand and technological constraints. Once basicdemand and technological conditions are reviewed, we discuss the theory of thefirm and the complex goals and aims of a firm. Constraints imposed by competitorswill be considered when we discuss firm strategy later in the book.1Legal constraints are also important and are taken as given until the end of the book.V.J. Tremblay and C.H. Tremblay, New Perspectives on Industrial Organization,Springer Texts in Business and Economics, DOI 10.1007/978-1-4614-3241-8_2,# Springer Science+Business Media New York 201225
  2. 2. 2.1 The Short Run and the Long RunBefore discussing demand and technological conditions, we first must be clearabout the time in which an economic agent has to make adjustments. On thedemand side, consumers will respond relatively quickly to a fall in the price ofapples, but it may take a considerable amount of time for consumer demand torespond to a drop in the price of an expensive sports car. For some consumers, itwill take time to find financing for the car. Others may have just purchased anew car, making it impractical or uneconomic for them to purchase another carfor years to come. We will see that the time period in question will be particu-larly important when discussing the demand for a durable good like anautomobile.On the production side, we normally divide up time into two periods: the shortrun and the long run. In the short run, some inputs are variable and others are fixed.If we assume just two inputs, labor and capital (i.e., plant and equipment), labor isthe variable input and capital is the fixed input. The short run is a period that is tooshort for the firm to change the size of its plant in response to a change in demand.Thus, capital is predetermined at its current level in the short run. In the long run, allinputs are variable. In this case, the firm has sufficient time to adjust the level of allof its inputs in response to a change in demand.2In short-run analysis, thisdistinction allows us to divide costs into variable costs (payments to variable inputs)and fixed costs (payments to fixed inputs).The length of time required for capital to be variable depends on the industry andtype of capital being used. The time it takes to expand the size of a fast-foodrestaurant may be less than a year, while it may take several years to expand thesize of a steel mill. Thus, the time period identified as the short run differs byindustry.The nature of technology is also related to time. Many firms spend large sums ofmoney on research and development to come up with a better technology, one thatwill lower production costs. In some cases, this can take a considerable amount oftime, but in others inspiration and application can be rather quick. The point is that atechnological change will alter the nature of technology, as described by the firm’scost function.In this book, we will focus on the long run. We are interested in investigatingpolicies that address social concerns with imperfectly competitive markets, andnew laws and regulations generally address long-run economic problems. Develop-ment and implementation of a new policy takes a considerable amount of time,making it infeasible for policy to address short-run or transitory marketimperfections.2There is also the very short run, a period when all inputs are fixed. In this case, the firm cannotadjust its production level in response to a change in demand.26 2 Demand, Technology, and the Theory of the Firm
  3. 3. 2.2 Consumer Theory and Demand3Consumer preferences are extraordinarily diverse and complex. Most people likeice cream, but some prefer vanilla while others prefer chocolate. One person likes tosnowboard, and another likes to ski. One chooses a clothing style because it is“cool,” while another does not care about fashion. And even for a simple productlike coffee, consider the variety and complexity of drink orders placed at Starbucks.These are just a few examples of differing preferences across individuals.Consumer demand depends not only on these complicated preferences but also onconstraints. We cannot afford to buy an unlimited amount of goods and services.4Ineconomics, we focus on the consumer’s budget constraint, but individuals face otherkinds of constraints as well. Time available for searching and consuming goods islimited. A diamond ring and a Hawaii vacation may cost the same, but the vacationuses up much more time to enjoy than the ring. We are also bound by laws, socialmores, and religious doctrines. The job of explaining how people seek to fulfill theirneeds and wants in line with their complicated preferences while subject to multipleconstraints is a tall order to say the least. We take a first step towards that challengeby starting with the introductory model of demand. We review this simple modelfirst and then turn to more complicated cases.2.2.1 The Introductory Model of Consumer ChoiceThe introductory model of consumer choice assumes that an individual’s utility(happiness or satisfaction) depends on the consumption of goods and services.5It also assumes a single constraint, the budget constraint. If there are only twogoods, we can represent an individual’s utility function as U ¼ U(q1, q2, t) where q1is the quantity of good 1, q2 is the quantity of good 2, and t represents tastes. Thetaste parameter, t, identifies the desires and characteristics of a particular consumer.Consumer i will demand the amounts of goods that generate the highest level ofutility within the consumer’s budget. That is, consumer i will choose q1 and q2 tomaximize Ui(q1, q2, ti) given that total spending equals income (that is, p1q1 + p2q2 ¼m where p1 ¼ price of good 1, p2 ¼ price of good 2, and m ¼ consumer i’s income).At a particular point in time, p1, p2, m, and t are given or predetermined. Demand3You can learn more about the details of consumer theory from any introductory or intermediatemicroeconomics textbook, such as Frank and Bernanke (2008), Mankiw (2011), Bernheim andWhinston (2008), Pindyck and Rubenfield (2009), and Varian (2010). For more advancedtreatments, see Nicholson and Snyder (2012), Varian (1992), and Mas-Colell et al. (1995).4Throughout the book, we frequently use product or good to mean goods and services.5Of course, economists know that happiness depends on more than just the consumption of goods.Examples include nontangibles such as health, friendships, familial relationships, and beliefs. Wefocus on the utility of goods because the realm of economics is the production and allocation ofgoods. For further discussion on the economics of happiness, see Bruni and Porta (2007).2.2 Consumer Theory and Demand 27
  4. 4. depends on these givens or parameters in the utility function and the budget constraint.Specifically,consumer i’sdemand function forgood 1 (d1) derivesfromthe constrainedoptimization process and can be written asq1 ¼ d1ðp1; p2; mi; tiÞ: (2.1)In other words, demand originates from the consumer’s underlying preferences andbudget parameters.The demand curve graphs the relationship between quantity demanded (on thehorizontal axis) and price (on the vertical axis) for given levels of income, price ofgood 2, and tastes (see Fig. 2.1). The assumption that factors other than p1 are givenor held constant is known as the ceteris paribus assumption (as discussed inChap. 1). It allows us to focus on the price-quantity relationship separate fromother factors which affect demand. Later we will allow other factors to change, butfirst we start with this simplifying assumption.Figure 2.1 depicts a negative relationship between price and quantity demanded.That a consumer would prefer to buy less when price goes up is somewhat intuitive.The slope of demand derives from substitution and income effects. Consider Allison’sdemand for cake. Ifthe price of cake increases, Allison substitutes ice cream oranotherdessert for cake (the substitution effect). This diminishes her consumption of cake.Further, the higher price of cake diminishes her purchasing power, which also reducesher consumption of cake (assuming cake is a normal good). The magnitude of thesecombined effects determines the steepness of the demand curve.6This negativerelationship between price and quantity demanded is called the law of demand.$q1d1Fig. 2.1 An individualconsumer’s demandcurve (di)6With an inferior good, the income effect works against the substitution effect, making for asteeper demand curve. In theory, a super inferior good, called a Giffen good, results in a positivelysloped demand. We ignore the possibility of a Giffen good. For further discussion of normal,inferior, and Giffen goods, see Bernheim and Whinston (2008), Pindyck and Rubenfield (2009),and Varian (2010).28 2 Demand, Technology, and the Theory of the Firm
