question archive Consider a Cournot duopoly with the inverse demand P=260−2QP=260−2Q
Consider a Cournot duopoly with the inverse demand P=260−2QP=260−2Q
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Consider a Cournot duopoly with the inverse demand P=260−2QP=260−2Q . Firms 1 and 2 compete by simultaneously choosing their quantities. Both firms have constant marginal and average cost MC=AC=20MC=AC=20. Find each firm's best response function. Then, find the Cournot-Nash equilibrium quantities, profits and market price.
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Let Q1 and Q2 denote the production of firm 1 and 2, the market demand curve facing both firms is P = 260 - 2(Q1 + Q2), hence the marginal revenue for firm 1 is 260 - 4Q1 - 2Q2, and the marginal revenue for firm 2 is 260 - 4Q2 - 2Q1. Each will produce until marginal revenue = marginal cost, so the best response functions are
- For firm 1, 260 - 4Q1 - 2Q2 = 20, or 4Q1 = 240 - 2Q2.
- For firm 2, 260 - 4Q2 - 2Q1 = 20, or 4Q2 = 240 - 2Q1.
Solving the best response functions together we have, Q1 = Q2 = 40. Market price = 260 - 2(40 + 40) = 100. Profit for each firm = 40*(100 - 20) = 3200.
