501PS05 - ECON501 Advanced Microeconomic Theory 1 Fall...

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ECON501 Advanced Microeconomic Theory 1 Fall Semester 2007 Problem Set 5 The due date for this problem set is MONDAY Nov 12 1. (Polak) The following utility function (sometimes called Dixit- Stiglitz preferences) is often used in international trade applica- tions: u ( x 0 ,x 1 ,...,x L )= x 1 α 0 ³ X L c =1 x β c ´ α/β where α and β are both in the open interval (0 , 1). In the following assume p À 0and w> 0. Let G := { 1 ,...,L } . (a) Show that the proportion of wealth spent on x 0 is (1 α ). (b) Verify that we can express the Marshallian demand for each good c in G as a function just of prices ( p c ) c G and the ex- penditure on those goods w G . (c) Write down the expenditure function corresponding to an ap- propriately chosen subutility function for the goods in G . (d) Consider breaking the consumer’s maximization problem into a two-step budget process, where the f rst stage is to allo- cate expenditure between good 0 and the group of goods in G . Show that we can write the f rst-stage of the consumer’s maximization problem as max h x 0 ,X G i U ( x 0 ,X G ) subject to
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501PS05 - ECON501 Advanced Microeconomic Theory 1 Fall...

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