ps8_sol_fall11

# ps8_sol_fall11 - Department of Economics Columbia...

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Department of Economics W3211 Columbia University Fall 2011 SO L UTIONS T O Probl e m S e t 8 Int e rm e diat e Mi c ro ec onomi c s Prof . S e yhan E Arkona c 1 . Consider a town with a single movie theater, and that movie theater faces a downward sloping demand curve for its tickets. The movie theater has a fixed number of seats available for each show but the marginal cost of filling a seat is zero. Why might it be in the movie theater’s interest to not to sell out every show even though the marginal cost of selling additional seats is virtually zero? (A graph will help your answer). Answer: The firm may or may not choose to sell out the theater depending on the demand (and marginal revenue). The firm will sell up until the marginal revenue is zero. If this occurs at a quantity less than the theater capacity, then it’s optimal to leave empty seats. If the marginal revenue is zero beyond the capacity, then the firm will sell out all of its seats.

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2 . A monopolist faces the (inverse) demand for its product: p = 50- 2Q. The monopolist has a marginal cost of 10/unit and a fixed cost given by F. a . Assume that F is sufficiently small such that the monopolist produces a strictly positive level of output. What is the profit-maximizing price and quantity. b . Compute the maximum profit for the monopolist in terms of F. c . For what values of F will the monopolists profit be negative Answer: a. The monopolist will choose p=MR (or derive from first order condition of profit function). 50 - 4Q = 10 Solving for Q Q* = 10 The price follows from plugging the optimal output into the demand: p* = 30 b. The profit comes from plugging the price and quantity into the profit equation: P i * =300 - F c. Find F* such that P i * = 0: F* = 300 For F>300, profits will be negative. 3 . For profit-maximizing monopolies, explain why the boundaries on the Lerner Index are 0 and 1. Answer: The Lerner Index equals (p - MC)/p. Because marginal cost is greater than or equal to zero and the optimal price is greater than or equal to the marginal cost, then 0 ≤ p - MC ≤ p. So the Lerner Index ranges from 0 to 1 for a profit-maximizing firm. As price gets higher, the Lerner Index approaches 1. As price gets lower, the index approaches zero.
4 . Consider a monopolist with linear (inverse) demand p = a - bQ and constant average and marginal cost, c. Derive the monopolist's profit and the deadweight loss generated.

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ps8_sol_fall11 - Department of Economics Columbia...

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