Nội dung

CHAPTER NINE bay23224_ch09_325-363.qxd 12/28/12 8:13 AM Confirming Pages Page 325 Basic Oligopoly Models HEADLINE Learning Objectives After completing this chapter, you will be able to: Crude Oil Prices Fall, but Consumers in Some Areas See No Relief at the Pump Thanks to a recent decline in crude oil prices, consumers in most locations recently enjoyed lower gasoline prices. In a few isolated areas, however, consumers cried foul because gasoline retailers did not pass on the price reductions to those who pay at the pump. Consumer groups argued that this corroborated their claim that gasoline retailers in these areas were colluding in order to earn monopoly profits. For obvious reasons, the gasoline retailers involved denied the allegations. Based on the evidence, do you think that gasoline stations in these areas were colluding in order to earn monopoly profits? Explain. LO1 Explain how beliefs and strategic interaction shape optimal decisions in oligopoly environments. LO2 Identify the conditions under which a firm operates in a Sweezy, Cournot, Stackelberg, or Bertrand oligopoly, and the ramifications of each type of oligopoly for optimal pricing decisions, output decisions, and firm profits. LO3 Apply reaction (or best-response) functions to identify optimal decisions and likely competitor responses in oligopoly settings. LO4 Identify the conditions for a contestable market, and explain the ramifications for market power and the sustainability of long-run profits. 325 bay23224_ch09_325-363.qxd 326 12/28/12 8:13 AM Page 326 Confirming Pages Managerial Economics and Business Strategy INTRODUCTION Up until now, our analysis of markets has not considered the impact of strategic behavior on managerial decision making. At one extreme, we examined profit maximization in perfectly competitive and monopolistically competitive markets. In these types of markets, so many firms are competing with one another that no individual firm has any effect on other firms in the market. At the other extreme, we examined profit maximization in a monopoly market. In this instance there is only one firm in the market, and strategic interactions among firms thus are irrelevant. This chapter is the first of two chapters in which we examine managerial decisions in oligopoly markets. Here we focus on basic output and pricing decisions in four specific types of oligopolies: Sweezy, Cournot, Stackelberg, and Bertrand. In the next chapter, we will develop a more general framework for analyzing other decisions, such as advertising, research and development, entry into an industry, and so forth. First, let us briefly review what is meant by the term oligopoly. CONDITIONS FOR OLIGOPOLY oligopoly A market structure in which there are only a few firms, each of which is large relative to the total industry. Oligopoly refers to a situation where there are relatively few large firms in an industry. No explicit number of firms is required for oligopoly, but the number usually is somewhere between 2 and 10. The products the firms offer may be either identical (as in a perfectly competitive market) or differentiated (as in a monopolistically competitive market). An oligopoly composed of only two firms is called a duopoly. Oligopoly is perhaps the most interesting of all market structures; in fact, the next chapter is devoted entirely to the analysis of situations that arise under oligopoly. But from the viewpoint of the manager, a firm operating in an oligopoly setting is the most difficult to manage. The key reason is that there are few firms in an oligopolistic market and the manager must consider the likely impact of her or his decisions on the decisions of other firms in the industry. Moreover, the actions of other firms will have a profound impact on the manager’s optimal decisions. It should be noted that due to the complexity of oligopoly, there is no single model that is relevant for all oligopolies. THE ROLE OF BELIEFS AND STRATEGIC INTERACTION To gain an understanding of oligopoly interdependence, consider a situation where several firms selling differentiated products compete in an oligopoly. In determining what price to charge, the manager must consider the impact of his or her decisions on other firms in the industry. For example, if the price for the product is lowered, will other firms lower their prices or maintain their existing prices? If the price is increased, will other firms do likewise or maintain their