October 21, 2005 12:18masterSheet number 83 Page number 67Demand: Consumer Choice67c. The consumer chooses the bundle(x1,x2)which satisfiesx1/x2=p1/p2and costsw. (Does the utility functionu(x)=x21+x22rationalize theconsumer’s behavior?)Problem 7.(Moderately difficult)In this question, we consider a consumer who behaves differently from theclassic consumer we talked about in the lecture. Once again we consider aworld withKcommodities. 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 representedby a utility functionu.The consumer maximizes utility up to utility levelu0. If the budget setallows him to obtain this level of utility, he chooses the bundle in the budgetset with the highest quantity of commodity 1 subject to the constraint thathis utility is at leastu0.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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