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problemset7[1]

# problemset7[1] - b Derive the long-run total cost curve...

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EC201, Fall 2007, Prof. Jordi Jaumandreu Prob lemSet#7 Monopoly 1. The inverse demand curve a monopoly faces is p =100 Q. The f rm cost curve is C ( Q )=10+5 Q. What is the pro f t-maximizing solution? Find the welfare loss. Determine the Lerner Index. How does your answers change if C ( Q )=100+5 Q. 2. A f rm that delivers Q units of water to households has a total cost of Q = F + mQ. If any entrant would have the same cost, does this market have a natural monopoly? 3. Suppose the water utility of problem 2. Show graphically what happens if goverment imposes pricing at the level in which price equals the average cost of producing the quantity sold. Are there pro f ts? Is there a welfare loss? 4. A monopoly’s production function is Q = K 1 2 L 1 2 where K is capital and L is labor (recall that marginal products are MP K = 1 2 K 1 2 L 1 2 and MP L = 1 2 K 1 2 L 1 2 ) The demand function is p =100 Q . The wage w is \$1 per hour, and the rental cost of capital r is \$4 .
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Unformatted text preview: b. Derive the long-run total cost curve equation c. What quantity maximizes the f rm’s pro f t? d. Find the optimal input combination that produces the pro f t-maximizing quantity. Illustrate. 5. A duopoly faces a market demand of p = 120 − Q. Firm 1 has a constant marginal cost of MC 1 = 20 . Firm’s 2 constant marginal cost is MC 2 = 40 . Calculate the output of each f rm , market output, and price if there is (a) a collusive equilibrium or (b) a Cournot equilibrium. 6. Suppose that identical duopoly f rms have constant marginal costs of \$10 per unit. Firm 1 faces a demand function q 1 = 100 − 2 p 1 + p 2 , where q 1 is Firm’s 1 output, p 1 is Firm’s 1 price and p 2 is Firm’s 2 price. Similarly, the demand for Firm 2 is q 2 = 100 − 2 p 2 + p 1 . Find the Bertrand equilibrium. 1...
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