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# ps1_ans - Department of Economics University of California...

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Econ 121-Fall 2004 Page 1 Problem Set 1 Answers Department of Economics Fall 2004 University of California, Berkeley Woroch/Lopez/Sydnor Economics 121 PROBLEM SET 1 Due: Tuesday, September 21, 2004, 12:30 PM (in lecture) 1. Jive Record sells Britney Spears new album In the Zone, over two periods. The aggregate demand for the album is Q(P) = 25 – P, where Q is measured in millions of CDs. This means one million people willing to pay as much as \$25 for the album, while two million would pay \$24, and so on down to 25 million willing to pay \$1. Marginal cost of producing and distributing a CD is \$5. a) What price will the record label set in the first period if it sets the monopoly price? Draw the demand, marginal revenue, marginal costs and the monopoly price and quantity for the first period. MR = 25 – 2Q 1 MC = 5 MR = MC 25 – 2Q 1 = 5 2Q 1 = 20 Q 1 = 10, P 1 *= 15 b) Given your price in part a), what is the demand the record label faces in the second period? [Hint: which type of consumers did not purchase the CD in the first period?] In the first period, only people with valuations greater than \$15 would have purchased the CD. The demand in the second period is then just the demand in the first period below 15: Q 2 = 15 – P c) Show that the monopoly price it sets in the second period is \$10. MR 2 = 15 – 2Q MC 2 = 5 MR = MC 15 – 2Q 2 = 5 2Q 2 = 10 Q 2 = 5 and P 1 * = 10 P Q MC = 5 P 1 =15 Q 1 (P) = 25 – P Q 2 (P) = 15 – P P 2 =X 25 Q 1 =10

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Econ 121-Fall 2004 Page 2 Problem Set 1 Answers d) If consumers have zero costs to waiting, will the record label be able to charge the P = \$15 in period 1? Explain. If the record label sets a price of \$15 in the first period, then consumers can expect to pay \$10 in the second period. If there is no cost to waiting, however, consumers in the first period would not be willing to pay \$15 given they can pay \$10 in the second period. e) What would happen if the record label tried to set a price of \$10 in period 1? Again, setting a price of \$10 in the first period makes the demand in the second period Q = 10 – P. Given this, the firm’s best price in the second period would be \$7.50. But the same problem persists, consumers can simply wait until the second period for the lower price. f) Qualitatively, what do you think allows a producer of a durable good to be able to make a profit even if consumers know the producer will lower the price in the future? Clearly waiting costs are important. If some consumers value having the album now, the record label can set high price today and a lower price next month, these consumers will purchase as long as the price drop is smaller than the cost of waiting. 2.
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ps1_ans - Department of Economics University of California...

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