  5. 5. Notice in (2.1) that quantity is on the left-hand side of the equality and its priceon the right hand-side. The graph of the demand curve, though, has price on they-axis and quantity on the x-axis, which is inconsistent with the usual way ofgraphing functions in mathematics. The reversal of axes was started by Marshall(1890), a convention that has continued to this day. The equation that is consistentwith the convention in mathematics, ignoring all variables except p1 and q1, isp1 ¼ d1(q1) or p1 ¼ p1(q1). This is known as the “inverse demand function.” In thiscase, p1 represents the maximum price the consumer is willing to pay for q1, whichis called the demand (or reservation) price. The distinction becomes important insolving for specific demand models later in the book. Nevertheless, keep in mindthat the inverse demand function and the demand function represent the samerelationship between price and quantity. To illustrate, the inverse demand functionp1(q1) ¼ a – b · q1 has a corresponding demand equal to q1(p1) ¼ (a – p1)/b. Witheither specification, the demand curve has the following qualities: (1) the priceintercept is a, (2) the quantity intercept is a/b, and (3) the slope (∂p1/∂q1) is b.7All other demand determinants (p2, m, and t) are known as demand shifters.If there is a change in any of the demand shifters, the demand curve changeslocation. A demand shifter that increases (decreases) demand will cause the demandcurve to shift to the right (left). An increase in demand means that quantitydemanded is greater at any given price. In Fig. 2.2, a shift from d to d0representsan increase in demand, and a shift from d0to d represents a decrease in demand.The effect of p2 on the demand curve depends on whether good 2 is a substitute orcomplement to good 1. If the goods are substitutes, an increase in the price of good2 would cause people to switch to good 1, increasing demand for good 1 (shiftingdemand to the right). Coke and Pepsi are examples of substitute goods. Goods thatare complements are consumed together, such as cameras and batteries or lattesand scones. If good 1 and good 2 are complements, an increase in the price of$qddFig. 2.2 A changein consumer demand7Throughout the book, we will frequently replace d with ∂ to remind us that there are many othervariables in the model that are implicitly assumed to be held fixed.2.2 Consumer Theory and Demand 29
  6. 6. good 2 (e.g., cameras) will reduce demand for good 2 and therefore reduce thedemand for good 1 (batteries).Changes in a consumer’s income also affect demand. When higher incomegenerates greater demand for a good, the good is said to be a normal good. Mostgoods are normal goods. When higher income leads to a reduction in demand, thegood is an inferior good. For some people, instant Macaroni ‘n Cheese or noodlesoups are inferior goods. In college you might buy a lot of these products becausethey are cheap, but as you graduate and earn more you may not eat them asfrequently. For inferior goods, an increase in income results in decreased demand,shifting the demand curve to the left. Finally, when the demand for a product isunaffected by income, the product is an income-neutral good, and the demandcurve does not shift.Changes in tastes will also shift the demand curve.8For instance, if a productbecomes fashionable, people who like to be in style will demand more of the good,shifting the demand curve to the right. Some people might demand less of a productthat is no longer popular, causing demand to fall.2.2.2 Market DemandSo far, we have looked at an individual consumer’s demand for a product, but weare also interested in aggregate or market demand. Market demand identifies thedeterminants of quantity demanded for all consumers, ceteris paribus. To constructthe aggregate demand curve, we simply sum up the demands of each consumer.Like individual demand curves, the market demand curve has a negative slope.Since the aggregate demand curve derives from individual demand curves, itdepends upon all of the factors in individual consumer demands: prices and theincome and tastes of each consumer. For simplicity, t is used to capture taste effectsfor all consumers and average income (m) is used to capture income effects. This isaccurate if the distribution of income remains unchanged. In this case, the marketdemand for good 1 isQ1 ¼ D1ðp1; p2; m; tÞ: (2.2)8It is common in economics to assume that tastes are fixed and to look for changes in relativeprices and income to explain changes in consumer behavior. In the words of Stigler and Becker(1977, 76), “tastes neither change capriciously nor differ importantly between people.” From thisperspective, changes in education, experience, and learning-by-doing may influence consumerbehavior by changing their consumption capital or the shadow or full price of purchasing acommodity. Regarding fashion, Karni and Schmeidler (1990) show how the fluctuating demandfor fashion goods can result from changes in a commodity’s “social attributes” rather than changesin tastes. Bikhchandani et al. (1992) show how demand fluctuations can derive from informationalimperfections. We are sympathetic to this viewpoint but continue to use the taste moniker becauseit simplifies the discussion.30 2 Demand, Technology, and the Theory of the Firm
  7. 7. To distinguish the individual from the market, we use capital Q to representmarket output and capital D to represent market demand. Changes the demandshifters (prices of complements and substitutes, income, and tastes) shift the marketdemand curve in the same way as with individual demand curves. Demand shiftsright with an increase in demand and shifts left with a decrease in demand. Thereare situations when we will want to focus only on the relationship between price andquantity. In that case, we will write demand as Q(p) and inverse demand as p(Q).This implicitly assumes that all other relevant variables are held constant.2.2.3 Demand ElasticitiesAt times, we want to know how much market demand responds to a change in ademand determinant, such as price or income. A measure of the responsiveness ofdemand (Q) to a change in its price (p) is the price elasticity of demand. It isdefined as the percentage change in quantity demanded divided by the percentagechange in price. For large changes it is defined as (DQ/Q)/(Dp/p). At times, we areinterested in the effect on demand of a small change in price, which requires the useof calculus. In this case, the price elasticity of demand equals9E @Q@ppQ: (2.3)Because demand is negatively sloped (i.e., ∂Q/∂p 0), the convention is toconvert the price elasticity of demand to a positive value, a convention we adopthere. To avoid confusion with notation, we refer to the price elasticity of demand as ¼ ÀE. Normally, the price elasticity of demand is used to identify the absolutevalue of the percentage change in quantity demanded in response to a 1% changein price.10If ¼ 2, for example, this means that a 1% increase in price will lead to a2% decrease in quantity demanded. When 1, demand is said to be elastic orrelatively responsive to a price change. If ¼ 1, demand is said to be unit elastic.When 1, demand is said to be inelastic or relatively unresponsive to a pricechange.Consider the example of a linear inverse demand function, p ¼ a – bQ, where aand b are positive constants. In this case, ∂Q/∂p ¼ –1/b, and the price elasticity is9The percentage change in Q is ∂Q/Q and the percentage change in p is ∂p/p. Thus, ¼(∂Q/Q)/(∂p/p) ¼ (∂Q/∂p)(p/Q).10Percentage changes are used because they are invariant to how output and price are measured.Across industries, it would be difficult to compare changes in gallons of milk with units of cars.Across countries, it would be difficult to compare price changes in dollars versus Euros.2.2 Consumer Theory and Demand 31
  8. 8. ¼1bpQ¼1ba À bQQ¼abQÀ 1: (2.4)For a linear demand function, the elasticity varies along the demand curve.For the example where p ¼ a – bQ, demand is unit elastic when Q ¼ a/(2b), iselastic when Q a/(2b), and is inelastic when Q a/(2b). This is illustrated inFig. 2.3. Notice that the unit elastic point is halfway between the origin and thepoint where demand crosses the quantity axis. In general, the demand function isrelatively more inelastic for necessities and for products that have few substitutes.We are also interested in analyzing the effect of a change in consumer income ondemand. We capture this effect with the income elasticity of demand (m), whichmeasures the percentage change in quantity demanded resulting from a 1% change inincome:m @Q@mmQ: (2.5)As an example, if m ¼ 1.5, a 1% increase in income results in a 1.5% increase inquantity demanded. As implied by the discussionabove, a positive value of the incomeelasticity indicates that the good is a normal good, a negative value indicates that thegood is inferior, and a zero value indicates that income has no effect on demand.Another useful elasticity measure is the cross-price elasticity of demandbetween products i and j (ij). This measures the percentage change in the demandfor good i resulting from a unit change in the price of good j:ij @Qi@pjpjQi: (2.6)$Qaa/2b a/ba/2DMRη 1η = 1η 1Fig. 2.3 Market demand, marginal revenue, and price elasticity32 2 Demand, Technology, and the Theory of the Firm
