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Unformatted text preview: Economics 104A Solution for Final Exam Winter 2008 1. Jerry consumes good 1 and good 2. His utility function is u ( x 1 ,x 2 ) = x 1 1 x 2 . a) (6pt) 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 effect, and total effects of the quantity tax. 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 = ¯ I + Δ I and z * = (20 √ . 8 , √ 1 . 25) if his optimal bundle at p 1 , ¯ p 2 , ¯ I . Thus, SE = y * 1 x * 1 = 0 . 8 √ . 8 = . 09 and IE = z * 1 y * 1 = 4 . 8. Answer: b) (4pt) If the government asks Jerry at most how much of his income he would be willing to give up to prevent this quantity tax, what would his answer be, assuming he does not lie? Answer: Jerry’s utility level at optimal bundle after tax is 1 u ( z * ) = 20 2 √ . 8 . 1 u ( z * ) = z * 1 1 z * 2 = ¯ I p 1 q ¯ p 2 p 1 1 q p 1 ¯ p 2 = ¯ I p 1 2 q ¯ p 2 p 1 ....
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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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