University of Hong Kong ECON6021 Microeconomic Analysis Oligopoly


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1 1 Introduction University of Hong Kong ECON6021 Microeconomic Analysis Oligopoly There are many real life examples that the participants have nonnegligible influence on the market. In such markets, every firm is aware that other firms decisions will have profound effects on it, tries to anticipate these decisions, and chooses a best decision based on this anticipation. Think of newspapers, TV channels, mobile service providers, or even MBA programmes. Between the two extremes of perfect competition and monopoly, economists have identified two interesting intermediate market structures: monopolistic competition and oligopoly. Monopolistic competition, first proposed by Chamberlain and Joan Robinson in late 1920s, is a market structure characterized by both monopoly and competition. In the original model the goods sold in the market are differentiated, and hence each firm has some market power the firm will not lose all its customers by rising its price above the market price (hence monopoly). On the other hand, because of easy entry and exit, there are many firms in themarketandeachfirm will just earn a zero profit (hence competition). There has been a great variety of models of monopolistic competition since Chamberlain and Robinson. The framework is particularly useful for us to study product quality choice. The Chamberlain model (known as the location model) also places an instrumental role in the study of political competition. Finally, in 1980s monopolistic competition was employed to help develop new international trade models to understand intraindustrial trade, viz., why Germany and US trade with each other. (Future generations will accolade Paul Krugman as a central hero in the revolution of trade theory, comparable to David Ricardo in his time.) In this lecture note, we will concentrate instead on oligopoly a market structure in which there are only a few firms, and entry barriers are so high that the incumbent firms can earn positive profits without luring new firms to enter. The particular type of oligopoly that deserves most of our attention is duopoly an oligopoly with just two firms. There are three different models of duopoly/oligopoly and we will go through one by one. 1
2 Figure 1: 2 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 and output to charge, one firm must consider the impact of its 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 firm believes other firms 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. As a point of reference, suppose the firm initially is at point B in Figure 1, charging a price of P 0. Demand curve D 1 is based on the assumption that rivals will match any price change, while D 2, is based on the assumption that they will not match a price change. Note that demand is more inelastic 2
3 where 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 (D 2 ) than it will if they lower their prices (D 1 ). 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 where rivals also raise their prices (D 1 )thanitwill when they maintain their existing prices (D 2 ). 3 Cournot Competition An industry is characterized as 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. 3.1 Reaction Functions and Equilibrium. To highlight the implications of Cournot oligopoly, suppose there are only two firms competing in a Cournot duopoly. Since this is a Cournot duopoly, firm 1 believes firm 2 will hold its output constant as it changes its own output. The profitmaximizing level of output for firm 1 depends on the output of firm 2. This information is summarized in the reaction function. A reaction function defines the profitmaximizing level of output for a firm for given output levels of the other firm. More formally, the profitmaximizing level of output for firm 1 given that firm 2 produces Q 2 units of output is Q 1 = r 1 (Q 2 ). Similarly, the profitmaximizing level of output for firm 2 given that firm 1 produces Q 1 units of output is given by Q 2 = r 2 (Q 1 ). Cournot reaction functions for a duopoly are illustrated in Figure 2, where firm 1 s output is measured on the horizontal axis and firm 2 s output is measured on the vertical axis. 3
