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Consider a Market with Inverse Demand P = 100 -

Question 42

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Consider a market with inverse demand p = 100 - 2Q.Firms have no fixed cost and constant marginal cost c.
a.Derive the firms' outputs and profits when this market is served by Cournot duopolists.
b.How do outputs and profits vary with c? Specifically,use calculus to find the derivative of the output of each firm and profit of each firm with respect to c.
c.Suppose the firm's also have a fixed cost of F in addition to the marginal cost c.How does F alter the best response functions and NE? Explain in words.(For technical reasons,assume that both firms still produce a positive level of output in equilibrium)

Correct Answer:

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a.First,the profit for firm 1 is:
π1 = (1...

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