midterm2

# Intermediate Microeconomics: A Modern Approach, Seventh Edition

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14.04 Midterm Exam 2 Prof. Sergei Izmalkov Wed, Nov 5 1. Consumer 1 has expenditure function e 1 ( p 1 , p 2 , u 1 ) = u 1 p 1 p 2 and consumer 2 has utility function u 2 ( x 1 , x 2 ) = 2003 x 3 1 x a 2 . (a) What are Marshallian (market) demand functions for each of the goods by each of the consumers? Denote the income of consumer 1 by m 1 and the income of consumer 2 by m 2 . (b) For what value(s) of the parameter a will there exists an aggregate demand functions that is independent of the distribution of income? 2. Suppose that utility maximization problems and expenditure minimization problems are well de fi ned and utility and expenditure functions satisfy all necessary “nice” properties. (a) Show (prove) that utility maximization implies expenditure minimization and vice versa. (b) List all relevant identities that are result of a. (c) Derive Roy’s identity. (d) Derive Slutsky equation. 3. An economy has two kinds of consumers and two goods. Type A and type B consumers have the following utility functions 2 U A ( x 1 , x 2 ) = 4 x 1
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