1. 1 Welcome to EC 209: Managerial Economics- Group A By: Dr. Jacqueline Khorassani Week Ten

2. 2 Managerial Economics- Group A Week Ten- Class 1 Monday, November 5 11:10-12:00 Fottrell (AM) 11:10-12:00 Fottrell (AM) Aplia assignment is due tomorrow before 5 PM

3. 3 Chapter 9 of Baye Basic Oligopoly Models

4. 4 What are the characteristics of oligopolistic market structure? Relatively few firms, usually less than 10. Relatively few firms, usually less than 10. –Duopoly - two firms –Triopoly - three firms The products firms offer can be either differentiated or homogeneous. The products firms offer can be either differentiated or homogeneous.

5. 5 Interdependence Your actions affect the profits of your rivals. Your actions affect the profits of your rivals. Your rivals’ actions affect your profits. Your rivals’ actions affect your profits.

6. 6 An Example You and another firm sell differentiated products such as cars. You and another firm sell differentiated products such as cars. How does the quantity demanded for your cars change when you change your price? How does the quantity demanded for your cars change when you change your price?

7. 7 P Q D 1 (demand for your cars when rival holds its price constant) P0P0 PLPL D 2 (demand for your cars when rival matches your price change) PHPH Q0Q0 Q L2 Q L1 Q H1 Q H2

8. 8 P Q D1D1 P0P0 Q0Q0 D 2 (Rival matches your price change) (Rival holds its price constant) D Your demand if rivals match price reductions but not price increases “Kinked Demand Curve” P1 Q1 P2 Q2 What if your rivals match your price reductions but not your price increases?

9. Cournot Model A few firms produce goods that are either perfect substitutes (homogeneous) or imperfect substitutes (differentiated). A few firms produce goods that are either perfect substitutes (homogeneous) or imperfect substitutes (differentiated). Firms set output, as opposed to price. Firms set output, as opposed to price. The output of rivals is viewed as given or “fixed”. The output of rivals is viewed as given or “fixed”. Barriers to entry exist. Barriers to entry exist.

10. 10 Cournot Model: General Linear Case Market demand in a homogeneous-product Cournot duopoly is Market demand in a homogeneous-product Cournot duopoly is Total Revenue for firm 1 is Total Revenue for firm 1 is PQ 1 = aQ 1 – bQ 1 2 – bQ 1 Q 2 Total Revenue for firm 2 is Total Revenue for firm 2 is PQ 2 = aQ 2 – bQ 2 2 – bQ 1 Q 2

11. 11 What are the marginal revenues? TR 1 = PQ 1 = aQ 1 – bQ 1 2 – bQ 1 Q 2 TR 2 = PQ 2 = aQ 2 – bQ 2 2 – bQ 1 Q 2 Each firm’s marginal revenue depends on the output produced by the other firm. Each firm’s marginal revenue depends on the output produced by the other firm.

12. 12 Where do the quantities come from? Golden rule of profit maximization says get the output from the intersection of MC and MR Golden rule of profit maximization says get the output from the intersection of MC and MRMC=MR Firm 1’s MC = c 1 And its MR = a- bQ 2 -2bQ 1 c 1 = a- bQ 2 -2bQ 1 2bQ 1 = -c 1 +a-bQ 2 –This is called Firm 1’s best response function Q1 depends on Q2 Q1 depends on Q2 –Both firms produce identical products So if Firm two produces more  firm 1 must produce less So if Firm two produces more  firm 1 must produce less

13. 13 Best-Response Function for a Cournot Duopoly Firm 1’s best-response function is Firm 1’s best-response function is Similarly, Firm 2’s best-response function is (c 2 is firm 2’s MC) Similarly, Firm 2’s best-response function is (c 2 is firm 2’s MC)

14. 14 Graph of Firm 1’s Best-Response Function Q2Q2 Q1Q1 (Firm 1’s Reaction Function) Q2Q2 Q1Q1 r1r1 (a-c 1 )/b Q 1 = r 1 (Q 2 ) = (a-c 1 )/2b - 0.5Q 2 If Q 1 = 0  Q 2 = (a-c1)/b (a-c 1 )/2b

15. 15 Cournot Equilibrium Exist when Exist when –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. A point where the two firm’s best-response functions intersect.