4 Figure 2: 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 profitmaximizing level of output for firm 1 would be Q M 1, since this is the point on firm 1 s reaction function (r 1)thatcorresponds to zero units of Q 2. This combination of outputs corresponds to the situation where only firm 1 is producing a positive level of output; thus, Q M 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 profitmaximizing level of output for firm 1 would be Q 1, since this is the point on r 1 that corresponds to an output of Q 2 by firm 2. The reason the profitmaximizing 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 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 profitmaximizing response by firm1istoreduceitslevelof output. To examine equilibrium in a Cournot duopoly, suppose firm 1 produce units of output. Given this output, the profitmaximizing level of output Q M 1 4
5 for firm 2 will correspond to point A on r 2 in Figure 2. Given this positive level of output by firm 2, the profitmaximizing level of output for firm 1 will no longer be Q M 1, but will correspond to point B on r 1. 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 2 is reached. At point E, firm 1 produces Q 1 and firm 2 produces Q 2 ; unit 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. Howdowedothis? Tomaximizeprofits, a manager in a Cournot oligopoly produces where marginal revenue equals marginal cost. The calculation of marginal cost is straight forward; it is done just as in the other market structures we have analyzed. The calculation of marginal revenue is a little more subtle. Consider the following formula: Formula: Marginal Revenue for Cournot Duopoly. If the (inverse) demand in a homogeneousproduct Cournot duopoly is P = a b(q 1 + Q 2 ), where a and b are positive constants, then the marginal revenues of firms 1 and 2 are MR 1 (Q 1,Q 2 ) = a bq 2 2bQ 1 MR 2 (Q 1,Q 2 ) = a bq 1 2bQ 2 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 the other firm s output, the profit maximizing output of each firm also depends on the other firm s output. This dependence is summarized in a firm s reaction function. 5
6 3.2 Model Assumptions: two identical firms (duopoly); homogenous product; constant marginal cost c 1 and c 2 (no fixed costs); one period simultaneous moves; linear demand p = A B(q 1 + q 2 ); quantity as choice variable firm 1 s objective function: max q 1 π 1 (q 1,q 2 )=(A B (q 1 + q 2 ))q 1 c 1 q 1 The first order condition for a local maximum is That is, dπ 1 (q 1,q 2 ) = A B(q 1 + q 2 ) Bq 1 c dq 1 {z } {z} 1 =0 MC MR q 1 (q 2 )=(A Bq 2 c 1 ) /2B. (1) which is called firm 1 s best response, or reaction function. The strategic interaction between the two firms optimal decisions are illustrated in such a reaction function. What is the best for firm 1 depends what the other firm is going to do. Note that (1) shows that firm 1 s optimal choice is decreasing in q 2. That is, firm 1 will produce a lower level if it knows that firm 2 is getting more aggressive. If you ask what firm 1 s best action is, the answer you will get back is it depends. Similarly, we have firm 2 s best response function q 2 (q 1 )=(A Bq 1 c 2 ) /2B. (2) A Nash equilibrium requires that the q 2 anticipated by firm 1 must be equal to the actual q 2 chosen by firm 2, and the q 1 anticipated by firm 2 must be equal to the actual q 1 chosen by firm 1. Plotting the two curves in a diagram with axes of q 1 and q 2, we can easily see that they intersect only once and the horizontal and vertical ordinates of the point of intersection (q1,q 2 ) constitutes an equilibrium. 3.3 Isoprofit Curves. Now that you have a basic understanding of Cournot oligopoly, we will examine how to graphically determine the firm s profits. Recall that the profits of a firm in an oligopoly depend not only on the output it chooses to produce but also on the output produced by other firms in the oligopoly. In a duopoly, for instance, increases in firm 2 s output will reduce the price of the output. This is due to the law of demand: As more output is sold 6
7 Figure 3: in the market, the price consumers are willing and able to pay for the good declines. This will, of course, alter the profits of firm 1. The basic tool used to summarize the profits of a firm in Cournot oligopoly is an isoprofit curve, which defines the combinations of outputs of all firms that yield a given firm the same level of profits. Figure 3 presents the reaction function for firm 1 (r 1 ), along with three isoprofit curves(labeled π 0, π 1, and π 2 ). Four aspects of Figure 3 are important to understand: 1. Every point on a given isoprofit curve yields firm 1 the same level of profits. For instance, points F, A, and G all lie on the isoprofit curve labeled π 0 ; thus, each of these points yields profits of exactly π 0 for firm Isoprofit curves that lie closer to firm l s monopoly output (Q M 1 )are associated with higher profits for that firm. For instance, isoprofit curve π 2 implies higher profits than does π 1,andπ 1 is associated with higher profits than π 0. In other words, as we move down firm l s reaction function from point A to point C, firm l s profits increase. 7
