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151homework_1_solutions

# 151homework_1_solutions - Economics 151a Spring 2008...

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Economics 151a Spring 2008 Homework 1 - Solutions 2-2 . What is the effect of an increase in the price of market goods on a worker’s reservation wage, probability of entering the labor force, and hours of work? Suppose the price of market goods increases from p to p and the person’s non-labor income is V . If she chooses not to work, she can purchase V/p units of consumption after the price change, whereas she could have consumed V/p units of consumption prior to the price increase. Thus, her endowment point has moved from E to E in Figure A. As long as leisure is a normal good, the indifference curve is steeper as we move up a vertical line, indicating that the slope of the indifference curve is steeper at E than at E . Thus, an increase in the price of goods lowers the reservation wage and makes the person more likely to work. Figure A. To simplify the illustration of the effect on hours of work, assume for simplicity that V = 0. The increase in the price of goods shifts the budget line from FE to GE , moving the worker from P to point R . This shift induces both an income effect and a substitution effect. The price increase in effect lowers the person’s real wage rate, increasing the demand for leisure and leading to fewer hours of work. This substitution effect is illustrated by the move from point P to point Q in Figure B. The price increase also reduces the worker’s wealth, lowering the demand for leisure and leading to more hours of work. This income effect is illustrated by the move from Q to R . As drawn the income effect dominates the substitution effect and the price increase lowers the demand for leisure and increases hours of work. It is, of course, possible for the substitution effect to dominate the income effect (not pictured), so that hours of work decreases. Thus, without further restrictions on preferences, an increase in the price of market goods has an ambiguous effect on hours worked. Goods V / p V / p Hours of Leisure T 0 E E 1

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Figure B. E F Goods Q P R G T Hours of Leisure 2
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 Tom’s weekly budget line. If Tom does not work, he leisures for 168 hours and consumes \$80. For all hours Tom works up to his first 40, his after-tax and after-child care wage equals (80 percent of \$15) – \$4 = \$8 per hour. Thus, if he works for 40 hours, he will be able to leisure for 128 hours and consume \$80 + \$8(40) = \$400. For all hours Tom works over 40, his after-tax and after-child care wage equals (80

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151homework_1_solutions - Economics 151a Spring 2008...

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