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Unformatted text preview: Economics 151a Spring 2008 Homework 1 2-2. What is the effect of an increase in the price of market goods on a workers reservation wage, probability of entering the labor force, and hours of work? 2-4. Tom earns $15 per hour for up to 40 hours of work each week. He is paid $30 per hour for every hour in excess of 40. Tom faces a 20 percent tax rate and pays $4 per hour in child care expenses for each hour he works. Tom receives $80 in child support payments each week. There are 168 hours in the week. Graph Toms weekly budget line. 2-5. Cindy gains utility from consumption C and leisure L . The most leisure she can consume in any given week is 168 hours. Her utility function is U(C,L) = C L . This functional form implies that Cindys marginal rate of substitution is C / L . Cindy receives $630 each week from her great- grandmother regardless of how much Cindy works. What is Cindys reservation wage? 2-8. Shellys preferences for consumption and leisure can be expressed as U(C,L) = ( C 200 ) ( L 80 ). This utility function implies that Shellys marginal utility of leisure is C 200 and her marginal utility of consumption is L 80 . There are 168 hours in the week available to split between work and leisure. Shelly earns $5 per hour after taxes. She also receives $320 worth of welfare benefits each week regardless of how much she works. (a) Graph Shellys budget line. (b) What is Shellys marginal rate of substitution when L = 100 and she is on her budget line? (c) What is Shellys reservation wage? (d) Find Shellys optimal amount of consumption and leisure. 2-9. Among single, college-educated women aged 22 25, average annual hours worked is 2,160 and the average wage is $22.50. If the average wage increases to $25 per hour, average annual hours worked increases to 2,340. What is the elasticity of labor supply for this group of workers? 2-10. Mikes utility for consumption and leisure is U(C,L) = C L so that his marginal rate of substitution between leisure and consumption is C/L . There are 168 hours in the week and he earns $10 per hour. (a) What is Mikes optimal amount of consumption and leisure? (b) If the government starts a welfare policy that pays B to all non-workers and pays $0 to all workers, at what value of B will Mike opt out of the labor force in order to go on welfare? 3-1. Consider two workers with identical preferences, Phil and Bill. Both workers have the same life cycle wage path in that they face the same wage at every age, and they know what their future wages will be. Leisure and consumption are both normal goods. (a) Compare the life cycle path of hours of work between the two workers if Bill receives a one-time, unexpected inheritance at the age of 35....
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