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##### Economics 150A Labor Economics

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Economics 150A Labor Economics;Spring 2010;Assignment 1;Due date: Wed, April 28 at the beginning of class.;Follow the homework guidelines as posted on the webpage. See http://econ.ucsb.edu/~benelli/homework_guidelines.htm Note that your answers must be typed. Handwritten answers will not be graded. There is a penalty of late homework.;1. Shane currently receives welfare in the amount of \$80 per day if he doesn?t work. His utility function is U(C,L) = C1/2L. Wages=\$9 and he has 18 hours to allocate between work and leisure.;1. Find his utility maximizing H and L. Assume he is not eligible for welfare.;2. Now assume he is eligible for welfare. Does he take welfare or work?;3. Assume he takes welfare and does not work. What is his reservation wage? He will not loose his welfare if he works.;4. Suppose he is working and receives no welfare, what is the minimum overtime pay needed for him to work 1 hour of overtime?;2. Phillip receives EITC. If he earns less than \$10,000 per year, the government subsidizes his wages by 0.25%. If he earns between \$10,000 and \$12,000 there is no tax. If he earns greater than \$12,000 then he is taxed 0.23%. His market wages are \$15 per hour. He has 5,000 hours per year to devote to labor or leisure. His utility function is U(C, L) = C1/2 L.;a. Find the maximum value of the subsidy.;b. Find the range of work hours that will provide the full value of the subsidy.;c. What is the sum of all hours worked (with and without the subsidy) takes until the subsidy goes to zero.;d. Find Phillip?s utility max combination of leisure and labor before the subsidy.;e. Now assume he is eligible for the subsidy. Given the information in parts a-d, does he receive any subsidy? If so, what is his income? For ease, assume the labor/leisure hours you found in part d remain constant.;f. On one graph, clearly label all your answers from parts a-e.;3. Alice?s utility function is U(C,L) = CL2. Wages=\$11 and she has 24 hours to allocate between work and leisure.;1. Find her utility maximizing work and leisure hours.;2. What is her consumption?;3. Her grandmother decides to give her \$25 indefinitely. Find her new utility maximizing work and leisure hours.;4. Now suppose she faces a time commute cost of 2 hours (total time loss commuting to and from work). How many hours will she devote to labor and leisure?;4. Alice?s wages are represented by W = 1/3 (abH1/3);a. What is her labor supply elasticity? Show all your math.;b. Is her labor supply elastic or inelastic?;c. Interpret the elasticity's numerical value from part b.;d. Which effect dominates? The substitution effect or income effect?;5. Mike has a utility function represented by U(C,L) = 3C2L. He has 20 hours to devote to labor and leisure. His current wage is \$12 per hour.;a. Find his utility maximizing H and L.;b. Now suppose he has non-labor income of \$60 per day. How many hours will he devote to leisure and labor?;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.;6. Bill currently receives \$1000 non-wage income per week and works 20 hours a week. His wage is \$8.00 an hour. His utility function is cobb-douglas.;a. Graphically demonstrate Bill?s current labor-leisure choice.;b. Suppose Bill now has his non-wage income cut to \$75 per week. Graphically decompose the income and substitution effects.

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