16. 16 Graph of Cournot Equilibrium Q2*Q2* Q1*Q1* Q2Q2 Q1Q1 A r2r2 Q2MQ2M Cournot Equilibrium (a-c 1 )/b (a-c 2 )/b r1r1 If Firm 1 produces A  Firm 2 produces B If Firm 2 produces B  Firm 1 produces C If Firm 1 produces C  Firm 2 produces D B C D Equilibrium Quantities are at intersection of the response curves

17. 17 Managerial Economics- Group A Week Ten- Class 2 Week Ten- Class 2 –Tuesday, November 6 –Cairnes –15:10-16:00 Aplia assignment is due before 5PM today Aplia assignment is due before 5PM today

18. 18 Last class we looked at Cournot Equilibrium Q2*Q2* Q1*Q1* Q2Q2 Q1Q1 A r2r2 Q2MQ2M Cournot Equilibrium (a-c 1 )/b (a-c 2 )/b r1r1 If Firm 1 produces A  Firm 2 produces B If Firm 2 produces B  Firm 1 produces C If Firm 1 produces C  Firm 2 produces D B C D Equilibrium Quantities are at intersection of the response curves

19. 19 What happens if Firm 1’s MC goes up? Q2Q2 Q1Q1 r 1 ** r2r2 r1*r1* Q1*Q1* Q2*Q2* Q 2 ** Q 1 ** Cournot equilibrium prior to firm 1’s marginal cost increase Cournot equilibrium after firm 1’s marginal cost increase (a-c 1 )/b When c 1 goes up  vertical intercept of firm 1’s reaction curves goes down Firm 1’s production goes down

20. 20 Example of Cournot Model (See textbook page 324 for another example) Consider a case where there are two firms: A and B. Consider a case where there are two firms: A and B. Market demand is given by Q = 339 – P Market demand is given by Q = 339 – P AC = MC = 147 AC = MC = 147 The residual demand for firm A is The residual demand for firm A is q A = Q – q B q A = 339 – P - q B, or P = 339 - q A – q B

21. 21 Firm A’s demand is P = 339 - q A – q B Revenue for firm A Revenue for firm A = P q A = q A (339 - q A – q B ) = 339 q A - q A 2 - q A q B Marginal Revenue for firm A Marginal Revenue for firm A = 339 - 2 q A – q B

22. 22 Firm A’s best response (or reaction function) is derived by setting its MR= MC 339 - 2 q A – q B = 147 or q A = 96 – 1/2 q B Consider q B = 0; q A = 96 By the same reasoning q B = 96 – 1/2 q A

23. 23 Cournot Nash equilibrium is a combination of q A and q B so that both firms are on their reaction functions. Firm A’s reaction function is Firm A’s reaction function is q A = 96 – 1/2 q B Firm B’s reaction function is Firm B’s reaction function is q B = 96 – 1/2 q A q A = 96 – 1/2 (96 – 1/2 q A ) Solve to find q A = 64 Similarly q B = 64

24. 24 What are the profits at equilibrium? What is the Price? What is the Price? P = 339 - q A - q B P = 339 - 64 - 64 P = 211 Remember that AC = 147 Each firm’s profit = q (P-AC) Each firm’s profit = 64*(211-147) = 64 * 64 = 4096

25. 25 Could the two firms do better than this if they formed a cartel and act as a monopoly? The monopoly outcome is found by taking the marginal revenue curve for the industry and setting it equal to MC. The monopoly outcome is found by taking the marginal revenue curve for the industry and setting it equal to MC. Recall that market demand was Q = 339 – P Recall that market demand was Q = 339 – P Or P = 339-Q Or P = 339-Q Revenue will be Revenue will be PQ = 339Q – Q 2 PQ = 339Q – Q 2 MR = 339 – 2Q MR = 339 – 2Q MC = 147 MC = 147 339-2Q = 147 339-2Q = 147 or Q = 96 & P = 243 or Q = 96 & P = 243 Suppose the two firms divided the market between them so that each produced 48 units. Suppose the two firms divided the market between them so that each produced 48 units. Each would earn profits of 48 * (243-147) = 4608 Each would earn profits of 48 * (243-147) = 4608 4608> 4096 4608> 4096