  9. 9. Thecross-priceelasticityidentifieswhentwogoodsaresubstitutesorcomplements.The cross-price elasticity is positive for substitute goods, negative for complementgoods, and zero for unrelated goods. Estimating the cross-price elasticity of demand isuseful for a firm producing multiple brands. For instance, Kellogg’s produces Corn-flakes and Special K (as well as a number of other brands of cereal). If Kellogg’s isconsidering lowering the price of Cornflakes, the cross-price elasticity of demandwould indicate the potential negative impact on the demand for Special K. Kellogg’scan then judge the overall impact on revenues from a price reduction of Cornflakes.The cross-price elasticity is also useful to antitrust authorities in defining a market, thegroup of goods that constitute reasonably close substitutes.2.2.4 Total Revenue, Marginal Revenue, Average Revenue,and Price ElasticityTotal, average, and marginal revenue are key concepts in economics. Total reve-nue (TR) or the total dollar value of sales equals price multiplied by quantity sold.Total revenue can be calculated for a firm or for the industry as a whole. Averagerevenue (AR) is the revenue per unit of output, and marginal revenue (MR) is thechange in total revenue associated with a small change in output. For the industry asa whole, where total output is Q,TR pðQÞ Á Q; (2.7)AR TRQ¼ p; (2.8)MR @TR@Q: (2.9)Because AR equals price, the average revenue function is the same as the inversedemand function in the market. Along with (2.7), we can say that TR ¼ AR · Q.From these definitions, we can derive a relationship between average revenue andmarginal revenue. Given that TR ¼ AR · Q, marginal revenue can be written asMR ¼@TR@Q¼@AR@QQ þ AR: (2.10)2.2 Consumer Theory and Demand 33
  10. 10. Note that @AR=@Q is the slope of the AR function. If @AR=@Q 0, thenMR AR; if @AR=@Q 0 then MR AR; and if @AR=@Q ¼ 0, then MR ¼AR.11Because the slope of demand is negative, @AR=@Q is always less than 0,and MR is always less than AR.Next, we derive the relationship between marginal revenue and the price elas-ticity of demand. That is,12MR ¼@TR@Q¼@½pðQÞQŠ@Q;MR ¼ p þ@p@QQ;MR ¼ p 1 þ@p@QQp ;MR ¼ p 1 À1 : (2.11)Alternatively, by solving for , (2.11) becomes ¼pp À MR: (2.12)This tells us that if MR ¼ 0, ¼ 1; if MR 0, 1; and if MR 0, 1.As a simple example, consider the following linear inverse demand function,p(Q) ¼ a – bQ, which is the same as the average revenue function in the market.Total revenue isTR ¼ pðQÞ Á Q ¼ aQ À bQ2; (2.13)and marginal revenue isMR ¼@TR@Q¼ a À 2bQ: (2.14)The slope of the marginal revenue function is –2b, implying that it is twice as steepas the inverse demand function. As we saw above in (2.4), the price elasticity ofdemand in this linear case is11This relationship holds for the average and marginal of any function, whether it be a revenue,production, or cost function. That is, the average is falling when marginal is below the average, theaverage is rising when the marginal is above the average, and the average is constant when themarginal equals the average.12This is an application of the product rule, as discussed in the Mathematics and EconometricsAppendix at the end of the book. That is, if y ¼ wz where w ¼ f(x) and z ¼ g(x), then dy/dx ¼w(dz/dx) + z(dw/dx). The derivative of the product of two functions equals the first function times thederivative of the second function plus the second function times the derivative of the first function.34 2 Demand, Technology, and the Theory of the Firm
  11. 11. ¼1bpQ¼1ba À bQQ¼abQÀ 1: (2.15)Notice that a market with these qualities has several interesting features:• Total revenue reaches a maximum when MR ¼ 0, where Q ¼ a/(2b). At thisoutput level, demand is unit elastic ( ¼ 1).13• When Q a/(2b), MR 0 and demand is elastic ( 1). In the elastic region ofdemand, a decrease in price (increase in output) causes total revenue to increase.• When Q a/(2b), MR 0 and demand is inelastic ( 1). In the inelastic regionof demand, a decrease in price (increase in output) causes total revenue to decrease.These relationships are illustrated in Figs. 2.3 and 2.4. As a final point, becauseMR is the change in TR with respect to a small change in Q, TR is also the areaunder the MR curve for a given value of Q.14In the next section, we extend the introductory demand model. We elaborate onthe role of tastes and preferences when they are allowed to vary and depend upon acomplex set of phenomena. The constructs of nonfunctional demand and behavioraleconomics allow us to accommodate varying tastes and preferences in the utilityand demand equations.2.2.5 Nonfunctional Demand and Behavioral EconomicsThe demand function discussed above corresponds to what Leibenstein (1950)called functional demand. With functional demand, a consumer purchases a$Qa/2bTRFig. 2.4 The totalrevenue curve13We find Q that maximizes TR by taking its derivative (which is MR) and setting it to 0.Geometrically, the maximum or minimum occurs where the slope of a tangent line to a curveequals zero. Because TR is concave from below, TR reaches a maximum when MR ¼ 0.14That is, adding up all of the marginals gives us the total. In calculus, this is the integral of themarginal revenue function.2.2 Consumer Theory and Demand 35
  12. 12. product based only on its intrinsic characteristics. We extend the model by allowingfor nonfunctional motives of demand. This will enable us to better understand someof the marketing strategies used by real firms in the marketplace. Nonfunctionaldemand is motivated by qualities other than a product’s inherent characteristics.One source of nonfunctional demand occurs when utility functions are interdepen-dent. An example of interdependence is the bandwagon effect, sometimes called anetwork effect, in which a consumer’s demand for a good increases as more and moreconsumers purchase it. For example, your utility of contracting with a wireless phonecompany increases as more of your friends and relatives contract with the samecompany. The bandwagon effect can also occur when a person simply wants to feela part of a particular group. Fads and fashion trends are types of bandwagon effects.The presence of bandwagon effects can cause market demand to be more elastic,because a drop in the price that causes more consumers to purchase the good willinduce still more consumers to jump on thebandwagon and purchase the good as well.Another example of interdependent utility is the snob effect which is theopposite of the bandwagon effect. A snob effect is present when someone enjoysbeing different from the crowd. Because a snob will experience greater utility whenmarket demand is low, the demand curve with a snob effect will be less elastic thanfor the functional demand curve, ceteris paribus.A third example is the Veblen or conspicuous consumption effect in whichpeople purchase a good simply to impress others. Goods that are expensive and thathave the quality that their consumption is readily observed by others are liable tohave this conspicuous effect. Veblen effects are more likely to be present with aRolls Royce automobile than with generic aspirin. The presence of Veblen effectscauses demand to become more inelastic, as a higher price adds to the prestigefactor and keeps demand from falling appreciably. Like a Giffen good, the Vebleneffect could produce a positively sloped demand, at least in theory for a certainregion of demand, when it dominates functional motives of demand.15Leibenstein discussed two other types of nonfunctional demand: speculative andirrational. With the speculative motive, a consumer purchases a good only as aninvestment in the hope that the price will go up. Irrational demand stems fromwhims or sudden urges, a topic of behavioral economics.Behavioral economics melds evidence from psychology and economics toprovide a more accurate picture of consumer preferences. The evidence showsthat consumers are not always fully rational. For instance, individuals tend to beoverconfident, starting businesses that have a lower probability of success than theyanticipate. People also make mistakes in optimizing when addressing complexproblems. If you have money to invest, would you buy bonds, stocks, property,leave your money in the bank, or some combination? If you decide on stocks, whichstocks would you buy and how many shares? It would be very difficult to choose theportfolio that maximizes utility within a budget. In addition to complexity,15Anti-Veblen effects are also possible in which some consumers prefer goods that areinconspicuous.36 2 Demand, Technology, and the Theory of the Firm
