501PS03

# 501PS03 - ECON501 Advanced Microeconomic Theory 1 Fall...

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ECON501 Advanced Microeconomic Theory 1 Fall Semester 2007 Problem Set 3 The due date for this problem set is Friday October 26. 1. (a) Derive the expenditure function e ( p 1 ,p 2 ,u ) from preferences represented by the utility function u ( x 1 ,x 2 )= x 2 1 + x 2 2 where x 1 0and x 2 0. (b) For this expenditure function derive and draw the set V 4 = © ( x 1 ,x 2 ) R 2 + : p 1 x 1 + p 2 x 2 e ( p 1 ,p 2 , 4) for all p 1 > 0, p 2 > 0 ª (c) Draw on the same picture the upper contour set S 4 = © ( x 1 ,x 2 ) R 2 + : x 2 1 + x 2 2 4 ª (d) Explain the relationship between V 4 and S 4 , in particular ex- plain why are they not equal. (e) Without further calculation, write down the expenditure func- tion b e ( p 1 ,p 2 ,u )derived from preferences represented by the utility function b u ( x 1 ,x 2 )= x 3 1 + x 3 2 and also draw the set b V 8 = © ( x 1 ,x 2 ) R 2 + : p 1 x 1 + p 2 x 2 b e ( p 1 ,p 2 , 8) for all p 1 > 0, p 2 > 0 ª 2. You are given the following partial information about the purchases

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501PS03 - ECON501 Advanced Microeconomic Theory 1 Fall...

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