ps3 - buying in the second and θ(the marginal consumer...

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Problem Set 2 (Due on 15th Oct) 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 θ. A consumer receives utility u = 2 θ - p if she purchases the good in the first period (and enjoys it for two periods) and u = θ - 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. ii. Solve this program for θ (the marginal consumer indifferent between buying in the first period and
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Unformatted text preview: buying in the second), and θ (the marginal consumer indifferent between buying in the second and not buying at all.) Warning! – you may be violating an implicit constraint (chances are, you are.) Find out what implicit constraint is being broken, then impose the constraint and solve again. iii. Find q1, p1, q2, and p2. b. Assuming that the monopolist cannot commit to a second period price, find θ 1 , θ 2 , q 1 , p 1 , q 2 , and p 2 . Which outcome does the monopolist prefer, that of part a. or part b.? c. Repeat parts a. and b. but assuming that the utility to a consumer is u = 3θ- p 1 if she purchases in period 1, u = θ - p 2 if she purchases in period 2, 0 if she does not buy, and MC = 0. (This is someone who gets extra value from owning something brand new.)...
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