  13. 13. consumers can make mistakes when they operate on “autopilot,” making routinechoices automatically without thinking about them. As discussed in the nextchapter, operating on autopilot works well much of the time but can lead to seriouserrors when economic conditions change.We can augment the utility function by adding a set of variables, z, to control forerrors and nonfunctional motives for demand. This set of variables also includesother taste and preference factors, which we identified as t in the introductory modeldiscussed above. We underline z to imply that it is a vector, i.e., it represents morethan just one variable. A consumer’s utility function then becomes U ¼ U(q1, q2, z)and the demand function for good 1 can be written: q1 ¼ d1(p1, p2, m, z).2.3 Technology and Costs16The nature of technology also imposes a constraint on firm production. By technol-ogy we mean the entire body of knowledge concerning the methods used to bringinputs together to produce goods and services. This body of knowledge identifies theset of feasible production plans that are technically efficient, that is, the firm is notwasting inputs. This can be thought of in two different ways: (1) a firm is using thefewest inputs to produce a given output and (2) a firm is producing the maximumoutput from a given set of inputs.17Thus, a change in technology means that we addto technological knowledge, making inputs more productive in producing output.One way to describe a given technology is with a production function. If just twoinputs, labor (L) and physical capital (K),18are used to produce total output (q), theproduction function can be written asq ¼ q L; K; Tð Þ; (2.16)where T represents the level of technology. The production function identifies themaximum output that can be produced for this technology from a given quantity ofinputs. It is sometimes called the frontier production function, because it representsthe maximum level of output for a given quantity of inputs and technology. Fromproduction theory, the average product of input x (APx) is defined as q/x and themarginal product (MPx) is defined as ∂q/∂x, where x equals L or K.To provide a concrete example, consider a Cobb–Douglas production functionof the following form: q ¼ a · L1/2· K1/2. This functional form has just one16You can learn more about the details of production and cost theory from any introductory orintermediate microeconomics textbook, such as Mankiw (2011), Bernheim and Whinston (2008),Pindyck and Rubenfield (2009), and Varian (2010). For more advanced treatments, see Nicholsonand Snyder (2012), Varian (1992), and Mas-Colell et al. (1995).17Technical and other types of efficiency are discussed in Chap. 5.18This is different from financial capital, which is money used to make investments. In this simplemodel, other inputs such as raw materials are assumed to be included in capital.2.3 Technology and Costs 37
  14. 14. parameter, a, which increases with a technological change. Regarding laborproductivity, APL ¼ a · L–1/2· K1/2and MPL ¼ (½)a · LÀ1/2· K1/2. If L ¼ 9,K ¼ 16, and a ¼ 1, then q ¼ 12, APL ¼ 1.33, and MPL ¼ 0.67. In this model, atechnological change will cause a to increase, which increases total, average, andmarginal productivity. For example, if a were to increase to 1.25, then q ¼ 15,APL ¼ 1.67, and MPL ¼ 0.83.Duality theory demonstrates that a cost function contains the same economicallyrelevant information about technology as a production function (Varian 1992).Thus, because many of the issues of interest in this book relate directly to costs,we will generally focus on cost functions rather than production functions. By costswe mean economic costs, which include the opportunity cost of all inputs used bythe firm, whereas accounting costs typically mean historic costs (what a factororiginally cost rather than its cost if purchased today).A cost function is defined as the minimum expenditure of producing a givenoutput for a given technology and is sometimes referred to as a frontier cost function.In our model with two inputs where wL is the price of labor and wK is the price (orrental rate) of capital, the long-run total cost function (TC) is given by19TC ¼ TC wL; wk; q; Tð Þ: (2.17)Costs increase with an increase in output and input prices, and costs decreasewith a technological change, ceteris paribus. When a firm operates on its costfunction, it is both technically and economically efficient. Economic efficiencymeans that the firm chooses the cost minimizing combination of inputs to produce agiven output. If the firm were inefficient, it would produce a given output at a highercost than the minimum identified by the cost function.From the long-run total cost function, we can derive the average and marginalcost functions. The long-run average cost is AC ¼ TC/q, and the long-run mar-ginal cost is MC ¼ ∂TC/∂q.20In many cases, we will assume a U-shaped ACcurve, as depicted in Fig. 2.5. It illustrates two important scale concepts: economiesof scale and diseconomies of scale. The cost function exhibits economics of scalewhen long-run average cost falls as output increases. There are many reasons whythis may occur. For example, a large firm may have less demand fluctuation than asmaller firm, enabling the larger enterprise to hold a smaller proportion of its salesas inventories. The presence of set-up costs that do not vary with output can alsoproduce a declining average cost function. For instance, if a publisher pays anauthor $10,000 to write a book and the average cost of printing and distributing thebook is constant, then average total cost falls with production.19This solves the following long-run problem where all inputs are variable: minimize totalexpenditures, wL · L + wK · K, with respect to L and K given the production function. For furtherdiscussion, see Varian (2010, Chap. 20).20In future chapters, we will usually be discussing long-run phenomena and will refer to long-runaverage cost as AC and long run marginal cost as MC.38 2 Demand, Technology, and the Theory of the Firm
  15. 15. Another principle reason for economies of scale is associated with gains fromspecialization. Adam Smith’s (1776) discussion of a British pin factory provides themost striking historical example:. . .One man draws out the wire, another straights it, a third cuts it, a fourth points it, afifth grinds it at the top for receiving, the head; to make the head requires two or threedistinct operations; to put it on is a peculiar business, to whiten the pins is another; it is evena trade by itself to put them into the paper; and the important business of making a pin is, inthis manner, divided into about eighteen distinct operations . . . I have seen a smallmanufactory of this kind where ten men only were employed . . . [who] could makeamong them upwards of forty-eight thousand pins in a day. Each person . . . might beconsidered as making four thousand eight hundred pins in a day. But if they had all wroughtseparately and independently . . . they certainly could not each of them have made twenty,perhaps not one pin in a day . . .This illustrates how the specialization of labor can produce economies of scale.Of course, average costs cannot decline forever. At some point, long-run averagecost must begin to rise. When this occurs, the cost function exhibits diseconomiesof scale. Organization rather than technological considerations causes scalediseconomies. Management costs may eventually rise disproportionately withsize. When surveyed, most people indicate that they would prefer to work for alarger organization if they were lazy and less productive than the average worker.When the cost of supervising a larger number of employees rises sufficiently withfirm size, a larger enterprise will have a larger set-up (managerial) cost per unit ofproduction. We will talk more about costs such as these subsequently.In reality, long-run cost functions may be constant over a particular range ofoutput. This is depicted between x and y in Fig. 2.6. When the long-run averagecost function remains unchanged for an increase in output (i.e., region x – y), thecost function exhibits constant returns to scale.21The notion of replicationexplains why this segment is flat. Once all scale economies have been exploited,$qMCACFig. 2.5 The long-runaverage and marginal costcurves21Note that because AC reaches a minimum between x and y, MC equals AC from x to y.2.3 Technology and Costs 39
  16. 16. replicating what has been done before assures that long-run average costs remainconstant. The minimum level of production needed to take advantage of alleconomies of scale is a useful concept in industrial organization and is given aspecial name, minimum efficient scale (MES).In many cases, we will assume a simple U-shaped AC. One way to describe sucha technology is to assume that AC is a parabola. As an example, assume that it isAC ¼100 À 20q þ q2þ 40a4a; (2.18)where a 0 is a parameter which indicates how fast the parabola will open up.A larger a means that AC is flatter, implying that technology is approachingconstant returns to scale.22In this example, MC isMC ¼100 À 40q þ 3q2þ 40a4a: (2.19)Notice that at q ¼ 10, AC reaches a minimum and equals MC (AC ¼ MC¼ 10). AC and MC are described in Fig. 2.7 for two different technologies, one$qMESx yMCACFig. 2.6 The long-run average and marginal cost curves when there are constant returns to scaleover a range of output22More generally, we can write this as AC ¼ ½ q À x1ð Þ þ 4ay1Š 4a= , where (x1, y1) is the vertex ofthe parabola (where it reaches a maximum or a minimum). When a 0, the parabola is concavefrom above (i.e., it opens up from above), as in (2.18). When a 0, the parabola is concave frombelow (i.e., it opens up from below). We can also describe a parabola that opens up from the left orright by reversing x1 and y1 and reversing AC and q in the equation above. In this case, the parabolaopens to the right when a 0 and opens to the left when a 0. In both cases, the parabola opensup faster with a larger value of a.40 2 Demand, Technology, and the Theory of the Firm