current prices? The optimal decision of whether to raise or lower price will depend on how the manager believes other managers will respond. If other firms lower their prices when the firm lowers its price, it will not sell as much as it would if the other firms maintained their existing prices. bay23224_ch09_325-363.qxd 12/28/12 8:13 AM Confirming Pages Page 327 327 Chapter 9: Basic Oligopoly Models FIGURE 9–1 A Firm’s Demand Depends on Actions of Rivals Price C Demand if rivals match price changes A B P0 Demand if rivals do not match price changes D2 D1 0 Q Q0 As a point of reference, suppose the firm initially is at point B in Figure 9–1, charging a price of P0. Demand curve D1 is based on the assumption that rivals will match any price change, while D2 is based on the assumption that they will not match a price change. Note that demand is more inelastic when rivals match a price change than when they do not. The reason for this is simple. For a given price reduction, a firm will sell more if rivals do not cut their prices (D2) than it will if they lower their prices (D1). In effect, a price reduction increases quantity demanded only slightly when rivals respond by lowering their prices. Similarly, for a given price increase, a firm will sell more when rivals also raise their prices (D1) than it will when they maintain their existing prices (D2). Demonstration Problem 9–1 Suppose the manager is at point B in Figure 9–1, charging a price of P0. If the manager believes rivals will not match price reductions but will match price increases, what does the demand for the firm’s product look like? Answer: If rivals do not match price reductions, prices below P0 will induce quantities demanded along curve D2. If rivals do match price increases, prices above P0 will generate quantities demanded along D1. Thus, if the manager believes rivals will not match price reductions but will match price increases, the demand curve for the firm’s product is given by CBD2. bay23224_ch09_325-363.qxd 328 12/28/12 8:13 AM Page 328 Confirming Pages Managerial Economics and Business Strategy Demonstration Problem 9–2 Suppose the manager is at point B in Figure 9–1, charging a price of P0. If the manager believes rivals will match price reductions but will not match price increases, what does the demand for the firm’s product look like? Answer: If rivals match price reductions, prices below P0 will induce quantities demanded along curve D1. If rivals do not match price increases, prices above P0 will induce quantities demanded along D2. Thus, if the manager believes rivals will match price reductions but will not match price increases, the demand curve for the firm’s product is given by ABD1. The preceding analysis reveals that the demand for a firm’s product in oligopoly depends critically on how rivals respond to the firm’s pricing decisions. If rivals will match any price change, the demand curve for the firm’s product is given by D1. In this instance, the manager will maximize profits where the marginal revenue associated with demand curve D1 equals marginal cost. If rivals will not match any price change, the demand curve for the firm’s product is given by D2. In this instance, the manager will maximize profits where the marginal revenue associated with demand curve D2 equals marginal cost. In each case, the profit-maximizing rule is the same as that under monopoly; the only difficulty for the firm manager is determining whether or not rivals will match price changes. PROFIT MAXIMIZATION IN FOUR OLIGOPOLY SETTINGS In the following subsections, we will examine profit maximization based on alternative assumptions regarding how rivals will respond to price or output changes. Each of the four models has different implications for the manager’s optimal decisions, and these differences arise because of differences in the ways rivals respond to the firm’s actions. Sweezy oligopoly An industry in which (1) there are few firms serving many consumers; (2) firms produce differentiated products; (3) each firm believes rivals will respond to a price reduction but will not follow a price increase; and (4) barriers to entry exist. Sweezy Oligopoly The Sweezy model is based on a very specific assumption regarding how other firms will respond to price increases and price cuts. An industry is characterized as a Sweezy oligopoly if 1. There are few firms in the market serving many consumers. 2. The firms produce differentiated products. 