26. 26 Collusion Incentives in Cournot Oligopoly QBQB QAQA rArA rBrB 48 After Collusion

27. 27 But will the cartel be a stable outcome? No No Given that firm B is producing 48 units what should firm A produce? Given that firm B is producing 48 units what should firm A produce? Look at Firm’s reaction function Look at Firm’s reaction function q A = 96 – 1/2 q B q A = 96 – 1/2 (48) q A = 72

28. 28 Firm A has an incentive to cheat QBQB QAQA rArA rBrB 48 72

29. 29 Conclusion The numerical example makes it clear that in a duopoly firms have an incentive to restrict output to the monopoly level. However they also have an incentive to cheat on any agreement. The numerical example makes it clear that in a duopoly firms have an incentive to restrict output to the monopoly level. However they also have an incentive to cheat on any agreement.

30. 30 Managerial Economics- Group A Week Ten- Class 3 Week Ten- Class 3 –Thursday, November 8 –15:10-16:00 –Tyndall Next Aplia Assignment is due before 5 PM on Tuesday, November 13 Next Aplia Assignment is due before 5 PM on Tuesday, November 13

31. 31 Stackelberg Model: Characteristics Firms produce differentiated or homogeneous products. Firms produce differentiated or homogeneous products. Barriers to entry. Barriers to entry. Firm one is the leader. Firm one is the leader. –The leader commits to an output before all other firms. Remaining firms are followers. Remaining firms are followers. –They choose their outputs so as to maximize profits, given the leader’s output.

32. 32 Stackelberg Model: General Linear Case Two firms in the market Two firms in the market Market demand is P = a – b(Q 1 + Q 2 ) Market demand is P = a – b(Q 1 + Q 2 ) Marginal cost for firm 1 and firm 2 is c 1 and c 2 Marginal cost for firm 1 and firm 2 is c 1 and c 2 Firm 1 is the leader Firm 1 is the leader We showed earlier that Firm 2’s best response (reaction) function is given by We showed earlier that Firm 2’s best response (reaction) function is given by Q 2 = (a – c 2 )/2b – 1/2Q 1

33. 33 What does the leader do? The leader “Firm 1” substitutes Firm 2’s reaction function into market demand function. The leader “Firm 1” substitutes Firm 2’s reaction function into market demand function. –Where market demand function is P = a – b(Q 1 + Q 2 ) –And Firm2’s reaction function is Q 2 = (a – c 2 )/2b – 1/2Q 1 P = a – b(Q 1 + (a – c 2 )/2b – 1/2Q 1 ) P = a – b(Q 1 + (a – c 2 )/2b – 1/2Q 1 ) This is multiplied by Q 1 to get the revenue function for Firm 1. This is multiplied by Q 1 to get the revenue function for Firm 1. Differentiate the revenue function with respect to Q to get Firm 1’s marginal revenue function. Differentiate the revenue function with respect to Q to get Firm 1’s marginal revenue function. Set the MR = MC Set the MR = MC Solve for Q 1. Solve for Q 1. Q 1 is equal to (a + c 2 -2c 1 )/2b. Q 1 is equal to (a + c 2 -2c 1 )/2b. Use the reaction function for Q 2 to find the expression for Q 2. Use the reaction function for Q 2 to find the expression for Q 2.

34. 34 Stackelberg Equilibrium Q1Q1 Q1MQ1M r1r1 Q2CQ2C Q1CQ1C r2r2 Q2Q2 Q1SQ1S Q2SQ2S Note: Firm 1 is producing on Frim 2’s reaction function (maximizes its profits given the reaction of Firm 2) Cournot equilibrium

35. 35 Stackelberg Summary Leader produces more than the Cournot equilibrium output. Leader produces more than the Cournot equilibrium output. –Larger market share, higher profits. –First-mover advantage. Follower produces less than the Cournot equilibrium output. Follower produces less than the Cournot equilibrium output. –Smaller market share, lower profits.

