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**Unformatted text preview: **Stanford University Department of Management Science and Engineering MS&E 241 Economic Analysis Optional Problem Session 3 Winter 2010 Friday, January 29, 2010 Practice Problem 3.1 (Choice under Uncertainty) Charlie wants to buy w = $30 worth of ground coffee and cocoa powder for his birthday party. Usually he goes to Mr. Wonkas store, which is a short walk from his home. Based on Charlies past experience, Mr. Wonka has always a very good cocoa powder, but the quality q { , 1 } of his coffee is always random, with a 60% chance of high quality ( q = 1) and a 40% chance of low quality ( q = 0). 1 The prices for cocoa powder and ground coffee are p 1 = $1 / ounce and p 2 = $1 . 50 / ounce, respectively. Charlies utility for having x 1 ounces of cocoa powder and x 2 ounces of ground coffee of quality q is u ( x ; q ) = x 1 x 2 + 10 x q 2 , where x = ( x 1 ,x 2 ) 0. (i) Find the consumption bundle x ( p,w ) that maximizes Charlies expected utility EU( x ) = E [ u ( x ;...

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