24. Monopoly - Solutions

# 24. Monopoly - Solutions - Chapter 24 NAME Monopoly...

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Chapter 24 NAME Monopoly Introduction. The proft-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 fnd the monopolist’s price by plugging the proft-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 fnd 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 frst 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 ,whe re 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 Bong’s book is R ( Q )= 20 Q Q 2 / 100 . (b) The total cost Function For producing ProFessor Bong’s 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 proft-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 frst 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

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304 MONOPOLY (Ch. 24) 0 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 Peter’s proFts? 50. What price will Peter charge per pie? 50 cents.
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## This note was uploaded on 07/16/2010 for the course ECON 21 taught by Professor Johng.sessions during the Summer '09 term at Dartmouth.

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24. Monopoly - Solutions - Chapter 24 NAME Monopoly...

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