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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 ). Terris utility function was given by u ( x 1 ,x 2 ) = ( x 1 ) ( x 2 ) 1 where > . (a) Find Terris demands for x 1 and x 2 . Are Terris demands homothetic? L = ( x 1 ) ( x 2 ) 1 + ( I p 1 x 1 + p 2 x 2 ) Taking first order conditions and setting them equal to 0: L x 1 = x 2 x 1 1  p 1 = 0 L x 2 = (1 ) x 2 x 1   p 2 = 0 L = I p 1 x 1 + p 2 x 2 = 0 Solving this system gives the marshallian demand: x * 1 ( p 1 ,p 2 ,I ) = I p 1 + (1 ) x * 2 ( p 1 ,p 2 ,I ) = (1 ) p 1 p 2 I p 1 Since MRS is not invariant to a proportional change in the ratio x 1 x 2 the utility function is not homothetic. MRS = 1 x 2 x 1 (b) Derive Terris indirect utility function. The indirect utility function is v ( x * 1 ( p 1 ,p 2 ,I ) ,x * 2 ( p 1 ,p 2 ,I )) = I p 1 (1 ) p 1 p 2 I p 1 1 (c) Derive Terris expenditure fuction....
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 Fall '09
 CUR
 Microeconomics, Utility

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