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hw8 - degree price discrimination that is he can offer a...

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Homework Assignment # 8 Econ 121b. Intermediate Microeconomics due April 18, 2011 (in class) Please put your discussion-section time on your answer. 1. A monopolist with total cost function C.q/ D 100 C 5q faces consumers of two types, A and B , who are evenly distributed in the population. Consumer A ’s inverse demand function is p A .x A / D 15 10x A and consumer B ’s inverse demand is p B .x B / D 20 5x B . (a) What is the market (inverse) demand function? What is the marginal revenue func- tion? (Hint: Take into account the zero demand regions for linear demand func- tions. See Lecture 9.) (b) If the monopolist cannot price discriminate, what is the monopolist’s total output and unit price? How much each consumer is going to buy? (c) Now, suppose the monopolist can engage in first-degree price discrimination. What quantity / total price combination is the monopolist going to offer each consumer? (d) Suppose the consumer’s type, A or B , is his private information, so the monopolist cannot perfectly price discriminate. Suppose the monopolist can engage in second-
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Unformatted text preview: degree price discrimination, that is, he can offer a menu f .x A ;t A /;.x B ;t B / g of quantity / total price combinations and the consumer is free to choose any combi-nation in the menu. What is the profit-maximizing menu? (e) Suppose now that the monopolist knows each consumer’s type, so he can charge different prices to different consumers. However, the monopolist is not allowed to charge any consumer different prices for different units of the good. That is, the monopolist can charge different unit prices to different consumers, but any given consumer pays the same unit price irrespective of the number of units he buys (third degree price discrimination). What is the price that the monopolist is going to charge each of the two consumer? How much are they going to consume? Interpret the result in terms of the consumer’s price elasticities. 1...
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