2010-Problem-Session-5 - Stanford University Department of...

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

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 (....
View Full Document

Ask a homework question - tutors are online