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Unformatted text preview: Stanford University Department of Management Science and Engineering MS&E 241 Economic Analysis Optional Problem Session 5 Winter 2010 Friday, February 19, 2010 Practice Problem 5.1 (Monopoly Pricing) Consider a single-product monopolist in a market, with inverse demand function p ( q ) = a- bq , where a,b > 0. At time t = 0, the monopolist decides what amount I 0 to invest on cost reduction, and at time t = 1 what quantity q of products to produce. His unit production cost c ( I ) > 0 is decreasing and convex in I . Profits are realized at time t = 1. Throughout this problem, assume that p ( q ) and c ( I ) are such that the maximizations are concave and the solutions have strictly positive production and investment. (i) Formulate the monopolists profit-maximization problem and determine the corresponding first- order necessary optimality conditions. (ii) Provide the social-welfare function W ( q,I ) as a function of the monopolists decision variables q and I . Compare the monopolists (second-best) choice of (....
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