3. Each firm believes rivals will cut their prices in response to a price reduction but will not raise their prices in response to a price increase. 4. Barriers to entry exist. Because the manager of a firm competing in a Sweezy oligopoly believes other firms will match any price decrease but not match price increases, the demand curve for the firm’s product is given by ABD1 in Figure 9–2. For prices above P0, bay23224_ch09_325-363.qxd 12/28/12 8:13 AM Confirming Pages Page 329 329 Chapter 9: Basic Oligopoly Models FIGURE 9–2 Sweezy Oligopoly P MC0 A B MC1 P0 D2 C E MR2 MR 0 Q0 D1 Q F MR 1 the relevant demand curve is D2; thus, marginal revenue corresponds to this demand curve. For prices below P0, the relevant demand curve is D1, and marginal revenue corresponds to D1. Thus, the marginal revenue curve (MR) the firm faces is initially the marginal revenue curve associated with D2; at Q0, it jumps down to the marginal revenue curve corresponding to D1. In other words, the Sweezy oligopolist’s marginal revenue curve, denoted MR, is ACEF in Figure 9–2. The profit-maximizing level of output occurs where marginal revenue equals marginal cost, and the profit-maximizing price is the maximum price consumers will pay for that level of output. For example, if marginal cost is given by MC0 in Figure 9–2, marginal revenue equals marginal cost at point C. In this case the profit-maximizing output is Q0 and the optimal price is P0. Since price exceeds marginal cost (P0  MC0), output is below the socially efficient level. This situation translates into a deadweight loss (lost consumer and producer surplus) that does not arise in a perfectly competitive market. An important implication of the Sweezy model of oligopoly is that there will be a range (CE) over which changes in marginal cost do not affect the profit-maximizing level of output. This is in contrast to competitive, monopolistically competitive, and monopolistic firms, all of which increase output when marginal costs decline. To see why firms competing in a Sweezy oligopoly may not increase output when marginal cost declines, suppose marginal cost decreases from MC0 to MC1 in Figure 9–2. Marginal revenue now equals marginal cost at point E, but the output corresponding to this point is still Q0. Thus the firm continues to maximize profits by producing Q0 units at a price of P0. In a Sweezy oligopoly, firms have an incentive not to change their pricing behavior provided marginal costs remain in a given range. The reason for this stems purely from the assumption that rivals will match price cuts but not price increases. bay23224_ch09_325-363.qxd 330 12/28/12 8:13 AM Page 330 Confirming Pages Managerial Economics and Business Strategy Firms in a Sweezy oligopoly do not want to change their prices because of the effect of price changes on the behavior of other firms in the market. The Sweezy model has been criticized because it offers no explanation of how the industry settles on the initial price P0 that generates the kink in each firm’s demand curve. Nonetheless, the Sweezy model does show us that strategic interactions among firms and a manager’s beliefs about rivals’ reactions can have a profound impact on pricing decisions. In practice, the initial price and a manager’s beliefs may be based on a manager’s experience with the pricing patterns of rivals in a given market. If your experience suggests that rivals will match price reductions but will not match price increases, the Sweezy model is probably the best tool to use in formulating your pricing decisions. Cournot Oligopoly Cournot oligopoly An industry in which (1) there are few firms serving many consumers; (2) firms produce either differentiated or homogeneous products; (3) each firm believes rivals will hold their output constant if it changes its output; and (4) barriers to entry exist. Imagine that a few large oil producers must decide how much oil to pump out of the ground. The total amount of oil produced will certainly affect the market price of oil, but the underlying decision of each firm is not a pricing decision but rather the quantity of oil to produce. If each firm must determine its output level at the same time other firms determine their output levels, or more generally, if each firm expects its own output decision to have no impact on rivals’ output decisions, then this scenario describes a Cournot oligopoly. More formally, an industry is a Cournot oligopoly if 1. There are few firms in the market serving many consumers. 