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Rubinstein2005-page85 - 12:18 master Sheet number 83 Page...

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October 21, 2005 12:18 master Sheet number 83 Page number 67 Demand: Consumer Choice 67 c. The consumer chooses the bundle ( x 1 , x 2 ) which satisfies x 1 / x 2 = p 1 / p 2 and costs w . (Does the utility function u ( x ) = x 2 1 + x 2 2 rationalize the consumer’s behavior?) Problem 7. ( Moderately difficult ) In this question, we consider a consumer who behaves differently from the classic consumer we talked about in the lecture. Once again we consider a world with K commodities. The consumer’s choice will be from budget sets. The consumer has in mind a preference relation that satisfies continuity, monotonicity, and strict convexity; for simplicity, assume it is represented by a utility function u . The consumer maximizes utility up to utility level u 0 . If the budget set allows him to obtain this level of utility, he chooses the bundle in the budget set with the highest quantity of commodity 1 subject to the constraint that his utility is at least u 0 . a. Formulate the consumer’s problem. b. Show that the consumer’s procedure yields a unique bundle. c. Is this demand procedure rationalizable?
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