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

Welcome to EC 209: Managerial Economics- Group A By: Dr. Jacqueline Khorassani. Week Ten. Managerial Economics- Group A. Week Ten- Class 1 Monday, November 5 11:10-12:00 Fottrell (AM) Aplia assignment is due tomorrow before 5 PM. Chapter 9 of Baye. Basic Oligopoly Models.

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

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

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

  3. Chapter 9 of Baye Basic Oligopoly Models

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

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

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

  7. P0 QH1 QH2 QL2 QL1 Q0 D2 (demand for your cars when rival matches your price change) P PH PL D1 (demand for your cars when rival holds its price constant) Q

  8. D2 (Rival matches your price change) P P0 D1 (Rival holds its price constant) Q Q0 What if your rivals match your price reductions but not your price increases? Your demand if rivals match price reductions but not price increases “Kinked Demand Curve” P2 P1 D Q1 Q2

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

  10. Cournot Model: General Linear Case • Market demand in a homogeneous-product Cournot duopoly is • Total Revenue for firm 1 is PQ1 = aQ1 – bQ12 – bQ1Q2 • Total Revenue for firm 2 is PQ2 = aQ2 – bQ22 – bQ1Q2

  11. What are the marginal revenues? TR1= PQ1 = aQ1 – bQ12 – bQ1Q2 TR2 = PQ2 = aQ2 – bQ22 – bQ1Q2 • Each firm’s marginal revenue depends on the output produced by the other firm.

  12. Where do the quantities come from? • Golden rule of profit maximization says get the output from the intersection of MC and MR MC=MR Firm 1’s MC = c1 And its MR = a- bQ2 -2bQ1 c1 =a- bQ2 -2bQ1 2bQ1= -c1+a-bQ2 • This is called Firm 1’s best response function • Q1 depends on Q2 • Both firms produce identical products • So if Firm two produces more firm 1 must produce less

  13. Best-Response Function for a Cournot Duopoly • Firm 1’s best-response function is • Similarly, Firm 2’s best-response function is (c2 is firm 2’s MC)

  14. Q1 = r1(Q2) = (a-c1)/2b - 0.5Q2 Graph of Firm 1’s Best-Response Function Q2 (a-c1)/b If Q1 = 0  Q2 = (a-c1)/b Q2 r1 (Firm 1’s Reaction Function) Q1 Q1 (a-c1)/2b

  15. Cournot Equilibrium • 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.

  16. Graph of Cournot Equilibrium 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 Q2 (a-c1)/b Cournot Equilibrium Q2M Q2* D B r2 r1 Q1* A (a-c2)/b Q1 C Equilibrium Quantities are at intersection of the response curves

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

  18. Last class we looked at Cournot Equilibrium 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 Q2 (a-c1)/b Cournot Equilibrium Q2M Q2* D B r2 r1 Q1* A (a-c2)/b Q1 C Equilibrium Quantities are at intersection of the response curves

  19. 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* What happens if Firm 1’s MC goes up? When c1 goes up  vertical intercept of firm 1’s reaction curves goes down Q2 r1* (a-c1)/b Q1 Firm 1’s production goes down

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

  21. Firm A’s demand is P = 339 - qA – qB • Revenue for firm A = P qA = qA (339 - qA – qB) = 339 qA- qA2 - qAqB • Marginal Revenue for firm A = 339 - 2 qA – qB

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

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

  24. What are the profits at equilibrium? • What is the Price? P = 339 - qA - qB 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. 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. • Recall that market demand was Q = 339 – P • Or P = 339-Q • Revenue will be • PQ = 339Q – Q2 • MR = 339 – 2Q • MC = 147 • 339-2Q = 147 • or Q = 96 & P = 243 • Suppose the two firms divided the market between them so that each produced 48 units. • Each would earn profits of 48 * (243-147) = 4608 • 4608> 4096

  26. Collusion Incentives in Cournot Oligopoly QB rA After Collusion 48 rB QA 48

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

  28. Firm A has an incentive to cheat QB rA 48 rB QA 48 72

  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.

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

  31. Stackelberg Model: Characteristics • 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.

  32. Stackelberg Model: General Linear Case • Two firms in the market • Market demand is P = a – b(Q1 + Q2) • Marginal cost for firm 1 and firm 2 is c1 and c2 • Firm 1 is the leader • We showed earlier that Firm 2’s best response (reaction) function is given by Q2 = (a – c2)/2b – 1/2Q1

  33. What does the leader do? • The leader “Firm 1” substitutes Firm 2’s reaction function into market demand function. • Where market demand function is P = a – b(Q1 + Q2) • And Firm2’s reaction function is Q2 = (a – c2)/2b – 1/2Q1 • P = a – b(Q1 + (a – c2)/2b – 1/2Q1) • This is multiplied by Q1 to get the revenue function for Firm 1. • Differentiate the revenue function with respect to Q to get Firm 1’s marginal revenue function. • Set the MR = MC • Solve for Q1. • Q1 is equal to (a + c2 -2c1)/2b. • Use the reaction function for Q2 to find the expression for Q2.

  34. Cournot equilibrium Stackelberg Equilibrium Q2 r1 Stackelberg Equilibrium Q2C Q2S r2 Q1M Q1C Q1S Q1 Note: Firm 1 is producing on Frim 2’s reaction function (maximizes its profits given the reaction of Firm 2)

  35. Stackelberg Summary • 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.

  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 • Find each firm’s output and profit

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

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

  39. Firm A’s demand is P = 243- 1/2 qA Firm A’s revenue is PqA = 243 qA– 1/2 qA2 MR = 243 – qA Set this equal to MC 147 = 243- qA qA = 96 Use B’s reaction function qB = 96 – 1/2 qA, qB = 96 – 1/2 (96), qB = 48

  40. Profits Remember that P = 339 - qA – qB 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. Bertrand Model: Characteristics • 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. • Zero transaction costs.

  42. Bertrand Equilibrium • Firms set P1 = P2 = MC! Why? • Suppose not AC= MC = 10 , P1=15 , P2= 18 • How much is Firm 1’s profit per unit? P1 – AC= 5 • How much is Firm 2’s profit per unit? • None, Firm Can’t sell any

  43. What would Firm 2 do? • Cut the price slightly below Firm 1’s (to 14) • Firm 1 then has an incentive to undercut firm 2’s price. (to 13) • This undercutting continues... until • Equilibrium: Each firm charges P1 = P2 = MC = 10.

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

  46. Contestable Markets • 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. 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. • Find the Cournot, Stackelberg, Monopoly and Bertrand outcomes.

  48. 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.

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