24. Under Cournot duopoly, two firms (A and B) produce the entire output of a particular homogenous good. Both firms know the market demand curve is given by P = 250 - 2Q, where Q is the sum of total industry output. Firm outputs are denoted by A and B. Both firms face the same costs: there are no fixed costs and marginal cost is 10 per unit for all levels of output. (a) Explain what is meant by a 'best response' function in this context. Mathematically derive the best response functions for each firm. (b) Sketch both best response functions on a diagram and explain the significance of the intersection of these two best response functions. (c) Find the Nash equilibrium in quantities for this duopoly market. What are Q and Pin this Nash equilibrium?
24. Under Cournot duopoly, two firms (A and B) produce the entire output of a particular homogenous good. Both firms know the market demand curve is given by P = 250 - 2Q, where Q is the sum of total industry output. Firm outputs are denoted by A and B. Both firms face the same costs: there are no fixed costs and marginal cost is 10 per unit for all levels of output. (a) Explain what is meant by a 'best response' function in this context. Mathematically derive the best response functions for each firm. (b) Sketch both best response functions on a diagram and explain the significance of the intersection of these two best response functions. (c) Find the Nash equilibrium in quantities for this duopoly market. What are Q and Pin this Nash equilibrium?
Economics (MindTap Course List)
13th Edition
ISBN:9781337617383
Author:Roger A. Arnold
Publisher:Roger A. Arnold
Chapter24: Monopolistic Competition, Oligopoly, And Game Theory
Section: Chapter Questions
Problem 9QP
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