8 3. The isoprofit curves for firm 1 reach their peak where they intersect firm l s reaction function. For instance, isoprofit curveπ 0 peaks at point A, where it intersects r 1 ; π 1 peaks at point B, where it intersects r 1,andsoon. 4. The isoprofit curves do not intersect one another. With an understanding of these four aspects of isoprofit curves, we now provide further insights into managerial decisions in a Cournot oligopoly. Recall that one assumption of Cournot oligopoly is that each firm takes as given the output decisions of rival firms and simply chooses its output to maximize profits given other firms output. This is illustrated in Figure 4, whereweassumefirm 2 s output is given by Q 2.Sincefirm 1 believes firm 2 will product this output regardless of what firm 1 does, it chooses its output level to maximize profits when firm 2 produces Q 2. One possibility is for firm1toproduceq A 1 units of output, which would correspond to point A on isoprofit curveπ A 1. However, this decision does not maximize profits, because by expanding output to Q B 1, firm1movestoahigherisoprofit curve (π B 1, which corresponds point B). Notice that profits can be further increased if firm 1 expands output to Q C 1, which is associated with isoprofit curve π C 1. It is not profitable for firm 1 to increase output beyond Q C 1, given that firm 2 produces Q 2?To see this, suppose firm 1 expanded output to, say, QD 1. This would result in a combination of outputs that corresponds to point D, whichliesonanisoprofit curve that yields lower profits. We conclude that the profit maximizing output for firm 1 is Q C 1 whenever firm 2 produces Q 2 units. This should not surprise you: This is exactly the output that corresponds to firm 1 s reaction function. To maximize profits, firm 1 pushes its isoprofit curveasfardownas possible (as close as possible to the monopoly point), until it is just tangent to the given output of firm 2. This tangency occurs at point C in Figure 4. We can use isoprofit curves to illustrate the profits of each firm in a Cournot equilibrium. Recall that Cournot equilibrium is determined by the intersection of the two firms reaction functions, such as point C in Figure 5. Firm l s isoprofit curve through point C is given by π C 1 and firm 2 s isoprofit curve is given by π C Changes in Marginal Costs. To see the effect of a change in marginal cost, suppose the firms initially are in equilibrium at point E in Figure 6, where firm 1 produces Q 1 units and 8
9 Figure 4: firm 2 produces Q 2 units. Now suppose firm 2 s marginal cost declines. At the given level of output, marginal revenue remains unchanged but marginal cost is reduced. This means that for firm 2, marginal revenue exceeds the lower marginal cost, and it is optimal to produce more output for any given level of Q 1. Graphically, this shifts firm 2 s reaction function up from r 2 to r2, leading to a new Cournot equilibrium at point F. Thus, the reduction in firm 2 s marginal cost leads to an increase in firm 2 s output, from Q 2 to Q 2, and a decline in firm l s output from Q 1 to Q 1. Firm 2 enjoys a larger market share due to its improved cost situation. 3.5 Collusion Whenever a market is dominated by only a few firms, firms can benefit at the expense of consumers by agreeing to restrict output or, equivalently, charge higher prices. Such an act by firms is known as collusion. In the next chapter, we will devote considerable attention to collusion; for now, it is useful to use the model of Cournot oligopoly to show why such an incentive exists. In Figure 7, point C corresponds to a Cournot equilibrium; it is the 9
10 Figure 5: 10
11 Figure 6: 11
12 Figure 7: 12