  17. 17. where a ¼ 1 (AC1) and the other where a ¼ 2 (AC2). In the limit, as a approachesinfinity, both AC and MC approach horizontal lines at the value 10; technologyexhibits constant returns to scale for all values of output.There are occasions when we will assume a technology that exhibits constantreturns to scale. This simplification can be useful in oligopoly models wherestrategic interaction complicates the analysis. In this case, long-run total, average,and marginal cost functions are linear:TC ¼ c Á q; (2.20)AC ¼TCq¼ c; (2.21)MC ¼@TC@q¼ c: (2.22)Notice that AC ¼ MC ¼ c, a constant value regardless of output level. The costfunctions for this model are graphed in Fig. 2.8. Note that this cost function exhibitsconstant returns to scale for all values of output.As we said previously, a technological change will cause a decrease in costs,ceteris paribus. Recall from our discussion of the production function that atechnological change increases the total, average, and marginal product. The firmcan use fewer inputs to produce a given output, enabling total, average, andmarginal costs to fall with a technological change.23$q1010AC2AC1Fig. 2.7 Curvature of long-run average cost curves23To illustrate, in our two input example, total cost equals wL · L + wK · K. AC ¼ TC/q ¼ wL·L/q +wK · K/q ¼ wL/APL + wK/APK. MC ¼ ∂TC/∂q ¼ wL · ∂L/∂q + wK · ∂K/∂q ¼ wL/MPL +wK/MPK. Because a technological change increases the average and marginal product of each input,AC and MC fall with a technological change.2.3 Technology and Costs 41
  18. 18. Although most of our attention will be devoted to the technologies describedabove, there is another cost structure that will be useful when discussinginvestments that affect entry. An entrant may face an initial set-up cost, which iscalled a quasi-fixed cost (F).24These are costs that must be paid before any outputcan be produced. Traditional fixed costs are associated with fixed inputs that arepresent in the short run but not the long run, whereas quasi-fixed costs inputs doexist in the long run. Assuming a linear total cost function when there are set-upcosts, TC ¼ c · q + F and MC ¼ c. Average cost is nonlinear, however: AC ¼c + F/q. Thus, average cost declines with output.When we consider the cost of entering a market, it will be important to identifythe portion of F that is a sunk cost. A sunk cost is an expenditure that cannot berecovered once it is made. To illustrate, a firm may buy a factory with a marketvalue of $10 million and spend $2 million on an advertising campaign. Both arefixed costs. If the firm goes out of business, the money spent on advertising isentirely sunk. On the other hand, if the market value of the plant is $9, only $1million of the $10 million spent on the plant is sunk.The cost function is more complex for firms that produce multiple products, acommon feature in the real world. For example, General Electric provides financialservices and produces electrical equipment. General Mills produces over 30 differ-ent types of breakfast cereal. When this occurs, we use a multiproduct cost functionto describe technology. To illustrate this idea, consider the case with just two goods,1 and 2. The total cost of producing both goods would depend upon the quantityproduced of both goods, the price of inputs, and the state of technology:TC ¼ TC wL; wk; q1; q2; Tð Þ: (2.23)$qcTCAC = MC1cFig. 2.8 Linear total,average, and marginalcost curves24For further discussion of variable, fixed, and quasi-fixed costs, see Varian (2010, Chap. 20).42 2 Demand, Technology, and the Theory of the Firm
  19. 19. An important motive for multiproduct production is the presence of economiesof scope (Baumol et al. 1982). In our two good example, there are economies ofscope if joint production by a single firm is cheaper than production by two separatefirms. Ignoring other variables, scope economies exist ifTC q1 ¼ x; q2 ¼ yð Þ TC q1 ¼ x; q2 ¼ 0ð Þ þ TC q1 ¼ 0; q2 ¼ yð Þ; (2.24)where x and y are positive constants.Economies of scope can arise for a variety of reasons. One is the presence ofcomplementarities in production. For example, hides are a by-product of beefproduction, and beef is a by-product of hide production. Clearly, separate productionwould be cost ineffective, with the beef producer throwing hides away and the hidesproducer throwing beef away. Economies of scope can also result when productionof different products share a common input. In the railroad industry, for instance, thesharing of a common railroad track makes the joint offering of passenger and freightservices cost effective for a single firm.2.4 The Theory of the FirmTo this point, we have referred rather loosely to the concept of a firm. Firms arecomplex and multifaceted enterprises, making it difficult to provide a simpleexplanation of the goals and nature of a firm. As a result, most theories focus ona few key elements. In this section, we discuss the motives of the firm and the mostimportant forces that shape its boundaries.25In the USA, there are two basic types of business enterprises, unincorporatedfirms, which include single proprietorships (single owner) and partnerships(multiple owners), and corporations. The primary distinction between them isthe degree of owner liability if the firm goes out of business. In an unincorporatedbusiness, owners are liable for all the firm’s debts, which may exceed the amount ofmoney that owners have invested in the firm. In a corporation, stockholders(owners) risk only the amount of money they have invested in the firm. This limitedliability makes it easier for an incorporated firm to raise the financial capital neededto build a large business enterprise. In 2008, only 18% of businesses werecorporations, but they accounted for 81% of total US sales.2625For a more complete discussion of the theory of the firm, see Tirole (1988), Shughart (1990),Hay and Morris (1991), and Greer (1992).26This information is available at http://www.census.gov/compendia/statab/2012/tables/12s0744.pdf, accessed November 22, 2011.2.4 The Theory of the Firm 43
  20. 20. 2.4.1 Firm MotivesIn the simple neoclassical approach, the firm is considered a “black box” orinstitution that transforms inputs into outputs to maximize profits. In this case,profits mean economic profits, not accounting profits. Economic profits equal totalrevenue minus economic costs.27Profit maximization requires cost minimization,so the neoclassical firm is always technically and economically efficient. Whattakes place within the black box is assumed to be efficient and is ignored. Assumingthat profit maximization is the goal of the firm simplifies the analysis of both firmsand markets alike. But how realistic is this assumption?There are two main concerns with the profit maximization assumption. First, itpresumes a static world in which a decision today affects current but not futureprofits. When this is true, the firm can ignore the future when making a decisiontoday, but this would be untrue in some markets. As an example, cigarettecompanies have been known to give away free cigarettes. Setting price to zero isnot profit maximizing in a static market, but it may be wealth maximizing in adynamic market. That is, giving away cigarettes today will lead to greater consumeraddiction and enable the firm to charge a higher price tomorrow. Thus, the firmmust weigh the gain tomorrow against the loss today of giving away cigarettes.In dynamic markets such as this, firms are more likely to utilize the dynamic versionof profit maximization—maximization of the value of the firm.From a financial perspective, the fundamental value of an asset such as thesecurity (stock) of a firm equals the present value of the stream of its expectedfuture returns (profits).28Analysis of such problems is complicated by the fact that$1 received a year from today is not valued the same as a $1 received today. Formost of us, including financial planners, $1 received in the future is worth less andmust be discounted to obtain its present value (i.e., its value today).The discount factor (D) is used to convert future dollars to their present value. It isdefined as the current or present value of $1 received next period. At one extreme,when D equals 1, there is no discounting: $1 received next period is worth $1 today.At the other extreme, when D equals 0, the future does not matter at all: $1 receivednext period is worth nothing today. Thus, D ranges from 0 to 1, with a higher Dimplying that a greater value is placed on the future. For example, if D ¼ 0.9, then27Accounting profits equal total revenue minus accounting costs, which ignore the opportunitycost of the resources supplied by company owners. Thus, zero economic profit means that the firmwould stay in business, because all input suppliers are paid their opportunity costs and owners earna normal rate of return on their financial investments. Zero economic profit corresponds to apositive accounting profit that would earn the firm a normal rate of return. For further discussion ofthe distinctions between accounting profit and economic profit, see Frank and Bernanke (2008),Pindyck and Rubenfield (2009), or Varian (2010).28According to Fama (1965), the market value of a security will equal its fundamental value in anefficient market. This is called the efficient market hypothesis. Nevertheless, market frictions maycause market values to deviate from fundamental values, and they may take time to converge(Farmer and Lo, 1999; Lo, 2004; Malkiel, 2011).44 2 Demand, Technology, and the Theory of the Firm
