Answers to Selected Problems

For Chapter 5, Exercise 3.4
p, $ per unit
p 2
p 1
A
C
Relatively inelastic
demand (at e 1 )
B
e 3 D
Q 3
e 2
Q 2
Q, Units per week
5.8 The proposed tax system exempts an individual’s
first $10,000 of income. Suppose that a flat 10%
rate is charged on the remaining income. Someone
who earns $20,000 has an average tax rate of 5%,
whereas someone who earns $40,000 has an average
tax rate of 7.5%, so this tax system is progressive.
5.10 As the marginal tax rate on income increases, people
substitute away from work due to the pure substitution
effect. However, the income effect can be
either positive or negative, so the net effect of a tax
increase is ambiguous. Also, because wage rates differ
across countries, the initial level of income differs,
again adding to the theoretical ambiguity. If
we know that people work less as the marginal
tax rate increases, we can infer that the substitution
effect and the income effect go in the same
direction or that the substitution effect is larger.
However, Prescott’s (2004) evidence alone about
hours worked and marginal tax rates does not
allow us to draw such an inference because U.S. and
European workers may have different tastes and face
different wages.
5.11 The figure shows Julia’s original consumer equilibrium:
Originally, Julia’s budget constraint was a
straight line, L1 with a slope of -w, which was tangent
to her indifference curve I1 at e1 , so she worked
12 hours a day and consumed Y1 = 12w goods. The
maximum-hours restriction creates a kink in Julia’s
new budget constraint, L2 . This constraint is the
same as L1 up to eight hours of work, and is horizontal
at Y = 8w for more hours of work. The highest
indifference curve that touches this constraint is I2 .
Because of the restriction on the hours she can work,
e 1
Q 1
Relatively elastic
demand (at e 1 )
Answers to Selected Problems
E-37
Julia chooses to work eight hours a day and to consume
Y 2 = 8w goods, at e 2 . (She will not choose to
work fewer than eight hours. For her to do so, her
indifference curve I 2 would have to be tangent to the
downward-sloping section of the new budget constraint.
However, such an indifference curve would
have to cross the original indifference curve, I 1 , which
is impossible: see Chapter 3.) Thus, forcing Julia to
restrict her hours lowers her utility: I 2 must be below
I 1 .Comment: When I was in college, I was offered
a summer job in California. My employer said,
“You’re lucky you’re a male.” He claimed that, to
protect women (and children) from overwork, an
archaic law required him to pay women, but not
men, double overtime after eight hours of work. As
a result, he offered overtime work only to his male
employees. Such clearly discriminatory rules and
behavior are now prohibited. Today, however, both
females and males must be paid higher overtime
wages—typically 1.5 times as much as the usual
wage. Consequently, many employers do not let
employees work overtime.
For Chapter 5, Problem 5.11
Y, Goods per day
Y1 = 12w
Y 2 = 8w
L 1
L2
e 1
Time
constraint
I 1
I 2
24 H1 = 12 H2 = 8 H, Work hours
per day
6.2 Parents who do not receive subsidies prefer that
poor parents receive lump-sum payments rather
than a subsidized hourly rate for child care. If the
supply curve for child-care services is upward sloping,
by shifting the demand curve farther to the
right, the price subsidy raises the price of child-care
for these other parents.
6.3 The government could give a smaller lump-sum subsidy
that shifts the L LS curve down so that it is parallel
to the original curve but tangent to indifference
curve I 2 . This tangency point is to the left of e 2 , so
the parents would use fewer hours of child care than
with the original lump-sum payment.
e 2