Oligopoly

Structure Assume Duopoly Firms know information about market demand Perfect Information

Strategy Simultaneous Movement Cooperative Quantity Cournot Model Price Bertrand Model Non - Cooperative Cartel

Strategy Sequential Movement Quantity Stackelberg Model Price Price Leadership Model

Cournot Model Assume Homogeneous goods Given other Firm quantity is constant, and choose my quantity Simultaneous Decision Each firm want to maximize profit Quantity Taker

DMDM D 50 MR B = 50 Firm A 3020 Quantity 20 is best respond when B produce 50 Units MC A Q P

DMDM D 20 MR 20 B = 20 Firm A 35 Quantity 35 is best respond when B produce 20 Units MC A Q P

A output Cournot Equilibrium Cournot Reaction Curve B output Firm B reaction curve Firm A reaction curve

Firm A’ s output is a best respond to firm B’ s output. Firm B’ s output is a best respond to firm A’ s output. P Q DMDM D 30 MC 30 B = 30 Firm A MR 30 P Q DMDM D 30 MC 30 A = 30 Firm B MR 30

Linear Demand and Zero Marginal Cost Firm 1 Firm 2

Demand : P = 100 – Q ; Q = Q 1 + Q 2 Marginal Cost : MC 1 = MC 2 = 10 Demand : P = 100 – Q ; Q = Q 1 + Q 2 Marginal Cost : MC 1 = MC 2 = 10 Firm 1 TR = PQ 1 = ( 100 – Q 1 – Q 2 )Q 1 = 100Q 1 – Q 1 2 – Q 2 Q 1 MR = 100 – 2Q 1 – Q 2

Firm 1 MR = 100 – 2Q 1 – Q 2 = MC MR = 100 – 2Q 1 – Q 2 = 10 Reaction Curve of Firm 1

Q2Q2 MR = 100 – 2Q 1 -Q 2 Q1Q – 2Q – 2Q – 2Q – 2Q 1 0

Q1Q1 P D 1 ( 0 ) MR 1 ( 0 ) D 1 ( 50 ) MC 4520

Demand : P = 30 – Q ; Q = Q 1 + Q 2 Marginal Cost : MC 1 = MC 2 = 0 Demand : P = 30 – Q ; Q = Q 1 + Q 2 Marginal Cost : MC 1 = MC 2 = 0 Oligopoly ( 2 Firms ) Competitive Market Cartel ( 2 Firms )

Q1Q1 Q2Q2 Firm 2 ’ s Reaction Curve Firm 1 ’ s Reaction Curve

Many Firms in Cournot Equilibrium Assume : there are n Firms

Given

Exercise (a) Suppose that inverse demand is given by P = a – bQ, and that firms have identical marginal cost given by C. Assume that a > C so that part of the demand curve lies above the marginal cost curve ( otherwise the industry would not produce any input ). What is the monopoly equilibrium in this market? (b) What is the perfect competitive market outcome? (c) What is the Cournot equilibrium in market with two firms? (d) Suppose the market consists of N identical firms. What is the Cournot equilibrium quantity per firm, market quantity, and price?

Stackelberg Model Homogeneous Product Firm 1 moves first Firm 2 knows firm 1’ s output, and decide his output Firm 1 sets output by reaction function of firm 2

Follower’s Problem Assume MC F = 0 Contract Isoprofit

QLQL QFQF QL*QL* F 2 (Q L * ) Reaction Curve for firm F Isoprofit line for firm 2

Leader’s Problem Assume MC L = 0 S.t.

QLQL QFQF QL*QL* F 2 (Q L * ) Firm 1

Demand : P = 30 – Q ; Q = Q 1 + Q 2 Marginal Cost : MC 1 = MC 2 = 0 Demand : P = 30 – Q ; Q = Q 1 + Q 2 Marginal Cost : MC 1 = MC 2 = 0 Firm 1 Move First Exercise Demand : P = 100 – Q ; Q = Q 1 + Q 2 Marginal Cost : AC i = MC 1 = MC 2 = 10 Demand : P = 100 – Q ; Q = Q 1 + Q 2 Marginal Cost : AC i = MC 1 = MC 2 = 10

Bertrand Model ( Price Competition ) Price of other firm is constant and Simultaneous Movement Case 1 : Homogeneous Product Demand : P = 30 – Q ; Q = Q 1 + Q 2 Marginal Cost : MC 1 = MC 2 = 3 Demand : P = 30 – Q ; Q = Q 1 + Q 2 Marginal Cost : MC 1 = MC 2 = 3 MC = MR Demand : P = 100 – Q ; Q = Q 1 + Q 2 Marginal Cost : MC 1 = MC 2 = 10 Demand : P = 100 – Q ; Q = Q 1 + Q 2 Marginal Cost : MC 1 = MC 2 = 10

Case 2 : Differentiated Product Firm 1 ‘s Demand : Q 1 = 12 – 2P 1 + P 2 Firm 2 ‘s Demand : Q 2 = 12 – 2P 2 + P 1 Fixed Cost = 20 and MC 1 = MC 2 = 0 Firm 1 ‘s Demand : Q 1 = 12 – 2P 1 + P 2 Firm 2 ‘s Demand : Q 2 = 12 – 2P 2 + P 1 Fixed Cost = 20 and MC 1 = MC 2 = 0 P2P2 DemandP1P1 06 – 0.5Q – 0.5Q – 0.5Q 1 7

Firm 1’s Reaction Curve P1P1 P2P2 Firm 2’s Reaction Curve o

Price Leadership Model Homogeneous Product Leader ( MC lower ) will set price first Follower ( MC higher ) will set price follow Leader

Q P MC F DMDM DLDL MR L MC L QLQL D C B QTQT QFQF PLPL P1P1 A 0

Cartel Maximization profit of Cartel Same MC Structure ( for Simple ) P P QQ Total MC D MR MC i AC i QMQM E PePe PMPM S QF*QF* Q2Q2

Assume Cost = o

Q1Q1 Q2Q2 a/2b Firm 2

Punishment Strategy “If you stay at the production level that maximize joint industry project, fine. But if I discover you cheating by producing more than this amount, I will punish you by producing the Cournot level for output forever.” Cartel Behavior Defect Behavior

Keep Cartel Behavior