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Unformatted text preview: Economics 104A Solution for Problem Set #3 Winter 2009 1. Jerry consumes good 1 and good 2. His utility function is u ( x 1 ,x 2 ) = x 1 1 x 2 . a) Suppose initially ¯ p 1 = 4, ¯ p 2 = 4, and ¯ I = 100. Find the optimal bundle. Now suppose a quantity tax of $1 is imposed on good 1. Find the substitution, income, and total effects of the tax. Answer: The demand functions are x 1 ( p 1 ,p 2 ,I ) = I p 1 s p 2 p 1 for good 1 and x 2 ( p 1 ,p 2 ,I ) = s p 1 p 2 for good 2 when p 1 p 2 ≤ I 2 . Using these demand functions, we get x * = ( x * 1 ,x * 2 ) = (24 , 1) as the optimal bundle before tax. Next, the price of good 1 after tax is p 1 = 2 which implies Δ p 1 = p 1 ¯ p 1 = 1. Hence, to calculate the (Slutsky) substitution and income effects, we need to increase Jerry’s income by Δ I = Δ p 1 x * 1 = 24, in order to make bundle x * affordable for him after tax. Using the demand functions again, y * = ( y * 1 ,y * 2 ) = (24 . 8 √ . 8 , √ 1 . 25) is Jerry’s optimal bundle at p 1 , ¯ p 2 ,I =...
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This note was uploaded on 12/04/2010 for the course ECE 134 taught by Professor York during the Fall '08 term at UCSB.
 Fall '08
 York

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