2. The firms produce either differentiated or homogeneous products. 3. Each firm believes rivals will hold their output constant if it changes its output. 4. Barriers to entry exist. Thus, in contrast to the Sweezy model of oligopoly, the Cournot model is relevant for decision making when managers make output decisions and believe that their decisions do not affect the output decisions of rival firms. Furthermore, the Cournot model applies to situations in which the products are either identical or differentiated. Reaction Functions and Equilibrium To highlight the implications of Cournot oligopoly, suppose there are only two firms competing in a Cournot duopoly: Each firm must make an output decision, and each firm believes that its rival will hold output constant as it changes its own output. To determine its optimal output level, firm 1 will equate marginal revenue with marginal cost. Notice that since this is a duopoly, firm 1’s marginal revenue is affected by firm 2’s output level. In particular, the greater the output of firm 2, the lower the market price and thus the lower is firm 1’s marginal revenue. This means that the profit-maximizing level of output for firm 1 depends on firm 2’s output level: A greater output by firm 2 leads to a lower profit-maximizing output for firm 1. This relationship between firm 1’s profit-maximizing output and firm 2’s output is called a best-response or reaction function. bay23224_ch09_325-363.qxd 12/28/12 8:13 AM Confirming Pages Page 331 331 Chapter 9: Basic Oligopoly Models best-response (or reaction) function A function that defines the profitmaximizing level of output for a firm for given output levels of another firm. A best-response function (also called a reaction function) defines the profitmaximizing level of output for a firm for given output levels of the other firm. More formally, the profit-maximizing level of output for firm 1 given that firm 2 produces Q2 units of output is Q1  r1(Q2 ) Similarly, the profit-maximizing level of output for firm 2 given that firm 1 produces Q1 units of output is given by Q2  r2(Q1 ) Cournot reaction (best-response) functions for a duopoly are illustrated in Figure 9–3, where firm 1’s output is measured on the horizontal axis and firm 2’s output is measured on the vertical axis. To understand why reaction functions are shaped as they are, let us highlight a few important points in the diagram. First, if firm 2 produced zero units of output, the profit-maximizing level of output for firm 1 would be QM 1 , since this is the point on firm 1’s reaction function (r1) that corresponds to zero units of Q2. This combination of outputs corresponds to the situation where only firm 1 is producing a positive level of output; thus, QM 1 corresponds to the situation where firm 1 is a monopolist. If instead of producing zero units of output firm 2 produced Q*2 units, the profit-maximizing level of output for firm 1 would be Q*1, since this is the point on r1 that corresponds to an output of Q*2 by firm 2. The reason the profit-maximizing level of output for firm 1 decreases as firm 2’s output increases is as follows: The demand for firm 1’s product depends on the FIGURE 9–3 Cournot Reaction Functions Q2 r1 (Reaction function of firm 1) Q M2 E Q2* C A D r2 (Reaction function of firm 2) B 0 Q1* Q M1 Q1 bay23224_ch09_325-363.qxd 332 12/28/12 8:13 AM Page 332 Confirming Pages Managerial Economics and Business Strategy output produced by other firms in the market. When firm 2 increases its level of output, the demand and marginal revenue for firm 1 decline. The profit-maximizing response by firm 1 is to reduce its level of output. Demonstration Problem 9–3 In Figure 9–3, what is the profit-maximizing level of output for firm 2 when firm 1 produces zero units of output? What is it when firm 1 produces Q*1 units? Answer: If firm 1 produces zero units of output, the profit-maximizing level of output for firm 2 will be QM 2 , since this is the point on firm 2’s reaction function that corresponds to zero units of Q1. The output of QM 2 corresponds to the situation where firm 2 is a monopolist. If firm 1 produces Q*1 units, the profit-maximizing level of output for firm 2 will be Q*2, since this is the point on r2 that corresponds to an output of Q*1 by firm 1. Cournot equilibrium A situation in which neither firm has an incentive to change its output given the other firm’s output. To examine equilibrium