NAME 121
030405060
50
100
150
200
250
300
10
Leisure
Consumption
Black
budget
line
Blue
indifference
curve (3000)
20
Blue indifference curve
(4500)
Blue
indifference
curve
(7500)
9.9 (0) George Johnson earns $5 per hour in his job as a truffle snif-
fer. After allowing time for all of the activities necessary for bodily up-
keep, George has 80 hours per week to allocate between leisure and labor.
Sketch the budget constraints for George resulting from the following
government programs.
blue ink on the graph below.)
122 BUYING AND SELLING (Ch. 9)
0204060
80
100
200
300
Leisure
Consumption
400
Blue budget line
Red budget line
(b) All individuals receive a lump sum payment of $100 per week from the
(c) If an individual is not working, he receives a payment of $100. If he
NAME 123
0204060
80
100
200
300
Leisure
Consumption
400
Red budget line
Blue budget line
(d) The same conditions as in Part (c) apply, except that the first 20 hours
(e) All wages are taxed at 50%, but as an incentive to encourage work,
124 BUYING AND SELLING (Ch. 9)
0204060
80
100
200
300
Leisure
Consumption
400
Blue budget line
9.10 (0) In the United States, real wage rates in manufacturing have
risen steadily from 1890 to the present. In the period from 1890 to 1930,
Hourly Wages and Length of Work Week
in U.S. Manufacturing, 1890–1983
Sources: Handbook of Labor Statistics, 1983 and U.S. Economic History,
by Albert Niemi (p. 274). Wages are in 1983 dollars.
Year Wage Hours Worked
NAME 125
(a) Use these data to plot a “labor supply curve” on the graph below.
030405060
2
4
6
8
10
12
10
Hourly wage rate (in 1983 dollars)
20
Hours of work per week
(b) At wage rates below $4 an hour, does the workweek get longer or
shorter as the wage rate rises? Shorter.
(c) The data in this table could be consistent with workers choosing var-
ious hours a week to work, given the wage rate. An increase in wages
has both an endowment income effect and a substitution effect. The
shorter workweek. At wage rates below $4 an hour, the (substi-
tution, endowment income) endowment income effect appears
to dominate. How would you explain what happens at wages above $4
126 BUYING AND SELLING (Ch. 9)
in 1909 than they took in 1890.
9.11 (0) Professor Mohamed El Hodiri of the University of Kansas, in
a classic tongue-in-cheek article “The Economics of Sleeping,” Manifold,
17 (1975), offered the following analysis. “Assume there are 24 hours in
a day. Daily consumption being xand hours of sleep s, the consumer
maximizes a utility function of the form u=x2s,wherex=w(24 −s),
with wbeing the wage rate.”
(a) In El Hodiri’s model, does the optimal amount of sleeping increase,
(b) How many hours of sleep per day is best in El Hodiri’s model? 8.
9.12 (0) Wendy and Mac work in fast food restaurants. Wendy gets $4
an hour for the first 40 hours that she works and $6 an hour for every
hour beyond 40 hours a week. Mac gets $5 an hour no matter how many
hours he works. Each has 80 hours a week to allocate between work and
leisure and neither has any income from sources other than labor. Each
has a utility function U=cr,wherecis consumption and ris leisure.
Each can choose the number of hours to work.
would be if she does not work overtime. Use red ink for the part where
she would be if she worked overtime.
NAME 127
0204060
80
100
200
300
Leisure
Consumption
400
Blue part of line
Red part of line
(c) The blue line segment that you drew lies on a line with equation
point on the line and you know its slope.)
(d) If Wendy was paid $4 an hour no matter how many hours she worked,
On your graph, use black ink to draw her indifference curve through this
point.
(f) Suppose that the jobs are equally agreeable in all other respects. Since
Wendy and Mac have the same preferences, they will be able to agree
Calculate Wendy’s utility when she makes her best choice. Calculate what
her utility would be if she had Mac’s job and chose the best amount of
time to work.)
128 BUYING AND SELLING (Ch. 9)
9.13 (1) Wally Piper is a plumber. He charges $10 per hour for his work
and he can work as many hours as he likes. Wally has no source of income
other than his labor. He has 168 hours per week to allocate between labor
and leisure. On the graph below, draw Wally’s budget set, showing the
various combinations of weekly leisure and income that Wally can afford.
0 120 160 200 240
400
800
1200
1600
2000
2400
40
Income
80
Leisure
128
Red
budget
line
(b) While self-employed, Wally chose to work 40 hours per week. The
construction firm, Glitz and Drywall, had a rush job to complete. They
offered Wally $20 an hour and said that he could work as many hours as
he liked. Wally still chose to work only 40 hours per week. On the graph
you drew above, draw in Wally’s new budget line.
(c) Wally has convex preferences and no kinks in his indifference curves.
On the graph, draw indifference curves that are consistent with his choice
of working hours when he was self-employed and when he worked for Glitz
and Drywall.
(d) Glitz and Drywall were in a great hurry to complete their project and
wanted Wally to work more than 40 hours. They decided that instead of
paying him $20 per hour, they would pay him only $10 an hour for the
first 40 hours that he worked per week and $20 an hour for every hour of
NAME 129
“overtime” that he worked beyond 40 hours per week. On the graph that
you drew above, use red ink to sketch in Wally’s budget line with this
pay schedule. Draw the indifference curve through the point that Wally
chooses with this pay schedule. Will Wally work more than 40 hours or
9.14 (1) Felicity loves her job. She is paid $10 an hour and can work
as many hours a day as she wishes. She chooses to work only 5 hours
a day. She says the job is so interesting that she is happier working at
this job than she would be if she made the same income without working
at all. A skeptic asks, “If you like the job better than not working at
all, why don’t you work more hours and earn more money?” Felicity,
who is entirely rational, patiently explains that work may be desirable on
average but undesirable on the margin. The skeptic insists that she show
him her indifference curves and her budget line.
(a) On the axes below, draw a budget line and indifference curves that are
consistent with Felicity’s behavior and her remarks. Put leisure on the
horizontal axis and income on the vertical axis. (Hint: Where does the
indifference curve through her actual choice hit the vertical line l= 24?)
Income
Leisure
50
240
24
9.15 (2) Dudley’s utility function is U(C, R)=C−(12 −R)2,whereR
is the amount of leisure he has per day. He has 16 hours a day to divide
between work and leisure. He has an income of $20 a day from nonlabor
sources. The price of consumption goods is $1 per unit.
(a) If Dudley can work as many hours a day as he likes but gets zero
130 BUYING AND SELLING (Ch. 9)
(b) If Dudley can work as many hours a day as he wishes for a wage
budget constraint. Solve for the amount of leisure that maximizes his
utility subject to this constraint. Remember that the amount of labor he
wishes to supply is 16 minus his demand for leisure.)
(c) If Dudley’s nonlabor income decreased to $5 a day, while his wage
(d) Suppose that Dudley has to pay an income tax of 20 percent on all
of his income, and suppose that his before-tax wage remained at $10 an
hour and his before-tax nonlabor income was $20 per day. How many