Econ 339 Fall 2009 Problem Set 2 - Solutions

# Econ 339 Fall 2009 Problem Set 2 - Solutions - Econ 339...

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Econ 339 Fall Quarter 2009 Problem Set 2 - Solutions Solve the following Problems. Show your work. Book Problems (p. 66): 2-2 ,2-3 ,2-10, 2-11, 2-12 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. Goods V / p V / p Hours of Leisure T 0 E E 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,

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without further restrictions on preferences, an increase in the price of market goods has an ambiguous effect on hours worked. Figure B. E F Goods Q P R G T Hours of Leisure 2-3. Sally can work up to 3,120 hours each year (a busy social life and sleep take up the remaining time). She earns a fixed hourly wage of \$25. Sally owes a 10 percent payroll tax on the first \$40,000 of income. Above \$40,000 of income, there is no payroll tax. Sally also faces a progressive income tax rate. There is no income tax on the first \$10,000 of income. From \$10,000 up to \$60,000, the marginal income tax rate is 25 percent. Above \$60,000, the marginal income tax rate is 50 percent. Graph Sally’s budget line. Sally’s budget line will have kinks at gross income levels of \$10,000, \$40,000, and \$60,000. As her wage is \$25 per hour, these kinks occur after 400 hours, 1,600 hours, and 2,400 hours of work respectively, or, similarly, at 2,720, 1,520, and 720 hours of leisure.
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