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ps2_sol - Department of Economics University of California...

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Department of Economics Fall 2007 University of California, Berkeley Prof. Gilbert Problem Set 2 Solution Sketches 1. Let the inverse demand for gabions be given by P ( Q ) = 200 - 5 Q . Suppose that five gabion suppliers exist and that further entry into the market is infeasible. The cost structure of each supplier is given by C ( q i ) = 50 q i , where i q i = Q . (a) Assume the five firms are price-takers. Graph the supply and demand curves. Find the prices, quantities, and profits that arise in the competitive equilibrium. The firms price at marginal cost. Thus, in equilibrium it must be true that 50 = 200 - 5 Q , and Q = 30 . Plugging this back into demand yields P = 50 . Each firm produces 6 units and has zero profits. (b) Suppose that the firms form a “perfect cartel,” i.e. one that sets the monopoly price, and agree to split production evenly between firms. Find the new market price and quantity, and the firm-specific quantities and profits. The cartel will maximize the “monopoly” profits by setting MC = MR . Marginal revenue is MR = 200 - 10 Q so we know that the profit maximizing condition is 50 = 200 - 10 Q . Thus, the cartel produces a total of 15 units at a market price of 125. Each firm produces 3 units and earns profits of 225. (c) Let four firms set prices at the cartel level. What is the maximal profit that the remaining firm could earn by cheating on the cartel, given that market quantity is determined by the demand schedule? What is the corresponding market price and quantity, and how much would each firm produce? The fifth firm can undercut the cartel price and steal all of the cartel’s business. The profit maximizing price for the fifth firm is 124 . 999 which I’ll just approximate with 125. The fifth firm produces 15 units and earns 1125 in profits. The first four firms do not produce and earn zero profits.
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