36. 36 Let’s use the same numerical example we used last class for Cournot model to find the Stakelberg model’s results Only this time assume and Firm A is a leader Only this time assume and Firm A is a leader Find each firm’s output and profit Find each firm’s output and profit

37. 37 Example of Stackelberg Model Note: Firm A knows Firm B’s reaction function. Note: Firm A knows Firm B’s reaction function. Market demand is given by Market demand is given by Q = 339 – P, and AC = MC = 147

38. 38 Market demand is given by Q = 339 – P The residual demand for firm A is The residual demand for firm A is q A = Q – q B q A = 339 – P - q B or q A = 339 – P - q B or P = 339 - q A – q B Remember that firm B’s reaction function is Remember that firm B’s reaction function is q B = 96 – 1/2 q A Plug in Firm B’s reaction function into Firm A’s demand Plug in Firm B’s reaction function into Firm A’s demand P = 339 – q A - 96 + 1/2 q A P = 243- 1/2 q A

39. 39 Firm A’s demand is P = 243- 1/2 q A Firm A’s revenue is Pq A = 243 q A – 1/2 q A 2 MR = 243 – q A Set this equal to MC 147 = 243- q A q A = 96 Use B’s reaction function q B = 96 – 1/2 q A, q B = 96 – 1/2 (96), q B = 48

40. 40 Profits Remember that P = 339 - q A – q B P = 339 – 96 – 48 P = 195, AC = 147 Firm A’s profit = 96 (195 - 147) = 4608 Firm B’s profit is 48 (195 – 147) = 2304

41. 41 Bertrand Model: Characteristics 1. Few firms that sell to many consumers. 2. Firms produce identical products at constant marginal cost. 3. Each firm independently sets its price in order to maximize profits. 4. Barriers to entry. 5. Consumers enjoy –Perfect information. –Zero transaction costs.

42. 42 Bertrand Equilibrium Firms set P 1 = P 2 = MC! Why? Firms set P 1 = P 2 = MC! Why? Suppose not Suppose not AC= MC = 10, P 1 =15, P 2 = 18 How much is Firm 1’s profit per unit? How much is Firm 1’s profit per unit? P 1 – AC= 5 How much is Firm 2’s profit per unit? How much is Firm 2’s profit per unit? –None, Firm Can’t sell any

43. 43 What would Firm 2 do? Cut the price slightly below Firm 1’s (to 14) Cut the price slightly below Firm 1’s (to 14) Firm 1 then has an incentive to undercut firm 2’s price. (to 13) Firm 1 then has an incentive to undercut firm 2’s price. (to 13) This undercutting continues... until This undercutting continues... until Equilibrium: Each firm charges P 1 = P 2 = MC = 10. Equilibrium: Each firm charges P 1 = P 2 = MC = 10.

44. 44 Contestable Markets Key Assumptions 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.

45. 45 Key Implications Strategic interaction between incumbents and potential entrants Strategic interaction between incumbents and potential entrants Threat of entry disciplines firms already in the market. Threat of entry disciplines firms already in the market. Incumbents have no market power, even if there is only a single incumbent (a monopolist). Incumbents have no market power, even if there is only a single incumbent (a monopolist).

46. 46 Contestable Markets Important condition for a contestable market is the absence of sunk costs. Important condition for a contestable market is the absence of sunk costs. –Encourages new firms to enter –You enter the industry and if things don’t work out  exit

47. 47 Another example Consider a case where there are two firms – 1 and 2. Market demand is given by Q = 1,000 – P; AC = MC = 4. Consider a case where there are two firms – 1 and 2. Market demand is given by Q = 1,000 – P; AC = MC = 4. Find the Cournot, Stackelberg, Monopoly and Bertrand outcomes. Find the Cournot, Stackelberg, Monopoly and Bertrand outcomes.

48. 48 Conclusion Different oligopoly scenarios give rise to different optimal strategies and different outcomes. Different oligopoly scenarios give rise to different optimal strategies and different outcomes. Your optimal price and output depends on 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.