In Cournot equilibrium,each firm correctly assumes the amount that its competitor will produce and thereby maximizes its own profits.Therefore neither firm will move from this equilibrium
In Cournot equilibrium, each firm correctly assumes the amount that its competitor will produce and thereby maximizes its own profits. Therefore neither firm will move from this equilibrium
12.2.2 The Linear Demand Curve Suppose our duopolists face the following market demand curve: P=30-Q Also,suppose that both firms have zero marginal cost: MCI=MC2=0 To maximize profit,it sets marginal revenue equal to marginal cost.Its total revenue R is given by
12.2.2 The Linear Demand Curve Suppose our duopolists face the following market demand curve: P = 30 – Q Also, suppose that both firms have zero marginal cost: MC1 = MC2 = 0 To maximize profit, it sets marginal revenue equal to marginal cost. Its total revenue R1 is given by
R1=PQ1=(30-Q)Q1=30Q1-(Q1+Q2)Q1 =30Q1-Q12-Q2Q1 MR1=30-2Q1-Q2=MC1=0 Firm 1's reaction curve:Q1=15-(1/2)Q2 The same calculation applies to Firm 2: Firm 2's reaction curve:Q2=15-(1/2)Q Cournot equilibrium:Q1=Q2=10 R=2R1=2PQ1=2×(30-Q)×Q1=2×(30-20)×10=200
R1 = PQ1 = (30 – Q) Q1 = 30Q1 –(Q1 + Q2 )Q1 = 30Q1 – Q1 2 - Q2Q1 MR1 = 30 – 2Q1 - Q2 =MC1 = 0 Firm 1’s reaction curve: Q1 = 15 – (1/ 2) Q2 The same calculation applies to Firm 2: Firm 2’s reaction curve: Q2 = 15 – (1/ 2) Q1 Cournot equilibrium: Q1 = Q2 = 10 R = 2R1 =2 PQ1 = 2 (30 – Q) Q1 = 2 (30 – 20) 10 = 200
Also,suppose that both firms have identical marginal cost: MCI=MC2=3 To maximize profit,it sets marginal revenue equal to marginal cost. MR1=30-2Q1-Q2=MC1=3 Firm 1's reaction curve:Q1=13.5-(1/2)Q2 The same calculation applies to Firm 2: Firm 2's reaction curve:Q2=13.5-(1/2)Q Cournot equilibrium:Q=Q2=9 R=2R1=2PQ1=2×(30-Q)×Q1=2×(30-18)×9=216
Also, suppose that both firms have identical marginal cost: MC1 = MC2 = 3 To maximize profit, it sets marginal revenue equal to marginal cost. MR1 = 30 – 2Q1 - Q2 =MC1 = 3 Firm 1’s reaction curve: Q1 = 13.5 – (1/ 2) Q2 The same calculation applies to Firm 2: Firm 2’s reaction curve: Q2 = 13.5 – (1/ 2) Q1 Cournot equilibrium: Q1 = Q2 = 9 R = 2R1 =2 PQ1 = 2 (30 – Q) Q1 = 2 (30 –18) 9 = 216
Suppose,instead,that the antitrust laws were relaxed and the two firms could collude.They would set their outputs to maximize total profit,and presumably they would split that profit evenly. Total profit is maximized by choosing total output Q so that marginal revenue equals marginal cost,which in this example is zero
Suppose, instead, that the antitrust laws were relaxed and the two firms could collude. They would set their outputs to maximize total profit, and presumably they would split that profit evenly. Total profit is maximized by choosing total output Q so that marginal revenue equals marginal cost, which in this example is zero