Oligopoly_Cournot_sol

# Oligopoly_Cournot_sol - Comm 295 Solution to Practice...

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Comm 295 Solution to Practice Problems Oligopoly (Cournot Model) 1. Consider two firms facing the demand curve P = 10 - Q, where Q = Q 1 + Q 2 . The firms’ cost functions are C 1 (Q 1 ) = 4 + 2Q 1 and C 2 (Q 2 ) = 3 + 3Q 2 . a. Suppose both firms have entered the industry. What is the joint profit- maximizing level of output? How much will each firm produce? If both firms enter the market, and they collude, they will act as if a monopolist with MR = 10 - 2 Q . In the present case, MC 1 = 2 and MC 2 = 3. Since MC 2 > MC 1 for all levels of Q, firm 2 should shut down. Setting MR = MC 1 for profit maximization, we have 10 - 2 Q = 2, Q 1 = Q = 4. And Q 2 = 0 Substituting Q = 4 into the demand function: P = 10 - 4 = \$6. The profit for Firm 1: 1 = (6)(4) - (4 + (2)(4)) = \$12. The profit for Firm 2: 2 = (6)(0) - (3 + (3)(0)) = -\$3. Total industry profit T = 1 + 2 = 12 - 3 = \$9. b. W h a t i s e a c h f i rm s e q u i l i b r i um o u t p u t a n d p r o f i t i f t h e y b e h a v e noncooperatively (hint use the Cournot model)? Draw the firms’ reaction curves and show the equilibrium.

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Oligopoly_Cournot_sol - Comm 295 Solution to Practice...

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