ps3soln - Problem Set 3 Solutions ECON105 Industrial...

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Unformatted text preview: Problem Set 3 Solutions ECON105 Industrial Organization and Firm Strategy Professor Michael Noel University of California San Diego 1. A monopolist produces a durable good. All production takes place at constant MC= c in the first period and the good lasts until the end of the second period. There is a continuum of consumers uniformly distributed on [0, 1], indexed by . A consumer receives utility u = 2 - p if she purchases the good in the first period (and enjoys it for two periods) and u = - p if she buys in the second period. The monopolist can charge different prices in each period. a. Assume the monopolist can credibly commit to a specific second period price while still at the beginning of the first period. i. Set up the maximization program. First, lets consider the intuition behind the setup. Given any prices p 1 and p 2 , there will be a consumer with = 1 within [0, 1], such those with higher s will buy in the 1 st period and those directly below will buy in the 2 nd period if at all (if we change prices, then 1 will be at a different spot on the interval, but it will always exist somewhere). This consumer with 1 is indifferent between when to buy: 2 1-p 1 = 1 p 2 . This equation gives us the Incentive Compatibility constraint for 1 and, while it binds with equality for 1 , it also automatically holds with strict inequality for all people with even higher s: 2-p 1 > p 2 for all > 1 . I.e., those with > 1 strictly prefer to buy in the first period than buying in the second. Therefore, the mass of consumers with s higher than 1 will be the monopolists quantity sold in the first period alone: q 1 =1- 1 ....
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This note was uploaded on 10/20/2010 for the course ECON ECON 105 taught by Professor Noel during the Fall '10 term at UCSD.

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ps3soln - Problem Set 3 Solutions ECON105 Industrial...

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