Two firms, both with cost function C(q) = 30g compete in a market with inverse demand...

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Two firms, both with cost function C(q) = 30g compete in a market with inverse demand function p(Q) = 120-Q, where Q is the total output. Firms compete in quantities (Cournot model). (a) Obtain these equilibrium outputs. (b) Now suppose that firm I's cost function is C(q) = 45q instead, but firm 2's cost is unchanged. Analyze the new solution in the market. (c) Obtain the total surplus, consumer surplus, and industry profits in both cases, and compare. What is the effect of the worsening in firm I's cost? (d) Finally, assume that there is one firm with costs C(q) = 30q but two firms with costs C(q) = 45q. Solve the equilibrium again (using the fact that the two firms with equal costs will end up producing the same amount: the symmetry trick). What is the effect on consumer's surplus and total surplus of the higher degree of competition? Two firms, both with cost function C(q) = 30g compete in a market with inverse demand function p(Q) = 120-Q, where Q is the total output. Firms compete in quantities (Cournot model). (a) Obtain these equilibrium outputs. (b) Now suppose that firm I's cost function is C(q) = 45q instead, but firm 2's cost is unchanged. Analyze the new solution in the market. (c) Obtain the total surplus, consumer surplus, and industry profits in both cases, and compare. What is the effect of the worsening in firm I's cost? (d) Finally, assume that there is one firm with costs C(q) = 30q but two firms with costs C(q) = 45q. Solve the equilibrium again (using the fact that the two firms with equal costs will end up producing the same amount: the symmetry trick). What is the effect on consumer's surplus and total surplus of the higher degree of competition?

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a The equilibrium outputs of the two firms are 60 and 60 respectively b The equilibrium outputs of t... View the full answer