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Unformatted text preview: Stanford University Department of Management Science and Engineering MS&E 241 Economic Analysis Problem Set 1 Winter 2009 Issued: Tuesday, January 13, 2009 Due: Tuesday, January 20, 2009 Problem 1.1 (Walrasian and Hicksian Demand) John and Jane each have a budget of one hundred dollars to spend on apples and bananas at the local farmers market. Apples and bananas cost one dollar each. John and Jane have different preferences, by the utility functions u John ( x,y ) = p x 2 + y 2 and u Jane ( x,y ) = xy, respectively, where x denotes the number of apples in an individuals basket, and y the number of bananas in that basket. We will now determine utility-maximizing consumption bundles ( x,y ) for John and Jane as a function of market prices and budget constraints. (i) Explain why (10 , 80), i.e., ten apples and eighty bananas, cannot be a utility-maximizing bundle for either John or Jane. (ii) Explain (or show) why u John ( x,y ) = x 2 + y 2 can be used as an alternate utility function for John. (iii) Determine the budget set B ( p,w ), where w = 100 is an individuals budget and p = (1 , 1) is the vector of fruit prices. Draw this set in the commodity space....
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