【正文】 arson Education, Inc. Chapter 12 61 Competition Versus Collusion: The Prisoners’ Dilemma ?Competitor is not likely to follow ?Competitor can do better by choosing a lower price, even if they know you will set the collusive level price ?We can use example from before to better understand the firms’ choices 169。 Gamble ?Collusion with petitors will give larger profits ?If all agree to charge $, each earn profit of $20,000 ?Collusion agreements are hard to enforce 169。G’s Profit (in thousands of $ per month) 169。G choose and what is the expected profit? ?Can calculate profits by taking different possibilities of prices you and the other panies could charge ?Nash equilibrium is at $ – the point where petitors are doing the best they can as well 169。2020 Pearson Education, Inc. Chapter 12 57 A Pricing Problem: Procter amp。G’s demand curve was: Q = 3,(PU)(PK) Where P, PU, PK are Pamp。 Gamble ?Procter amp。 VC = $1/unit 169。 Gamble ?Procter amp。2020 Pearson Education, Inc. Chapter 12 54 Nash Equilibrium in Prices ?If Firm 1 sets price first and then Firm 2 makes pricing decision: ?Firm 1 would be at a distinct disadvantage by moving first ?The firm that moves second has an opportunity to undercut slightly and capture a larger market share 169。2020 Pearson Education, Inc. Chapter 12 52 Nash Equilibrium in Prices ?What if both firms collude? ?They both decide to charge the same price that maximizes both of their profits ?Firms will charge $6 and will be better off colluding since they will earn a profit of $16 169。 F i r m c u r v e r e a c t i o n s139。2020 Pearson Education, Inc. Chapter 12 51 Price Competition – Differentiated Products ?If P2 is fixed: 12212111413413041239。2020 Pearson Education, Inc. Chapter 12 49 Price Competition – Differentiated Products ?Example ?Duopoly with fixed costs of $20 but zero variable costs ?Firms face the same demand curves ?Firm 1’s demand: Q1 = 12 2P1 + P2 ?Firm 2’s demand: Q2 = 12 2P1 + P2 ?Quantity that each firm can sell decreases when it raises its own price but increases when its petitor charges a higher price 169。2020 Pearson Education, Inc. Chapter 12 47 Bertrand Model – Criticisms ?When firms produce a homogenous good, it is more natural to pete by setting quantities rather than prices ?Even if the firms do set prices and choose the same price, what share of total sales will go to each one? ?It may not be equally divided 169。 Q2 = ?Both firms earn zero profit 169。 P1 = P2 = $3 ?Q = 27。2020 Pearson Education, Inc. Chapter 12 44 Price Competition – Bertrand Model ?Assume here that the firms pete with price, not quantity ?Since good is homogeneous, consumers will buy from lowest price seller ?If firms charge different prices, consumers buy from lowest priced firm only ?If firms charge same price, consumers are indifferent who they buy from 169。2020 Pearson Education, Inc. Chapter 12 42 Price Competition ?Competition in an oligopolistic industry may occur with price instead of output ?The Bertrand Model is used ?Oligopoly model in which firms produce a homogeneous good, each firm treats the price of its petitors as fixed, and all firms decide simultaneously what price to charge 169。2020 Pearson Education, Inc. Chapter 12 40 First Mover Advantage – The Stackelberg Model ?Using Firm 2’s Reaction Curve for Q2: a n d 15:015211111????????MRRMR2111121112115 )2115(30R??????169。(Q1) 169。2020 Pearson Education, Inc. Chapter 12 37 First Mover Advantage – The Stackelberg Model ?Oligopoly model in which one firm sets its output before other firms do ?Assumptions ?One firm can set output first ?MC = 0 ?Market demand is P = 30 Q where Q is total output ?Firm 1 sets output first and Firm 2 then makes an output decision seeing Firm 1’s output 169。2020 Pearson Education, Inc. Chapter 12 36 Firm 1’s Reaction Curve Firm 2’s Reaction Curve Duopoly Example Q1 Q2 30 30 10 10 Cournot Equilibrium Collusion Curve Collusive Equilibrium For the firm, collusion is the best oute followed by the Cournot Equilibrium and then the petitive equilibrium 15 15 Competitive Equilibrium (P = MC。2020 Pearson Education, Inc. Chapter 12 34 Oligopoly Example ?Profit Maximization with Collusion MCMRMRRMRPQR????????????? and 15 Q w he n 023030)30(2169。2020 Pearson Education, Inc. Chapter 12 32 Oligopoly Example ?An Example of the Cournot Equilibrium 10302010)2115(21152111??????????QP2:mE q u i l i b r i u Co u r n o t169。 F i r mCu r v e Re a c t i on s139。2020 Pearson Education, Inc. Chapter 12 30 Oligopoly Example ?Firm 1’s Reaction Curve ? MR = MC 111 )30( PQR ??? :R e v e n u e T o t a l12211121130)(30??????169。2020 Pearson Education, Inc. Chapter 12 28 Oligopoly ? Cournot equilibrium is an example of a Nash equilibrium (CournotNash Equilibrium) ? The Cournot equilibrium says nothing about the dynamics of the adjustment process ? Since both firms adjust their output, neither output would be fixed 169。2020 Pearson Education, Inc. Chapter 12 26 Firm 2’s Reaction Curve Q*2(Q1) Reaction Curves and Cournot Equilibrium Q2 Q1 25 50 75 100 25 50 75 100 Firm 1’s Reaction Curve Q*1(Q2) x x x x In Cournot equilibrium, each firm correctly assumes how much its petitors will produce and thereby maximizes its own profits. Cournot Equilibrium 169。2020 Pearson Education, Inc. Chapter 12 24 Oligopoly ?The Reaction Curve ?The relationship between a firm’s profitmaximizing output and the amount it thinks its petitor will produce ?A firm’s profitmaximizing output is a decreasing schedule of the expected output of Firm 2 169。2020 Pearson E