# PS 4 Answers - Department of Economics University of...

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Unformatted text preview: Department of Economics University of California, Berkeley ECON 100A – Microeconomic Analysis Fall 2009 – Problem Set 4 Due: Tuesday, November 10, 2009, 11:00 AM (in lecture) True or False and Explain For each statement below, decide whether it is true or false, and explain the reasoning behind your answers in a few sentences. When appropriate, provide a diagram. 1. If a per-unit tax is imposed on a monopolist, the market price may rise more than the amount of the tax. True. See Figure 10.5. 2. Consumer surplus and total surplus are larger under perfect competition than under monopoly. Producer surplus is larger under monopoly. True. See Figure 10.10. 3. Suppose that a monopolist has two factories. Factory A has a cost function of C A ( q A ) = 8 q A and factory B has a cost function of C B ( q B ) = q 2 B / 3 . The demand is given by an inverse demand function P ( q T ) = 40- q T , where q T = q A + q B . The monopolist can earn more than 300 of profit. True. We know that the monopolist will choose q ’s such that MC A = MC B = MC T = MR : MR = MC A ∧ MR = MC B ⇔ 40- 2 ( q A + q B ) = 8 ∧ 40- 2 ( q A + q B ) = 2 q B 3 ⇔ q A = 4 ∧ q B = 12 . Or you can derive MC T and then find q T such that MC T = MR . The monopolist uses the factory B up to q B = 12 , where MC B = 8, and then switches to the factory A , which has the constant marginal cost of 8 . This marginal cost curve intersects with the marginal revenue curve at ( q T ,p ) = (16 , 24) . The associated profit is P ( q A + q B ) ( q A + q B )- C A ( q A )- C B ( q B ) = 24 · 16- 8 · 4- 12 2 3 = 304 > 300 . 1 Department of Economics University of California, Berkeley 4. If a firm can engage in first-degree price discrimination, the lowest price it offers is equal to the marginal cost of production. True. Under first-degree price discrimination, each consumer is charged his or her willingness- to-pay. The last consumer the firm is willing to sell a good is the one who has willingness-to-pay equal to marginal cost. 5. If a monopolist can devide the aggregate demand into multiple markets by some information that the firm can capture that will not be affected or changed by the firm’s pricing scheme (e.g. proof of age), he will set lower price on less elastic markets....
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## This note was uploaded on 02/12/2010 for the course ECON 100A taught by Professor Woroch during the Spring '08 term at Berkeley.

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PS 4 Answers - Department of Economics University of...

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