501PS01 - ECON501 Advanced Microeconomic Theory 1 Fall...

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ECON501 Advanced Microeconomic Theory 1 Fall Semester 2007 Problem Set 1 The due date for this problem set is Friday October 12. 1. (Polak) Social Preferences. Consider a social planner who has preferences over ‘welfare’ vectors w R N + , with the interpretation that the i th component w i is the welfare of the i th person in society. Suppose that the social planner’s only concern is to maximize the welfare of the least well-o f person in society; she does not care about anything else. (a) Write down a welfare function W : R N + R that represents this social planner’s preference relation over welfare vectors. Explain brie f y whether or not this preference relation is con- tinuous, monotone, strongly monotone, convex or strictly con- vex. It may help to sketch the indi f erence map. (b) How are monotone and strict monotone here related to Pareto critieria? (c) Now suppose the planner decides that, if the least well-o f person in w and w 0 are equally well o f , then she prefers
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501PS01 - ECON501 Advanced Microeconomic Theory 1 Fall...

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