Chapter 9 Basic Oligopoly Models EC 500 Chapter 9 Basic Oligopoly Models

Headline Crude Oil Prices Fall, but Consumers in Some Areas See No Relief at the Pump The price of crude oil declined during the summer of 2004, from about $43 to $35 per barrel. As a result of declining crude oil prices, consumers in most locations enjoyed lower gasoline prices. Not all consumers reaped the benefits of lower crude oil prices, however. In a few isolated areas, 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 reason, 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.

Overview I. Conditions for Oligopoly? II. Role of Strategic Interdependence III. Profit Maximization in Four Oligopoly Settings Sweezy (Kinked-Demand) Model Cournot Model Stackelberg Model Bertrand Model IV. Contestable Markets

Oligopoly Environment Relatively few firms, usually less than 10. Duopoly - two firms Triopoly - three firms The products firms offer can be either differentiated or homogeneous.

Role of Strategic Interaction Your actions affect the profits of your rivals. Your rivals’ actions affect your profits.

An Example How does the quantity demanded for your product change when you change your price? There are two cases. Rivals will not match price changes. Rivals will match price changes. Point: If rivals MATCH price changes, demand becomes more INELASTIC! (STEEPER Demand curve; D2 in the next slide).

D2 (Rival matches your price change) P PH QH1 QH2 P0 Q0 PL QL2 QL1 D1 (Rival holds its price constant) Q

Why more Inelastic (D2) if matched? Suppose that you DECREASE price (P0  PL). If rivals do not match price decrease, you will be able to sell MORE (QL1) than they match price (QL2) . If they will match price decrease, you will sell less than they do not match price. (QL2 < QL1) Suppose that you INCREASE price (P0  PH). If rivals do not match price increase, you will sell LESS (QH1) than they match price (QH2). (QH1 < QH2) Thus, if rival match price changes, demand curve will be D2.

Four Cases (see next slide) Rivals match price decrease but not price increase. (CAD) ; Sweezy model (kinked demand function!) Rivals match price increase but not price decrease. (EAF) Rivals match both price decrease and price increase. (EAD) Rivals match neither price decrease or price increase. (CAF)

(Rival matches your price change) Q D1 P0 Q0 (Rival matches your price change) (Rival holds its price constant) C E D2 Demand if Rivals Match Price Reductions but not Price Increases (CAD) A F D

Key Insight The effect of a price reduction on the quantity demanded of your product depends upon whether your rivals respond by cutting their prices too! The effect of a price increase on the quantity demanded of your product depends upon whether your rivals respond by raising their prices too! Strategic interdependence: You aren’t in complete control of your own destiny!

Sweezy (Kinked-Demand) Model Few firms in the market serving many consumers. Firms produce differentiated products. Barriers to entry. Each firm believes rivals will match (or follow) price reductions, but won’t match (or follow) price increases. Key feature of Sweezy Model Price-Rigidity.

Sweezy Demand and Marginal Revenue P D2 (Rival matches your price change) MR2 DS: Sweezy Demand D1 (Rival holds its price constant) MR1 P0 Q0 Q MRS: Sweezy MR

Sweezy Profit-Maximizing Decision D2 (Rival matches your price change) DS: Sweezy Demand MRS MC1 MC2 P0 MC3 Q0 D1 (Rival holds price constant) Q

Sweezy Oligopoly Summary Firms believe rivals match price cuts, but not price increases. Firms operating in a Sweezy oligopoly maximize profit by producing where MRS = MC. The kinked-shaped marginal revenue curve implies that there exists a range over which changes in MC will not impact the profit-maximizing level of output. Therefore, the firm may have no incentive to change price provided that marginal cost remains in a given range.

Cournot Model A few firms produce goods that are either perfect substitutes (homogeneous) or imperfect substitutes (differentiated). Firms set output, as opposed to price. Each firm believes their rivals will hold output constant if it changes its own output (The output of rivals is viewed as given or “fixed”). Barriers to entry exist.

Inverse Demand in a Cournot Duopoly Market demand in a homogeneous-product Cournot duopoly is Thus, each firm’s marginal revenue depends on the output produced by the other firm. More formally,

Best-Response Function Since a firm’s marginal revenue in a homogeneous Cournot oligopoly depends on both its output and its rivals, each firm needs a way to “respond” to rival’s output decisions. Firm 1’s best-response (or reaction) function is a schedule summarizing the amount of Q1 firm 1 should produce in order to maximize its profits for each quantity of Q2 produced by firm 2. Since the products are substitutes, an increase in firm 2’s output leads to a decrease in the profit-maximizing amount of firm 1’s product.

