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36396_10052603024214 - Advanced Microeconomic Theory I Fall...

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Advanced Microeconomic Theory I Fall 2009 Midterm Exam 11/1/2009 Answer all three questions. Write clearly and show all steps. I prefer English, but you may answer in Chinese if you feel it would help. The numbers in brackets are points for each question. 1. Dangdang°s consumption choice when facing a price vector p and income I is x ( p; I ) . We know that Dangdang always uses up her income. Hence, px ( p; y ) = y . Dangdang°s mother Fengfeng is trying to induce Dangdang to choose a consumption bundle x 2 < n + such that u ( x ) ° u for some objec- tive function u ( : ) that is increasing in x . She does so by o/ering Dangdang an allowance y and imposing a per-unit tax z i on Dangdang°s consumption of good i . (Fengfeng is subsidizing Dangdang°s consumption of good i if z i is negative.) Dangdang has no other source of income, and is e/ectively facing a budget constraint ( p + z ) x = y . De±ne f ( p; u ) ± min z;y ( y ² zx ( p + z; y )) s.t. u ( x ( p + z; y )) ° u as the minimum expenditure that Fengfeng needs to achieve her goal.
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