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Unformatted text preview: Problem Set 2 Due Thursday, Sept. 17th, by 10pm 1. Terri likes to consume chocolate ( x 1 ) and movies ( x 2 ). Terri’s utility function was given by u ( x 1 ,x 2 ) = ( x 1 γ ) α ( x 2 ) 1 α where γ > . (a) Find Terri’s demands for x 1 and x 2 . Are Terri’s demands homothetic? L = ( x 1 γ ) α ( x 2 ) 1 α + λ ( I p 1 x 1 + p 2 x 2 ) Taking first order conditions and setting them equal to 0: ∂ L ∂x 1 = α x 2 x 1 γ 1 α λp 1 = 0 ∂ L ∂x 2 = (1 α ) x 2 x 1 γ α λp 2 = 0 ∂ L ∂λ = I p 1 x 1 + p 2 x 2 = 0 Solving this system gives the marshallian demand: x * 1 ( p 1 ,p 2 ,I ) = α I p 1 + (1 α ) γ x * 2 ( p 1 ,p 2 ,I ) = (1 α ) p 1 p 2 I p 1 γ Since MRS is not invariant to a proportional change in the ratio x 1 x 2 the utility function is not homothetic. MRS = α 1 α x 2 x 1 γ (b) Derive Terri’s indirect utility function. The indirect utility function is v ( x * 1 ( p 1 ,p 2 ,I ) ,x * 2 ( p 1 ,p 2 ,I )) = α I p 1 αγ α (1 α ) p 1 p 2 I p 1 γ 1 α (c) Derive Terri’s expenditure fuction....
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This note was uploaded on 05/13/2010 for the course ECON 105D taught by Professor Cur during the Fall '09 term at Duke.
 Fall '09
 CUR
 Microeconomics, Utility

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