in a Cournot duopoly, suppose firm 1 produces QM 1 units of output. Given this output, the profit-maximizing level of output for firm 2 will correspond to point A on r2 in Figure 9–3. Given this positive level of output by firm 2, the profit-maximizing level of output for firm 1 will no longer be QM 1 , but will correspond to point B on r1. Given this reduced level of output by firm 1, point C will be the point on firm 2’s reaction function that maximizes profits. Given this new output by firm 2, firm 1 will again reduce output to point D on its reaction function. How long will these changes in output continue? Until point E in Figure 9–3 is reached. At point E, firm 1 produces Q*1 and firm 2 produces Q*2 units. Neither firm has an incentive to change its output given that it believes the other firm will hold its output constant at that level. Point E thus corresponds to the Cournot equilibrium. Cournot equilibrium is the situation where neither firm has an incentive to change its output given the output of the other firm. Graphically, this condition corresponds to the intersection of the reaction curves. Thus far, our analysis of Cournot oligopoly has been graphical rather than algebraic. However, given estimates of the demand and costs within a Cournot oligopoly, we can explicitly solve for the Cournot equilibrium. How do we do this? To maximize profits, a manager in a Cournot oligopoly produces where marginal revenue equals marginal cost. The calculation of marginal cost is straightforward; it is done just as in the other market structures we have analyzed. The calculation of marginal revenues is a little more subtle. Consider the following formula: Formula: Marginal Revenue for Cournot Duopoly. demand in a homogeneous-product Cournot duopoly is P  a  b(Q1  Q2 ) If the (inverse) market bay23224_ch09_325-363.qxd 12/28/12 8:13 AM Confirming Pages Page 333 333 Chapter 9: Basic Oligopoly Models where a and b are positive constants, then the marginal revenues of firms 1 and 2 are MR1(Q1, Q2 )  a  bQ2  2bQ1 MR2(Q1, Q2 )  a  bQ1  2bQ2 A Calculus Alternative Firm 1’s revenues are R1  PQ1  [a  b(Q1  Q2 )]Q1 Thus, MR1(Q1, Q2 )  R1  a  bQ2  2bQ1 Q1 A similar analysis yields the marginal revenue for firm 2. Notice that the marginal revenue for each Cournot oligopolist depends not only on the firm’s own output but also on the other firm’s output. In particular, when firm 2 increases its output, firm 1’s marginal revenue falls. This is because the increase in output by firm 2 lowers the market price, resulting in lower marginal revenue for firm 1. Since each firm’s marginal revenue depends on its own output and that of the rival, the output where a firm’s marginal revenue equals marginal cost depends on the other firm’s output level. If we equate firm 1’s marginal revenue with its marginal cost and then solve for firm 1’s output as a function of firm 2’s output, we obtain an algebraic expression for firm 1’s reaction function. Similarly, by equating firm 2’s marginal revenue with marginal cost and performing some algebra, we obtain firm 2’s reaction function. The results of these computations are summarized below. Formula: Reaction Functions for Cournot Duopoly. demand function P  a  b(Q1  Q2 ) and cost functions, C1(Q1 )  c1Q1 C2(Q2 )  c2Q2 the reaction functions are Q1  r1(Q2 )  a  c1 1  Q2 2b 2 Q2  r2(Q1 )  a  c2 1  Q1 2b 2 ˛ For the linear (inverse) bay23224_ch09_325-363.qxd 334 12/28/12 8:13 AM Confirming Pages Page 334 Managerial Economics and Business Strategy To see how the preceding formulas are derived, note that firm 1 sets output such that MR1(Q1, Q2 )  MC1 For the linear (inverse) demand and cost functions, this means that a  bQ2  2bQ1  c1 Solving this equation for Q1 in terms of Q2 yields Q1  r1(Q2 )  a  c1 1  Q2 2b 2 The reaction function for firm 2 is computed similarly. For a video walkthrough of this problem, visit www.mhhe.com/ baye8e Demonstration Problem 9–4 Suppose the inverse demand function for two Cournot duopolists is given by P  10  (Q1  Q2 ) and their costs are zero. 1. 2. 3. 4. What is each firm’s marginal revenue? What are the reaction functions for the two firms? What are the Cournot equilibrium outputs? What is the equilibrium price? Answer: 1. Using the formula for marginal revenue under Cournot duopoly, we find that MR1(Q1, Q2 )  10  Q2  2Q1 MR2(Q1, Q2 )  10  Q1  2Q2 2. Similarly, the reaction functions are 10 1  Q2 2 2 1  5  Q2 2 10 1 Q2  r2(Q1 )   Q1 2 2 1  5  Q1 2 Q1  r1(Q2 )