2-1. How many hours will a person allocate to leisure activities if her indifference curves between
consumption and goods are concave to the origin?
A worker will either work all available time or will not work at all. As drawn in Figure A, point B is
preferred to points A and C. Thus, the worker chooses not to enter the labor market. As drawn in Figure
B, point C is preferred to both points A and B. Thus, the worker chooses not to consume any leisure and
work all available time.
U 0 U 0
Hours of Leisure Hours of Leisure
2-2. What is the effect of a rise in the price of market goods on a workers reservation wage,
probability of entering the labor force, and hours of work?
Suppose the price of market goods increases from p to p the persons 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
1 Figure A.
0 T Hours of
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
persons 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 workers 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.
Hours of Leisure
22-3. 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 Sallys budget line.
Sallys 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.
From 0 to 400 hours, Sallys after-tax wage is $22.50 (90 percent of $25). If she works exactly
400 hours, her after-tax income is $9,000.
From 400 to 1,600 hours, Sallys after-tax wage is $16.25 (65 percent of $25). If she works
exactly 1,600 hours, her after-tax income is $9,000 + $16.25 (1600-400) = $28,500.
From 1,600 to 2,400 hours, Sallys after-tax wage is $18.75 (75 percent of $25). If she works
exactly 2,400 hours, her after-tax income is $28,500 + $18.75 (2400-1600) = $43,500.
From 2,400 to 3,120 hours, Sallys after-tax wage is $12.50 (50 percent of $25). If she works
exactly 3,120 hours, her after-tax income is $43,500 + $12.50 (3120-2400) = $52,500.
Sally's Budget Line