13 intersection of the reaction functions of the two firms in the market. The equilibrium profits of firm 1 are given by isoprofit curveπ C 1 and those of firm 2byπ C 2 Notice that the shaded lensshaped area in Figure 7 contains output levels for the two firms that yield higher profits for both firms than they earn in a Cournot equilibrium. For example, at point D each firm produces less output and enjoys greater profits, since each of the firm s isoprofit curves at point D is closer to the respective monopoly point. In effect, if each firm agreed to restrict output, the firms could charge higher prices and earn higher profits. The reason is easy to see. Firm l s profits would be highest at point A, where it is a monopolist. Firm 2 s profits would be highest at point B, whereitisamonopolist. Ifeachfirm agreed to produce an output that in total equaled the monopoly output, the firmswouldendupsomewhere on the line connecting points A and B. In other words, any combination of outputs along line AB would maximize total industry profits. The outputs on the line segment connecting points E and F in Figure 7 thus maximize total industry profits, and since they are inside the lensshaped area, they also yield both firms higher profits than would be earned if the firms produced at point C (the Cournot equilibrium). If the firms colluded by restricting output and splitting the monopoly profits, they would end up at a point like D, earning higher profits of π collude 1 and π collude 2. It is not easy for firms to reach such a collusive agreement, however. We will analyze this point in greater detail in the next chapter, but we can use our existing framework to see why collusion is sometimes difficult. Suppose firms agree to collude, with each firm producing the collusive output associated with point D in Figure 8 to earn collusive profits. Given that firm 2 produces Q collusive 2, firm 1 has an incentive to cheat on the collusive agreement by expanding output to point G. At this point, firm 1 earns even higher profits than it would by colluding, since π cheat 1 > π collude 1.This suggests that a firm can gain by inducing other firms to restrict output and then expanding its own output to earn higher profits at the expense of its collusion partners. Because firms know this incentive exists, it is often difficult for them to reach collusive agreements in the first place. This problem is amplified by the fact that firm 2 in Figure 8 earns less at point G(wherefirm 1 cheats) than it would have earned at point C (the Cournot equilibrium). 13
14 Figure 8: 14
15 4 Stackelberg Oligopoly Up until this point, we have analyzed oligopoly situations that are symmetric in that firm 2 is the mirror image of firm 1, In many oligopoly markets, however, firms differ from one another. In a Stackelberg oligopoly, firms differ with respect to when they make decisions. Specifically, one firm (the leader) is assumed to make an output decision before the other firms. Given knowledge of the leader s output, all other firms (the followers) take as given the leader s output and choose outputs that maximize profits. Thus, in a Stackelberg oligopoly, each follower behaves just like a Cournot oligopolist. However, firm 1 (the leader) does not act like a Cournot oligopolist. In fact, the leader does not take the followers outputs as given but instead chooses an output that maximizes profits given that each follower will react to this output decision according to a Cournot reaction function. An industry is characterized as a Stackelberg oligopoly if: 1. There are few firms in the market serving many consumers. 2. The firms produce either differentiated or homogeneous products. 3. A single firm (the leader) selects an output before all other firms choose their outputs. 4. All other firms (the followers) take as given the output of the leader and choose outputs that maximize profits given the leader s output. 5. Barriers to entry exist. To highlight a Stackelberg oligopoly, let us consider a situation where there are only two firms. Firm 1 is the leader and thus has a firstmover advantage; that is, firm 1 produces before firm 2. Firm 2 is the follower and maximizes profit given the output produced by the leader. Because the follower produces after the leader, the follower s profitmaximizing level of output is determined by its reaction function. This is denoted by r 2 in Figure 9. However, the leader knows the follower will react according to r 2.Consequently, the leader must choose the level of output that will maximize its profits given that the follower reacts to whatever the leader does. How does the leader choose the output level to produce? Since it knows the follower will produce along r 2, the leader simply chooses the point on the follower s reaction curve that corresponds to the highest level of its profits. Because the leader s profits increase as the isoprofit curves get closer to 15
