Gorman Problem

Gorman Problem - Econ 210A Problems November 9 2007 1 An...

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Econ 210A Problems , November 9, 2007 1) An economy has M consumers. For i = 1 ,...,M , Consumer i has utility function U i ( x 1 i ,x 2 i ) = x 1 i + 2 a i x 2 i where x ji is the amount of good j that i consumes and where a i > 0. a) Find Consumer i ’s demand function x i ( p,w i )for Goods 1 and 2. Be sure to take account of possible corner solutions. For what values of p 1 , p 2 , and w does Consumer i consume none of Good 1? b) Show that if “everyone has enough income”, all consumers will demand posi- tive amounts of both goods. What do we mean by everyone has enough income in this context? c) Write an expression for consumer i ’s indirect utility function. Are these indirect utilities of the Gorman form? d) In general, aggregate demand is the sum of individual demands which in turn depends on prices and the distribution of income. That is aggregate demand is a function D ( p,w 1 ,...,w M ) = X i x i ( p,w i ) . Show that with the utility functions in this problem, there is a range of income
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This note was uploaded on 02/01/2011 for the course ECONOMY 6 taught by Professor Fallahi during the Spring '10 term at Cambridge.

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