Best-Response Function for a Cournot Duopoly To find a firm’s best-response function, equate its marginal revenue to marginal cost and solve for its output as a function of its rival’s output. Firm 1’s best-response function is (c1 is firm 1’s MC) Firm 2’s best-response function is (c2 is firm 2’s MC)

Graph of Firm 1’s Best-Response Function Q2 (a-c1)/b Q1 = r1(Q2) = (a-c1)/2b - 0.5Q2 Q2 r1 (Firm 1’s Reaction Function) Q1 Q1 Q1M

Cournot Equilibrium Situation where each firm produces the output that maximizes its profits, given the the output of rival firms. No firm can gain by unilaterally changing its own output to improve its profit. A point where the two firm’s best-response functions intersect.

Graph of Cournot Equilibrium (a-c1)/b r1 Cournot Equilibrium Q2M Q2* r2 Q1* Q1M (a-c2)/b Q1

Summary of Cournot Equilibrium The output Q1* maximizes firm 1’s profits, given that firm 2 produces Q2*. The output Q2* maximizes firm 2’s profits, given that firm 1 produces Q1*. Neither firm has an incentive to change its output, given the output of the rival. Beliefs are consistent: In equilibrium, each firm “thinks” rivals will stick to their current output – and they do!

Numerical Example P = 280 – 2(Q1 + Q2) C1 = 3Q1, C2 = 2Q2 Find MR1 and MR2. Rev1 = PQ1 = [280 – 2(Q1 + Q2)] Q1 MR1 = 280 - 2Q2 - 4Q1 Rev2 = PQ2 = [280 – 2(Q1 + Q2)] Q2 MR1 = 280 - 2Q1 - 4Q2 Using MC1 and MC2, find the reaction functions for each firm. MR1 = MC1 implies 280 - 2Q2 - 4Q1 = 3 4Q1 = 280 - 2Q2 – 3 or Q1 = 69.25 - .5Q2 Similarly, from MR2 = MC2, we have Q2 = 69.5 - .5Q1

Exercise: Q. 2, p. 345 P = 100 – 2(Q1 + Q2) C1 = 12Q1, C2 = 20Q2 (c) How much output will each firm produce in equilibrium? Solve simultaneously, Q1 = 69.25 - .5Q2 Q2 = 69.5 - .5Q1 Q1* = 46 Q2* = 46.5 P* = 280 – 2(Q1* + Q2*) = 95 (d) What are the equilibrium profits for each firm? Profit1 = PQ1 – 3Q1 = 95*46 – 3*46 = $4,232 Profit2 = PQ2 – 2Q2 = 95*46.5 – 2*46.5 = $4,324.5. Exercise: Q. 2, p. 345 P = 100 – 2(Q1 + Q2) C1 = 12Q1, C2 = 20Q2

Firm 1’s Isoprofit Curve Q2 The combinations of outputs of the two firms that yield firm 1 the same level of profit Profit will be maximized for firm 1 if it can produce Q1M. Thus, moving downward increases its profit. r1 B C Increasing Profits for Firm 1 A 1 = $100 D 1 = $200 Q1M Q1

Another Look at Cournot Decisions Q2 r1 Firm 1’s best response to Q2* Q2*  1 = $100  1 = $200 Q1* Q1M Q1

Another Look at Cournot Equilibrium Firm 2’s Profits Cournot Equilibrium Q2M C Q2* Firm 1’s Profits r2 Q1* Q1M Q1

We can do further analysis using this framework; next slides. Point: Cournot equilibrium occurs at the intersection of the two firms’ reaction functions (point C). We can do further analysis using this framework; next slides.

Impact of Rising Costs on the Cournot Equilibrium Cournot equilibrium after firm 1’s marginal cost increase r1** r2 Q2** Q1** Cournot equilibrium prior to firm 1’s marginal cost increase Q2* Q1* Q1

Points Exercise r1 shifts in! Why? New output for firm 1 will be Q1**. Why? What happened to Q1 and Q2 in the end? Exercise What if MC2 has declined? Draw a diagram and explain what will happen to Q1 and Q2 in the end.

Collusion Incentives in Cournot Oligopoly Q2 r1 Q2M r2 Q1M Q1

Collusion Incentives in Cournot Oligopoly Moving to Point D will make both firms better off! Why?

However, collusion is not easy. Why? If Firm 1 cheats (point G), its profit increases! Why?

Stackelberg Model In the Sweezy and Cournot models, We assume that firms are symmetric and they are equal. But, there may be a leader, and others will follow the leader. In the Stackelberg model, Firm one is the leader. The leader commits to an output before all other firms. Remaining firms are followers. They choose their outputs so as to maximize profits, given the leader’s output. Firms produce differentiated or homogeneous products. Barriers to entry.

The leader can choose the point on the follower’s reaction curve that corresponds to the highest level of profits. Then, find the point tangent to the follower’s reaction function; Point S (next slide) and produce Q1S. That is, firm 1 chooses its output level using the reaction function of firm 2. The profit for firm 1 (leader) is higher at Point S and Point C. Why?

