150a_hw1_key

150a_hw1_key - Economics 150A Labor Economics Assignment 1...

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Economics 150A Labor Economics Assignment 1 Suggested Key Spring 2011 Due date: Fri, April 29 at the beginning of class. Follow the homework guidelines as posted on the webpage (see http://econ.ucsb.edu/~benelli/homework_guidelines.htm ). 1. Mike has a utility function represented by U(C,L) = 3C 2 L. He has 20 hours to devote to labor and leisure. His current wage is $12 per hour. a. Find his utility maximizing labor and leisure choice. L = (wT + v) / 3w = 6.67 H = 20 - 6.67 = 13.33 b. Now suppose he is given non-labor income of $60. Find his utility maximizing labor and leisure choice. L = (wT + v) / 3w = 8.33 H = 20 - 8.33 = 11.67 c. Find the non-labor income he would need to be indifferent between working (the number or hours you found in part a) and not working. You’re finding where U(C,L) work = U(C,L) no work U(C,L) work = 512,000 = U(C,L) no work → 512,000 = 3*C 2 *20 → C ≈ 113.4 so he needs to be given V≈ 92.38 1
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2. Shane currently receives welfare in the amount of $80 per day if he doesn’t work. His utility function is U(C,L) = C 1/2 L. Wages=$9 and he has 18 hours to allocate between work and leisure. a. Find his utility maximizing labor and leisure choice. Assume he is not eligible for welfare. L = (2wT + 2v) / 3w = 12 H = 18 - 12 = 6 b. Now assume he is eligible for welfare. His choice is to work or take welfare but not both. Find his utility maximizing labor and leisure choice. U(C,L)work = C 1/2 L = 88.18 U(C,L)welfare = C 1/2 L =161 utility under welfare is higher so take welfare. c. Assume he takes welfare and does not work. Find his reservation wage. Answer assumes he does NOT loose his welfare if he works. You can easily modify the answer to include V=0 (credit is given if you assumed V=0) By definition of reservation wage, H=0 or H=1 U(C,L)welfare = C 1/2 L =161, to get him to work 1 hour we have U(C,L)work 1 hour = (C + w res ) 1/2 (L-1) = (80 + w res ) 1/2 (17) = 161 w res $9.69 Another accepted method is MRS=w and solve for w. So you have 2C/L= w
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150a_hw1_key - Economics 150A Labor Economics Assignment 1...

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