  21. 21. $1 received in period 1 is worth 90¢ in period 0. To get the present value of $1received in period 2, we must multiply $1 by D twice (or by D2), which equals 81¢.Similarly, the present value of receiving $1 three periods from now is D3, and so on.Given this information about discounting, it is now rather easy to define thefundamental value of a firm. Consider the simple case where a firm is expected toearn the same profit (p) in each period, t, from t ¼ 0 (this period), 1, 2, 3, . . ., 1.In this case, the value of the firm (V) isV p; 1ð Þ ¼ D0p þ D1p þ D2p þ Á Á Á þ D1p;¼ pðD0þ D1þ D2þ Á Á Á þ D1Þ: (2.25)Although it may appear that the value of the firm is infinite, this is not the case. Aswe prove in Appendix 2.A,V p; 1ð Þ ¼p1 À D: (2.26)In our example where D ¼ 0.9 and p ¼ $1, V ¼ $10. That is, the present valueof receiving $1 every period starting today is $10.The assumption that the goal is to maximize the value of the firm is essentiallythe dynamic version of profit maximization. The model allows the firm to give upprofit today when it can gain sufficient profit tomorrow. If no such investmentopportunities across periods exist, static profit maximization in each period isequivalent to the maximization of the fundamental value of the firm.The second concern with assuming that the goal of a firm is to maximizeprofit (or value) is that most large corporations are run by managers, not owners(stockholders). Owners may want managers to maximize profit, but managers aremore likely to be concerned with their own utility, which may depend on income,prestige, and other psychological factors. This creates a conflict of interest, which canbe costly to rectify given that it can be expensive for owners to monitor the effort andbehavior of managers. Thus, managers may get away with pursuing goals other thanprofit maximization. This is called a principle–agent problem, which exists when theprinciple’s (owner’s) welfare depends on the actions of the agent (manager), and theirgoals are not aligned (Jensen and Meckling, 1976; Fama and Jensen, 1983).The principle–agent problem is especially difficult for large corporations withmany stockholders. First, it may be difficult to manage and observe manager effort ina large enterprise. After all, this is why owners hire managers in the first place.Second, when ownership is dispersed over many stockholders, each of whom owns asmall fraction of the company’s stock, it would not be cost effective for any onestockholder to closely monitor manager behavior. Consequentially, managers havesubstantial discretion. In theory, unprofitable conduct can be corrected for managerswho are income maximizers. In this case, owners would simply tie manager salariesto profits. This is a type of incentive-compatible contract, because it aligns theinterests of managers with owners. In practice, such contracts may make it difficultto hire good managers who are risk averse and want to avoid wide swings in incomeassociated with profit variation that is caused by exogenous shocks.2.4 The Theory of the Firm 45
  22. 22. Incentive compatibility is even more problematic when managers haveuneconomic motivations. Marris (1964) argues that managers have three dominantmotives: income, status, and power. Managers who are more interested in statusthan income may emphasize unprofitable growth over profits if this behavior placesthem on the cover of a business magazine, for example. In this case, tying managerincome to profits will fail to encourage profit-maximizing behavior.Of course, managers do not have unlimited discretion. In addition to incentive-compatible contracts, market forces also encourage managers to pursue profitmaximizing goals. Competition in product markets will pressure a managerto maximize profits; otherwise the firm will eventually go out of business. In thelong run, survivors will evolve and must be profit maximizers (Alchian 1950). Evenwhen insulated from competition, pressure to generate profits still persists. First,underperforming managers can be fired by the company’s board of directors whomonitor management performance and represent the interests of shareholders.Second, there is a labor market for managers, and those who are better atmaximizing profits will be more mobile and will command higher salaries. Third,there is a market for corporate control, where firms with successful managementteams buy firms with unsuccessful ones and replace underperforming managerswith those who have goals that are more in line with profit maximization.29Given the compelling arguments on both sides, we will not always usethe profit maximization assumption. For the most part, we will assume profitmaximization, because it simplifies the analysis and because profits certainlyhave a role to play in business. When managerial and behavioral motives are likelyto provide better explanations of actual firm behavior, especially regarding mergeractivity in Chap. 18, we relax the profit maximization assumption in favor ofother motives.2.4.2 The Boundaries of the FirmIn this section, we discuss the reasons why firms exist and the forces that shape thesize and boundaries of a firm. Economic activity can be coordinated throughmarkets, where price movements guide production, or within firms, wheremanagers make production decisions. At issue is the extent to which a firm shouldperform its own production and service tasks or purchase them in the market fromoutside suppliers. If we stick with the profit maximization assumption, then a firmwill exist and increase or decrease its size if it is profitable to do so.There are many advantages and disadvantages of setting up a firm to produceoutput. In terms of production costs, the presence of scale economies provides onereason why a firm may expand its scale of operation. This is referred to as horizontalgrowth. A merger between two firms within the same industry, such as McDonald’s29See Chap. 13 for a more complete discussion of the market for corporate control.46 2 Demand, Technology, and the Theory of the Firm
  23. 23. and Burger King, is called a horizontal merger. Economies of scope provideanother reason for firm growth. In this case, the firm may expand into related markets,such as passenger and freight rail service, or into unrelated markets, such as beefand hides. Expansion into unrelated markets is called conglomerate growth.Coase (1937) was the first to state that firms emerge for more than purelytechnological reasons. He argued that one advantage of organizing productionwithin a firm rather than through markets is that the firm reduces the number ofmarket transactions. Thus, transaction costs are lower as the firm expands its scaleand scope of operation. Transaction costs are those expenses that are associatedwith trading (and are in addition to the price itself). Besides price, a cabinetmanufacturer that transacts with an independent lumber supplier must negotiatethe type of wood and the delivery date of each order. These transaction costs can besubstantially reduced if the cabinet manufacturer buys the lumber supplier. When awholesaler grows by purchasing an input supplier or a retail distributor, this iscalled vertical growth.Of course, there are forces that limit firm size as well. Otherwise, the mostcost-efficient structure would be to have just one firm, call it the super firm(or government), that produces everything. Regarding vertical growth, Grossmanand Hart (1986) point out that when a manufacturer buys an input supplier, themerger reduces the input supplier’s flexibility and control, which may lead toinefficiencies. Second, when there are substantial scale economies at the inputsupply level, a scale-efficient input supplier may be too large to be profitablyowned by a single wholesaler.The size of the firm is also limited by managerial capacity, as organization andmonitoring costs may increase with the complexity and number of tasks found inlarger and larger enterprises. Alchian and Demsetz (1972) illustrate how this can