Stackelberg Equilibrium Followers π2C r1 Follower’s Profits Decline πFS Stackelberg Equilibrium C Q2C πLS S Q2S π1C r2 Q1C Q1S Q1M Q1 leader

Stackelberg Summary Stackelberg model illustrates how commitment can enhance profits in strategic environments. Leader produces more than the Cournot equilibrium output. Larger market share, higher profits. First-mover advantage. Follower produces less than the Cournot equilibrium output. Smaller market share, lower profits.

Example of Stackelberg Model P = 50 – (Q1 + Q2) C1 = 2Q1, C2 = 2Q2 Find MR1 and MR2. Rev1 = PQ1 = [50 – (Q1 + Q2)]Q1 MR1 = 50 - 2Q1 – Q2 Rev2 = PQ2 = [50 – (Q1 + Q2)]Q2 MR1 = 50 - Q1 - 2Q2 Using MC1 and MC2, find the reaction functions for each firm. MR1 = MC1 implies 50 - 2Q1 – Q2 = 2 Q1 = 24 - .5Q2 Similarly, from MR2 = MC2, we have Q2 = 24 - .5Q1 Note: so far, the above analysis is the same as that of Cournot Models.

(c) Find Firm1’s output of Stackelberg model. Rev1 = PQ1 – C1 = [50-(Q1+Q2)]Q1 – 2Q1 Point: Here, we replace Q2 with the reaction function of firm 2, Q2 = 24 - .5Q1. Why? Rev1 = [50-(Q1+ 24 - .5Q1)]Q1 – 2Q1 dRev1/dQ1 = 0 gives dRev1/dQ1 = 50 – 2Q1 – 24 + Q1 – 2 = 0  Q1* = 24  Q2* = 24 - .5(24) = 12 P* = 50 – Q1* – Q2* = 50 – 24 – 12 = 14

(d) Find the profit of each firm. Profit1 = PQ1 – 2Q1 = 14*24 – 2*24 = 288 Profit2 = PQ2 – 2Q2 = 14*12 – 2*12 = 144 Exercise: Re-do the above with the following. P = 280 – 2(Q1 + Q2) C1 = 3Q1, C2 = 2Q2

Bertrand Model Question: Does oligopoly power always imply firms will make positive profits? Not necessarily if there is a price war. Firms compete for price and react optimally to competitor’s prices. Bertrand Model explains that P = MC is possible. Conditions for Bertrand Model Few firms that sell to many consumers. Firms produce identical products at constant marginal cost. Each firm independently sets its price in order to maximize profits. Barriers to entry. Consumers enjoy Perfect information and Zero transaction costs.

Bertrand Equilibrium Firms set P1 = P2 = MC! Why? Suppose MC < P1 < P2. Firm 1 earns (P1 - MC) on each unit sold, while firm 2 earns nothing. Firm 2 has an incentive to slightly undercut firm 1’s price to capture the entire market. Firm 1 then has an incentive to undercut firm 2’s price. This undercutting continues... Equilibrium: Each firm charges P1 = P2 = MC.

The required key assumptions are Identical MCs Identical products Price competition Perfect information of consumers But, Bertrand Model can be useful for on-line sales Example P = 50 – (Q1 + Q2) C1 = 2Q1, C2 = 2Q2 Since P = MC, P = $2. Then, Q1 + Q2 = 48.

Contestable Markets Question: Should we have price wars to guarantee zero profits (P = MC)? Not necessarily, even there is only one single firm, if markets are contestable. There are potential entry Key Assumptions Producers have access to same technology. Consumers respond quickly to price changes. Existing firms cannot respond quickly to entry by lowering price. Absence of sunk costs.

Key Implications Threat of entry disciplines firms already in the market. Incumbents have no market power, even if there is only a single incumbent (a monopolist).

Example again (summary) Find the equilibrium outputs, and profits of each firm for each of (i) Cournot Model (ii) Stackelberg Model (iii) Bertrand Model (iv) Collusion Model. (Ex1) P = 50 – (Q1 + Q2) C1 = 2Q1, C2 = 2Q2 (Ex2) P = 50 – (Q1 + Q2)

Answering the Headline Although the price of oil fell, in a few areas there were no declines in the price of gasoline. The headline asks whether this is evidence of collusion by gasoline stations in those areas. To answer this question, notice that oil is an input in producing gasoline. A reduction in the price of oil leads to a reduction in the marginal cost of producing gasoline—say, from MC0 to MC1. If gasoline stations were colluding, a reduction in marginal cost would lead the firms to lower the price of gasoline. Also, it could lead to a greater collusive output. Thus, collusion cannot explain why some gasoline firms failed to lower their prices. It is possible that these gasoline producers are Sweezy oligopolists; see the diagram.

Conclusion Different oligopoly scenarios give rise to different optimal strategies and different outcomes. Your optimal price and output depends on … Beliefs about the reactions of rivals. Your choice variable (P or Q) and the nature of the product market (differentiated or homogeneous products). Your ability to credibly commit prior to your rivals.

Homework Q. 2 (Cournot) Q. 4 (Stackelberg) Q. 5 (Bertrand) Q. 7 (p. 346; all models)