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 P in 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 P in 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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solve (d)
Transcribed Image Text:(d) Suppose the two firms were now to collude and act as a monopoly in order to
maximize their joint profits. What price and quantity would be observed? How do
the levels of consumer and producer surplus in this situation compare with those
levels under the Cournot equilibrium?
Transcribed Image Text: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 P in
this Nash equilibrium?
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