problemPT.solution[1]

# problemPT.solution[1] - Solutions to Problem Set 2:...

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Solutions to Problem Set 2: Consumer Theory Compulsory Home Assignment. Deadline: 13 November 1. Consider the indirect utility function given by v ( p 1 ,p 2 ,m )= m p 1 + p 2 . (a) What are the (Marshallian) demand functions? Solution: Use Roy´s Identity: x 1 ( p 1 2 ∂v ( p 1 ,p 2 ,m ) ∂p 1 ( p 1 ,p 2 ,m ) ∂m = m ( p 1 + p 2 ) 2 1 p 1 + p 2 = m p 1 + p 2 , x 2 ( p 1 2 ( p 1 ,p 2 ,m ) 2 ( p 1 ,p 2 ,m ) = m ( p 1 + p 2 ) 2 1 p 1 + p 2 = m p 1 + p 2 . (b) What is the expenditure function? Solution: Use the identity v ( p, e ( p, u )) := u. Replacing m with e in the indirect utility function and setting it equal to u yields e p 1 + p 2 = u, implying e ( p 1 2 ,u )=( p 1 + p 2 ) u. (c) What is the direct utility function? Solution: Since the consumer demands exactly the same quantity of both goods, irrespective of relative prices, the utility function must be of the Leontief type, where the two goods are perfect complements in consumption. From the expression of the indirect utility function, we know that the utility function must be u ( x 1 ,x 2 )=min { x 1 2 } . 2. Use the utility function u ( x 1 2 x 1 2 1 x 1 3 2 and the budget constraint m = p 1 x 1 + p 2 x 2 to calculate 1

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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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problemPT.solution[1] - Solutions to Problem Set 2:...

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