bea problem when the firm is viewed as an institution that captures the benefits ofteam production. The role of the manager or coach is to monitor workers to ensureadequate performance. The case below provides an historical example whereworkers actually hired an overseer (manager) to perform the task of monitor.On the Yangtze River in China, there is a section of fast water over which boats are pulledupstream by a team of coolies [unskilled workers] prodded by an overseer using a whip.On one such passage an American lady, horrified at the sight of the overseer whippingthe men as they strained at their harnesses, demanded that something be done about thebrutality. She was quickly informed by the captain that nothing could be done: Those menown the right to draw boats over this stretch of water and they have hired the overseer andgiven him his duties. (McManus 1975, 341)If shirking of one’s duties among team members grows with firm size, managerialcosts will increase with the size of the firm.3030Alchian and Demsetz’ view also explains why football and track coaches behave differently. It ismore difficult to identify shirking (i.e., less that 100% effort) of an offensive lineman on a footballteam than of a sprinter on a track team. Thus, coaches spend more time monitoring performance andpromoting team spirit that is designed to minimizing shirking in football than in track.2.4 The Theory of the Firm 47
  24. 24. We can summarize the influence of these factors on cost-minimizing firm size bydividing costs into two groups. The first consists of those that decline with firm size,such as transaction costs. These are the costs associated with using the marketinstead of the firm. We call this the cost of using the market (CMKT). The secondincreases with firm size, as is true with managerial costs. We call this the cost ofmanaging a firm (CMGT). These costs are illustrated in Fig. 2.9. If they represent allrelevant costs, the firm size that minimizes total costs (CMKT + CMGT) is FS*.31At the same time, firm size is not driven by cost considerations alone. Strategicreasons can also influence the size and growth of a firm. For example, a horizontalmerger between McDonald’s and Burger King may be profitable only because itraises price by reducing competition. In addition, a firm that would like to chargedifferent prices to distributors in different geographic markets may buy up itsdistributors in the low price market, eliminating the possibility of arbitrage betweenlow and high priced distributors. Arbitrage is the purchase and almost immediatesale of a security or commodity to profit from price discrepancies. In this case, thefirm is engaging in price discrimination by charging a high price to distributors inregion H and a low price in region L. Without the merger, type-L distributors couldmake a profit by selling to H-type distributors, and the firm would be unable tocharge a high price to H-types. The merger would eliminate such trading.Analysis of the constraints imposed by competing firms is a key theme through-out the book. In the next chapter, we lay out the basics of game theory, which isused to identify firm strategy and the constraints imposed by rival firms.31Notice that unlike most problems in economics, the solution does not occur where the twocurves intersect.$Firm SizeFS*CMKTCMGTTC = CMGT + CMKTFig. 2.9 Cost-minimizing firm with market (CMKT) and management (CMGT) costs48 2 Demand, Technology, and the Theory of the Firm
  25. 25. 2.5 Summary1. The production process is generally divided up into two periods, the short runand the long run. In the short run, some inputs are variable and others are fixed.In the long run, all inputs are variable. In this book, we focus on long-runeconomic problems.2. Demand is derived from the individual’s pursuit of utility maximization, whilefacing budget and other constraints. The law of demand holds that consumerswill demand less of a good when its price increases, ceteris paribus.3. The factors that shift the demand curve are those that affect utility or the budgetconstraint: prices of substitute and complementary goods, tastes, and income.4. If the price of good 1 increases and the quantity demanded of good 2 rises, thegoods are substitutes. Chevy and Ford trucks are examples of substitute goods.Complements are goods that are used together. If the price of good 1 increases,the quantity demanded of good 2 will fall if goods 1 and 2 are complements.Cell phones and cell phone batteries are examples of complements.5. If an increase in income leads to an increase in demand, the good is a normalgood. If an increase in income decreases demand, the good is inferior. And ifan increase in income has no effect on demand, the good is income-neutral.6. Market demand is the horizontal sum of the demand curves for all of theindividuals in the market. It depends on the number of consumers, as well asprices of related goods, income, and tastes.7. The price elasticity of demand () measures the responsiveness of quantitydemanded to a change in price. If it exceeds 1, demand is elastic; if it equals 1,demand is of unitary elasticity; and if it is less than 1, demand is inelastic.8. The income elasticity of demand (m) measures the responsiveness of demandto a change in income. The sign determines whether a good is normal, inferior,or income-neutral.9. The cross-price elasticity of demand for goods 1 and 2 (12) indicates theresponsiveness of the demand for good 1 to a change in the price of good 2.A positive value indicates the goods are substitutes; a negative value indicatesthey are complements; and a zero value means that they are unrelated.10. Total revenue (TR) is price times the quantity sold of a good. Marginalrevenue (MR) is the change in total revenue associated with a small changein quantity sold. Average revenue (AR) is the revenue per unit and is totalrevenue divided by quantity sold. By definition, average revenue equals theprice, and total revenue equals average revenue times quantity sold.11. For a linear demand curve, the MR curve lies below and is twice as steep as thedemand curve. The relationship between MR and the price elasticity of demand() is: MR ¼ p(1 – 1/); ¼ p/(p – MR). When MR 0, 1; whenMR ¼ 0, ¼ 1; when MR 0, 1.12. Functional demand derives from the inherent characteristics of a commodity andfrom actually using or consuming the good. Nonfunctional demand refers to apart of demand that is not due to the intrinsic qualities of a good. The speculativemotive is one example, which occurs when a consumer buys a good as an2.5 Summary 49
  26. 26. investment in the hope that it will go up in value. Other non-functional motives arebandwagon, snob, and Veblen effects. Bandwagon effects occur when a persondesires a good because others do. Snob effects occur when a person desires a goodbecause others do not—he or she does not want to buy goods that are popular.Veblen effects (conspicuous consumption) occur when a person wants to showoff his or her wealth by buying prestigious and expensive goods.13. Behavioral economics integrates evidence from psychology into economics.It informs us that people make particular kinds of mistakes when they makechoices, such as being overconfident. People might also make mistakes becausechoices are too complex.14. The production function specifies how output depends on inputs and technol-ogy. The total cost function relates total cost to the quantity of output, inputprices, and technology.15. The total cost function is derived by minimizing costs for a specific technol-ogy (represented by the production function). Average cost or unit cost is totalcost divided by quantity produced. Marginal cost is the change in total costassociated with a small change in quantity produced.16. There may be regions of output under which long-run average cost declines, isconstant, or increases as output increases. When average cost is falling, marginalcost is below average cost. When average cost is constant or reaches a minimum,marginal cost equals average cost. When average cost is rising, marginal cost isabove average cost. Economies of scale arise when long-run average costsdecline as output increases. Gains from specialization provide one reason foreconomies of scale. Constant returns to scale means that average cost is constantwhen output changes. Efficient replication in the absence of managerialconstraints predicts constant returns to scale. Diseconomies of scale occurwhen long-run average costs rise with additional units of output and may arisebecause of increasing organization and monitoring costs associated with largeenterprises. The minimum level of production needed to take advantage of alleconomies of scale is called minimum efficient scale.17. Quasi-fixed costs are set-up costs that must be paid before output can be pro-duced. There are no fixed costs in the long run, but quasi-fixed costs do exist in thelong run.18. A fixed cost is an expenditure that is associated with fixed inputs and unaffectedby the level of production. A sunk cost is an expenditure that cannot berecovered once it is made.19. Many firms in the real world are multiproduct producers, companies thatproduce a variety of different products. A technological motive for multiprod-uct production is the presence of economies of scope, which exists when jointproduction is cheaper than separate production.20. There are two basic types of business enterprises: unincorporated firms,which include single proprietorships (single owner) and partnerships (multipleowners), and corporations. In an unincorporated business, owners are liablefor all the firm’s debts, which may exceed the amount of money owners50 2 Demand, Technology, and the Theory of the Firm
