Chapter 25 Solutions

Chapter 25 Solutions - Chapter 25 N AME Monopoly Behavior...

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Chapter 25 NAME Monopoly Behavior Introduction. Problems in this chapter explore the possibilities of price discrimination by monopolists. There are also problems related to spatial markets, where transportation costs are accounted for and we show that lessons learned about spatial models give us a useful way of thinking about competition under product differentiation in economics and in politics. Remember that a price discriminator wants the marginal revenue in each market to be equal to the marginal cost of production. Since he produces all of his output in one place, his marginal cost of production is the same for both markets and depends on his total output. The trick for solving these problems is to write marginal revenue in each market as a function of quantity sold in that market and to write marginal cost as a function of the sum of quantities sold in the two markets. The profit- maximizing conditions then become two equations that you can solve for the two unknown quantities sold in the two markets. Of course, if marginal cost is constant, your job is even easier, since all you have to do is find the quantities in each market for which marginal revenue equals the constant marginal cost. Example: A monopolist sells in two markets. The inverse demand curve in market 1 is p 1 = 200 q 1 . The inverse demand curve in market 2 is p 2 = 300 q 2 . The firm’s total cost function is C ( q 1 + q 2 ) = ( q 1 + q 2 ) 2 . The firm is able to price discriminate between the two markets. Let us find the prices that it will charge in each market. In market 1, the firm’s marginal revenue is 200 2 q 1 . In market 2, marginal revenue is 300 2 q 2 . The firm’s marginal costs are 2( q 1 + q 2 ). To maximize its profits, the firm sets marginal revenue in each market equal to marginal cost. This gives us the two equations 200 2 q 1 = 2( q 1 + q 2 ) and 300 2 q 2 = 2( q 1 + q 2 ). Solving these two equations in two unknowns for q 1 and q 2 , we find q 1 = 16 . 67 and q 2 = 66 . 67. We can find the price charged in each market by plugging these quantities into the demand functions. The price charged in market 1 will be 183.33. The price charged in market 2 will be 233.33. 25.1 (0) Ferdinand Sludge has just written a disgusting new book, Orgy in the Piggery . His publisher, Graw McSwill, estimates that the demand for this book in the United States is Q 1 = 50 , 000 2 , 000 P 1 , where P 1 is the price in America measured in U.S. dollars. The demand for Sludge’s opus in England is Q 2 = 10 , 000 500 P 2 , where P 2 is its price in England measured in U. S. dollars. His publisher has a cost function C ( Q ) = $50 , 000 + $2 Q , where Q is the total number of copies of Orgy that it produces. (a) If McSwill must charge the same price in both countries, how many copies should it sell 27,500, and what price should it charge
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304 MONOPOLY BEHAVIOR (Ch. 25) $13 to maximize its profits, and how much will those profits be?
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