16 Figure 9: 16
17 the monopoly output, the resulting choice by the leader will be at point S in Figure 9. This isoprofit curve,denotedπ S 1, yields the highest profits consistent with the follower s reaction function. It is tangent to firm 2 s reaction function. Thus, the leader produces Q S 1. The follower observes this output and produces Q S 2,whichistheprofitmaximizing response to QS 1. The corresponding profits of the leader are given by π S 1, and those of the follower by π S 2. Notice that the leader s profits are higher than they would be in Cournot equilibrium (point C), and the follower s profits are lower than in Cournot equilibrium. By getting to move first, the leader earns higher profits than would otherwise be the case. The algebraic solution for a Stackelberg oligopoly can also be obtained, provided firms have information about market demand and costs. In particular, recall that the follower s decision is identical to that of a Cournot model. For instance, with linear demand and constant marginal cost, the output of the follower is given by the reaction function Q 2 = r 2 (Q 1 )= a c 2 1 2b 2 Q 1, which is simply the follower s Cournot reaction function. However, the leader in the Stackelberg oligopoly takes into account this reaction function when it selects Q 1. With a linear inverse demand function and constant marginal costs, the leader s profits are ½ µ a c2 Π 1 = a b Q ¾ 2b 2 Q 1 Q 1 c 1 Q 1. The leader chooses Q 1 to maximize this profit expression. It turns out that the value of Q 1 that maximizes the leader s profits is Q 1 = a + c 2 2c 1. 2b Formula: Equilibrium Outputs in Stackelberg Oligopoly. For the linear (inverse) demand function and cost functions P a b(q 1 + Q 2 ) C 1 (Q 1 ) = c 1 Q 1 C 2 (Q 2 ) = c 2 Q 2, 17
18 the follower sets output according to the Cournot reaction function Q 2 = r 2 (Q 1 )= a c 2 1 2b 2 Q 1. The leader s output is Q 1 = a + c 2 2c 1. 2b 5 Bertrand Oligopoly To further highlight the fact that there is no single model of oligopoly a manager can use in all circumstances and illustrate that oligopoly power does no always imply firms will make positive profits,wewillnextexamine Bertrand oligopoly. The treatment here assumes the firms sell identical products; the case where firms sell differentiated products is presented in the appendix. The next chapter also contains a more detailed analysis of Bertrand oligopoly. An industry is characterized as a Bertrand oligopoly if: 1. There are few firms in the market serving many consumers. 2. The firms produce identical products as a constant marginal cost. 3. Firms engage in price competition and react optimally to prices charged by competitors. 4. Consumers have perfect information and there are no transaction costs. 5. Barriers to entry exist. From the viewpoint of the manager Bertrand oligopoly is undesirable, for it leads to zero profits even if there are only two firms in the market. From the viewpoint of consumers Bertrand oligopoly is desirable, for it leads to precisely the same outcome as a perfectly competitive market. To explain more precisely the preceding assertions, consider a Bertrand duopoly. Because consumers have perfect information, have zero transaction costs. and the products are identical, all consumers will purchase from the firm charging the lowest price. For concreteness, suppose firm 1 charges the monopoly price. By slightly undercutting this price, firm 2 would capture the entire market and make positive profits, while firm 1 would sell nothing. Therefore, firm 1 would retaliate by undercutting firm 2 s lower price, thus recapturing the entire market. 18
19 When would this price war end? When each firm charged a price that equaled marginal cost: P 1 = P 2 = MC. Given the price of the other firm, neither firm would choose to lower its price, for then its price would be below marginal cost and it would make a loss. Also no firm would want to raise it price, for then it would sell nothing. In short, Bertrand oligopoly and homogeneous products lead to a situation where each firm charges marginal cost and economic profits are zero. 6 Concluding Remarks We end this lecture note with the following typology. choice variable is quantity quality move simultaneously Cournot Bertrand move sequentially Stackelberg (Stackelberg  Bertrand??) 7 References See Chapter 13 in Frank. 19
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