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Unformatted text preview: Chapter 24 NAME Monopoly Introduction. The profit-maximizing output of a monopolist is found by solving for the output at which marginal revenue is equal to marginal cost. Having solved for this output, you find the monopolists price by plugging the profit-maximizing output into the demand function. In general, the marginal revenue function can be found by taking the derivative of the total revenue function with respect to the quantity. But in the special case of linear demand, it is easy to find the marginal revenue curve graphically. With a linear inverse demand curve, p ( y ) = a by , the marginal revenue curve always takes the form MR ( y ) = a 2 by . 24.1 (0) Professor Bong has just written the first textbook in Punk Economics. It is called Up Your Isoquant . Market research suggests that the demand curve for this book will be Q = 2 , 000 100 P , where P is its price. It will cost $1,000 to set the book in type. This setup cost is necessary before any copies can be printed. In addition to the setup cost, there is a marginal cost of $4 per book for every book printed. (a) The total revenue function for Professor Bongs book is R ( Q ) = 20 Q Q 2 / 100 . (b) The total cost function for producing Professor Bongs book is C ( Q ) = 1 , 000 + 4 Q . (c) The marginal revenue function is MR ( Q ) = 20 Q/ 50 and the marginal cost function is MC ( Q ) = 4 . The profit-maximizing quantity of books for professor Bong to sell is Q = 800. 24.2 (0) Peter Morgan sells pigeon pies from a pushcart in Central Park. Morgan is the only supplier of this delicacy in Central Park. His costs are zero due to the abundant supplies of raw materials available in the park. (a) When he first started his business, the inverse demand curve for pigeon pies was p ( y ) = 100 y , where the price is measured in cents and y measures the number of pies sold. Use black ink to plot this curve in the graph below. On the same graph, use red ink to plot the marginal revenue curve. 298 MONOPOLY (Ch. 24) 50 75 100 125 Pigeon pies 25 50 75 100 Cents 25 150 Black lines Blue line Red line (b) What level of output will maximize Peters profits? 50. What price will Peter charge per pie?price will Peter charge per pie?...
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- Spring '08