BUS 525: Managerial Economics Lecture 9 Basic Oligopoly Models

1. BUS 525: Managerial Economics Lecture 9 Basic Oligopoly Models

2. Overview 9-2 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

3. Oligopoly Environment 9-3 A market structure there are only a few Firms, each of which is large relative the total industry • Relatively few firms, usually less than 10. • Duopoly - two firms • Triopoly - three firms • The products firms offer can be either differentiated or homogeneous. • Firms’ decisions impact one another. • Many different strategic variables are modeled: • No single oligopoly model.

4. Role of Strategic Interaction 9-4 • Your actions affect the profits of your rivals. • Your rivals’ actions affect your profits. • How will rivals respond to your actions?

5. An Example 9-5 • You and another firm sell differentiated products. • How does the quantity demanded for your product change when you change your price?

6. P0 QH1 QH2 QL2 QL1 Q0 9-6 D1 (Rival matches your price change) P PH B PL D2 (Rival holds its price constant) Q

7. D2 (Rival matches your price change) P P0 D1 (Rival holds its price constant) Q Q0 9-7 Demand if Rivals Match Price Reductions but not Price Increases D2 Note that demand is more inelastic when rivals match a price change than when they do not Reason: 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

8. Key Insight 9-8 • 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!

9. Sweezy (Kinked-Demand) Model Environment 9-9 • 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.

10. D2 (Rival matches your price change) P0 D1 (Rival holds its price constant) MR1 MR2 Q0 Sweezy Demand and Marginal Revenue 9-10 P DS: Sweezy Demand Q MRS: Sweezy MR

11. MC1 MC2 P0 MC3 DS: Sweezy Demand MRS Q0 Sweezy Profit-Maximizing Decision 9-11 P D2 (Rival matches your price change) A C D1 (Rival holds price constant) E Q

12. Sweezy Oligopoly Summary 9-12 • 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.

13. Cournot Model Environment 9-13 • A few firms produce goods that are either perfect substitutes (homogeneous) or imperfect substitutes (differentiated). • Firms’ control variable is output in contrast 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.

14. Inverse Demand in a Cournot Duopoly 9-14 • 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,

15. Best-Response Function 9-15 • 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.

16. Best-Response Function for a Cournot Duopoly 9-16 • 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)

17. Q1 = r1(Q2) = (a-c1)/2b - 0.5Q2 Graph of Firm 1’s Best-Response Function 9-17 Q2 (a-c1)/b Q2 r1 (Firm 1’s Reaction Function) Q1 Q1M Q1

18. Cournot Equilibrium 9-18 • 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.

19. Graph of Cournot Equilibrium 9-19 Q2 (a-c1)/b r1 Cournot Equilibrium Q2M E Q2* C A B r2 Q1* Q1M (a-c2)/b Q1

20. Summary of Cournot Equilibrium 9-20 • The outputQ1* maximizes firm 1’s profits, given that firm 2 produces Q2*. • The outputQ2* 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!

21. The Isoprofit Curve

22. B C A 9-22 Firm 1’s Isoprofit Curve Q2 • The combinations of outputs of the two firms that yield firm 1 the same level of profit r1 Increasing Profits for Firm 1 0 = $100 D E 1 = $200 2 = $300 Q1M Q1

23. Another Look at Cournot Decisions 9-23 Q2 r1 Firm 1’s best response to Q2* A D Q2*  0 = $100 B C  1 = $200  2 = $300 QD QB QA Q1* Q1M Q1

24. CournotEquilibrium Another Look at Cournot Equilibrium 9-24 Q2 r1 Firm 2’s Profits Q2M Q2* Firm 1’s Profits r2 Q1M Q1* Q1

25. Collusion Incentives in Cournot Oligopoly 9-25 Q2 r1 Q2M r2 Q1M Q1

26. Cournot equilibrium after firm 1’s marginal cost increase r1** Q2** Cournot equilibrium prior to firm 1’s marginal cost increase Q2* r2 Q1** Q1* Impact of Rising Costs on the Cournot Equilibrium 9-26 Q2 r1* Q1

27. Price Leadership Model • In a price leadership model, one dominant firm takes reactions of all other firms into account in its output and pricing decisions • Competitive fringe: A group of firm that act as a price taker in a market dominated by a price leader • A dominant firms demand curve is the residual demand curve that shows what it can sell after accounting for sales by other firms • Other firms accept whatever price is set by the dominant firm and produce an output where P=MC • Note that P>MC for dominant firm, total industry output is less than competitive output

28. Dominant Firm Model Fig : Equilibrium in the Dominant Firm Model

29. Stackelberg Model Environment 9-29 • Few firms serving many consumers. • Firms produce differentiated or homogeneous products. • Barriers to entry. • 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.

30. The Algebra of the Stackelberg Model 9-30 • Since the follower reacts to the leader’s output, the follower’s output is determined by its reaction function • The Stackelberg leader uses this reaction function to determine its profit maximizing output level, which simplifies to

31. Stackelberg Summary 9-31 • 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.

32. Bertrand Model Environment 9-32 • 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 (price is each firms’ control variable). • Barriers to entry exist. • Consumers enjoy • Perfect information. • Zero transaction costs.

33. Bertrand Equilibrium 9-33 • 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.

34. Contestable Markets 9-34 • Key Assumptions • Producers have access to same technology. • Consumers respond quickly to price changes. • Existing firms cannot respond quickly to deter 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).

35. Conclusion 9-35 • 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.

36. . Basic model

38. Duopoly case

42. Price 120 Q = 120 - P 60 40 Q per period 0 120 60 80 . Zero cost monopoly P 120 . Q = 120 - P 60 Q 0 60 120 P MR Stackelberg solution Cournot solution 120 Monopoly 60 Cournot Equilibrium 40 Stackelberg 0 Q 60 120 40