  27. 27. have invested in the firm. In a corporation, stockholders risk only the amount ofmoney they have invested in the firm.21. The common, neoclassical assumption is that firms behave as profit maximizers.In dynamic markets, however, investments today increase revenues tomorrowbut not today. In this case, the dynamic equivalent of profit maximization ismaximization of the value of the firm. Another problem with profit maximiza-tion arises in large corporations where managers and owners are differentindividuals and their goals are not aligned. This creates a principle–agentproblem: the principle’s (owner’s) welfare depends on the behavior of theagent (manager) but their goals are not the same. In this case, managerialgoals may be pursued rather than profit maximization.22. If we assume that firms are profit (wealth) maximizers, then a firm will existand adjust its size if it is profitable to do so. The presence of high transactioncosts associated with using the market and substantial scale and scopeeconomies will lead to larger firms. The cost of managing a larger and largerenterprise limits firm size. These include the cost of organizing a complexenterprise and the cost of monitoring employees. Strategic considerations canalso influence firm size.23. A firm can expand its size through horizontal, vertical, and conglomerategrowth. Horizontal growth refers to an increase in the scale of operation ofa firm. One example is when a cabinet manufacturer increases its capacity toproduce kitchen cabinets. Vertical growth means that a manufacturer expandsalong its stream of production, such as a manufacturer that starts producing itsown inputs and distributing its final products to customers. Conglomerategrowth refers to an increase in the scope of operation of a firm. One exampleis if a cabinet manufacturer expanded into the fast-food industry.24. Arbitrage is the purchase and almost immediate sale of a security or commodityto profit from price discrepancies across markets.2.6 Review Questions1. Show how an increase in the number of consumers will affect the marketdemand for a good or service.2. What is the difference between the snob effect and conspicuous consumption?3. Suppose that goods 1 and 2 are substitutes, and that the price of good 2 falls.How would demand for good 1 be affected? Illustrate graphically.4. If income falls and demand for a good decreases, is the good normal, inferior,or income-neutral?5. The income elasticity of a good is 0.A. Interpret the value of the income elasticity.B. Is the good normal or inferior?2.6 Review Questions 51
  28. 28. 6. A firm sells two brands of a good, x and y. The firm is considering raising theprice of brand y. The cross-price elasticity is À0.5.A. Interpret the value of the cross-price elasticity.B. State whether the two brands are substitutes, complements, or unrelated.7. Consider a market with the following inverse demand function, p ¼ a À 2bQ,where a and b are positive constants.A. Write down the TR function and the MR function.B. Graph the demand curve and the MR curve.C. What is the value of MR when the price elasticity of demand () equals 1?D. What is the maximum value of TR, and what is the value of when TRreaches a maximum?8. In the 1940s and 1950s, tattoos were popular, but then tattoos fell out of favoruntil the first decade of the twenty-first century.A. Did the functional demand for tattoos change from 1950 to 1970? From1970 to 2010?B. Is the demand for tattoos influenced by speculative, snob, bandwagon, orconspicuous consumption effects?9. Fill in the appropriate numbers in the empty cells in the table below.Q Total cost Average cost Marginal cost0 70 – –1 200 200 1302 3203 153.3 139.910. A technological change improves the efficiency of the production of a good.How do you expect that this will affect a firm’s long-run average and marginalcosts?11. How do you think that the development and use of the Internet affects transac-tion costs for the firm? Do you think that it would affect the optimal firm sizeassociated with transaction costs? If so, how?12. Every day, a clothing design firm needs workers who sew. It could contract outthese services to tailor shops or hire tailors and conduct the business of sewingin house. Compare the relative firm versus market costs for this problem for twofirms: Firm 1 sells low-cost dresses, and firm 2 sells high cost, designer dresses.Which business is more likely to use the market and which is more likely tohave tailors within the firm?13. Why might a firm engage in horizontal, vertical, and conglomerate growth?52 2 Demand, Technology, and the Theory of the Firm
  29. 29. Appendix A: A Review of Present Value and Discounting32In general, people value assets differently when they are received today versussometime in the future. When children are given the option of receiving a candy barnow or tomorrow, most want it now. The candy dilemma exhibits a fundamentalprinciple about human behavior—a given asset is generally valued more whenreceived today than in the future. There are many reasons why preferences mayexhibit this quality. There is always the risk that we may not be here tomorrow.In addition, most people are impatient. As a person becomes more impatient, he orshe will place a higher value on the present.Given these tendencies, we need to adjust the value of a given asset whenreceived in different periods of time. One way to see how we might account fortime differences is to look at how an asset grows in value over time. Given thatpeople place a higher value on current dollars, they must receive some compensa-tion to induce them to loan it to others. Assuming that this rate equals r, the annualrate of return on an investment, then an investment of $x will be worth $y1 in 1 year(or period one) according to the following formula:Value of x in 1 Year : y1 ¼ x 1 þ rð Þ: (A.1)Ignoring risk and assuming that all assets earn a rate of r per year, we can workbackwards and determine today’s value of any asset worth y1 in 1 year. This iscalled the present value (PV) of asset y1 that is received 1 year from now. It simplyequals x and is calculated as follows:PV y1ð Þ : x ¼ y1= 1 þ rð Þ ¼ y1 Á D; (A.2)where D 1/(1 + r) is defined as the discount factor, the rate at which a paymentnext year must be discounted to give us its present value.33In other words, Drepresents the present value of $1 received next year.You can get a better feel for the discount factor by considering extreme values ofD. When D ¼ 1, there is no discounting. In this case, $1 received next period isworth $1 today. When D ¼ 0, future dollars are worthless today (i.e., there is notomorrow). If D ¼ 0.95, then $1 received next period is worth 95¢ today. Thus, Dwill range from 0 to 1, which can be written as D 2 0; 1½ Š.To determine the PV of asset y2 when it is received 2 years from now, we mustdiscount it twice. Discounting it one time gives the present value of the asset 1 yearfrom now. Discounting it again gives the present value of the asset today. Thus,PV y2ð Þ ¼ y2 Á D Á D ¼ y2 Á D2¼ y2= 1 þ rð Þ2: (A.3)32For a more detailed discussion, see Chiang (1984, 280–281; 462–464) and Simon and Blume(1994, 97–99).33Alternatively, r (1 – D)/D.Appendix A: A Review of Present Value and Discounting 53
  30. 30. More generally, an asset received t years from now isPV ytð Þ ¼ yt Á Dt¼ yt= 1 þ rð Þt: (A.4)In some problems in finance and economics, it is useful to identify the PV of astream of payoffs that will be received in every period from today (period 0) toinfinity. Assuming the payoff (p) is the same in each period,PV p; 1ð Þ ¼ p= 1 þ rð Þ0þ p= 1 þ rð Þ1þ p= 1 þ rð Þ2þ p= 1 þ rð Þ3þ Á Á Áþ p= 1 þ rð Þ1;¼ p Á 1 þ D1þ D2þ D3þ Á Á Á þ D1 Ã: (A.5)This can be simplified as follows. First, we definea0 1 þ D1þ D2þ D3þ Á Á Á þ D1 Ã; (A.6)a1 D1þ D2þ D3þ Á Á Á þ D1 ü a0 Á D: (A.7)Substituting (A.6) into (A.5) yieldsPV p; 1ð Þ ¼ p Á a0: (A.8)Note that a0 – a1 ¼ 1 or that a0 – a0 · D ¼ 1 by substitution. Thus,a0 ¼ 1= 1 À Dð Þ: (A.9)Substituting (A.9) into (A.8) yieldsPV p; 1ð Þ ¼ p= 1 À Dð Þ: (A.10)Equation (A.10) makes it easy to calculate the present value of a payoff streamthat is received each period from today to infinity. For example, if p ¼ $100 andD ¼ 0.9 (i.e., r ¼ 1/9), then PV(p ¼ 100, 1) ¼ $1,000.54 2 Demand, Technology, and the Theory of the Firm

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