ps2solutions

ps2solutions - Problem Set 2 Due Thursday Sept 17th by 10pm...

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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.

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ps2solutions - Problem Set 2 Due Thursday Sept 17th by 10pm...

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