Answers to Even Numbered Review Questions and Problems
Chapter 2
Problems
4.
Suppose the adult population of a city is 9,823,000, and there are 3,340,000 persons who are not in
the labor force and 6,094,000 who are employed.
a. Calculate the number of adults who are in the labor force and the number of adults who are
unemployed.
b. Calculate the labor force participation rate and the unemployment rate.
Answer: a. Number in labor force = number in population less those not in the labor force
= 9,823,000 – 3,340,000 = 6,483,000
Number unemployed = number in labor force minus number employed
= 6,483,000 – 6,094,000 = 389,000
b. Labor force participation rate = (labor force/population) × 100
= (6,483,000/9,823,000) × 100
= 66.0%
Unemployment rate = (unemployed/labor force) × 100
= (389,000/6,483,000) × 100
= 6.0%
Chapter 3
Review Questions
2.
Assume that wages for keyboarders (data entry clerks) are lower in India than in the United States.
Does this mean that keyboarding jobs in the United States will be lost to India? Explain.
Answer: Indian data entry clerks will be substituted for American ones only if the ratio of their
wage to their marginal productivity is lower. Thus, it is not wage alone that affects the
incentives to substitute; marginal productivity is also critical.
6.
Suppose the government were to subsidize the wages of all women in the population by paying their
employers 50 cents for every hour they worked. What would be the effect on the wage rate women
received? What would be the effect on the net wage employers paid? (The net wage would be the
wage women received less 50 cents.)
Answer: Consider a simple competitive labor market in which the demand and supply of women
are both expressed in terms of the wage received by women (which, in the absence of any
subsidy, is assumed to be equal to the wage paid by employers). Given the demand curve,
D0, and the supply curve, S0, market clearing wage and employment levels will be W0 and
E0, respectively.
Suppose the government now subsidizes employers by paying them 50 cents for every
hour women work. Viewed in terms of the wage received by women, the employers’
demand curve will shift up by exactly 50 cents (reflecting the fact that this amount will be
paid by the government). At the old market clearing wage received by women, W0, the
number of women employers want to hire, E2, exceeds the number who are willing to
work, E0. This puts upward pressure on the wage received by women, and this wage rises
until the excess demand for labor is eliminated. This equilibrium occurs at the wage rate
W1, and the employment level E1.
It is clear from the figure that the wage received by women increases by less than 50 cents
as long as the supply of labor curve is not vertical (i.e., as long as labor supply is responsive
to wages). Indeed, the more responsive labor supply is to the wage rate, the less the
women’s wage will rise. Since the wage paid by employers now equals the wage women
receive
less the 50-cent subsidy, it is also clear that the wage paid by employers declines (by 50
cents minus the increase in the wage women receive).
It is important to stress to students that one would reach identical conclusions if one
analyzed the subsidy in terms of the wage employers pay. If supply and demand curves are
drawn in terms of this variable, a 50-cent-an-hour subsidy for women would shift the
female labor supply curve down by 50 cents. At the old wage paid by employers, the
supply of female labor would now exceed the demand. Downward pressure would be
placed on the wage paid by employers and it would fall by less than 50 cents (as long as
labor supply was responsive to the wage). As a result, the wage received by women would
rise by 50 cents less the fall in the wage paid by employers.
Problems
2.
The marginal revenue product of labor in the local saw mill is MRPL = 20 − 0.5L, where L = the
number of workers. If the wage of saw mill workers is $10 per hour, then how many workers will
the mill hire?
Answer: The mill will hire workers until MRPL = W.20 − 0.5L = 10 when L = 20 workers.
4.
The output of workers at a factory depends on the number of supervisors hired (see below). The factory
sells its output for $0.50 each, it hires 50 production workers at a wage of $100 per day, and needs to
decide how many supervisors to hire. The daily wage of supervisors is $500 but output rises as more
supervisors are hired, as shown below. How many supervisors should it hire?
Supervisors
Output (units per day)
0
1
2
3
4
5
11,000
14,800
18,000
19,500
20,200
20,600
Answer: The firm needs to compare the marginal cost to the marginal revenue of hiring an
additional supervisor. The marginal cost is always $500 for each extra supervisor. The
marginal revenue is the number of additional units produced times the price of output.
Number of Supervisors
MC
MR
1
2
3
4
5
$500
$500
$500
$500
$500
$0.50 × 3800 = $1900
$0.50 × 3200 = $1600
$0.50 × 1500 = $750
$0.50 × 700 = $350
$0.50 × 400 = $200
The firm will hire three supervisors since the marginal revenue generated from hiring the
third supervisor exceeds $500 but the marginal revenue generated from hiring the fourth
supervisor is less than $500.
6.
The table below shows the number of cakes that could be baked daily at a local bakery, depending
on the number of bakers.
Number of Bakers
Number of Cakes
0
1
2
3
4
0
10
18
23
27
a.
b.
c.
d.
e.
Calculate the marginal product of labor.
Do you observe the law of diminishing marginal returns? Explain.
Suppose each cake sells for $10. Calculate the marginal revenue product of labor.
Draw the marginal revenue product of labor curve, which is the demand curve for bakers.
If each baker is paid $80 per day, how many bakers will the bakery owner hire, given that the
goal is to maximize profits? How many cakes will be baked and sold each day?
Answer: a.
Number of Bakers
Number of Cakes
MPL
MRPL
0
1
2
3
4
0
10
18
23
27
—
10
8
5
4
—
100
80
50
40
The marginal product of labor (MPL) is calculated in the third column, using the
following formula:
MPL = Δ(Number of cakes)/ΔL
b. Yes, the marginal product of labor declines as more bakers are hired.
c. The marginal revenue product of labor (MRPL) is calculated in the fourth column,
using the following formula:
MRPL = MPL × P
d. The demand for labor is the MRPL curve:
e. If each baker is paid $80 per day, 2 bakers would be hired and 18 cakes would be
baked and sold daily.
8.
The demand curve for gardeners is GD = 19 − W, where G = the number of gardeners and W = the
hourly wage. The supply curve is GS = 4 + 2W.
a. Graph the demand curve and the supply curve. What is the equilibrium wage and equilibrium
number of gardeners hired?
b. Suppose the town government imposes a $2 per hour tax in all gardeners. Indicate the effect of
the tax on the market for gardeners. What is the effect on the equilibrium wage and the equilibrium
number of gardeners hired? How much does the gardener receive? How much does the customer
pay? How much does the government receive as tax revenue?
Answer: a.
To calculate the equilibrium wage and equilibrium quantity:
GD = GS
19 – W = 4 + 2W
15 = 3W
W = 5 [equilibrium wage]
Next solve for equilibrium quantity:
GD = 19 − W = 19 − 5 = 14
[equilibrium quantity]
b. With the imposition of the tax on gardeners, the new supply is GS = 4 + 2(W − 2).
To calculate the equilibrium wage and equilibrium quantity:
GD = GS
19 − W = 4 + 2(W − 2)
19 − W = 2W
3W = 19
W = 19/3 = 6.33 [equilibrium wage]
Next solve for equilibrium quantity:
GD = 19 − W = 19 − 6.33 = 12.67
[equilibrium quantity]
With the imposition of the tax, the customer pays $6.33 per hour to the gardener. The
government collects the tax of $2.00 per hour, the gardener keeps $4.33 per hour, and
total tax revenues are $25.34 ($2 per hour from 12.67 gardeners).
Chapter 4
Problems
2.
Professor Pessimist argues before Congress that reducing the size of the military will have grave
consequences for the typical American worker. He argues that if one million individuals were
released from the military and were instead employed in the civilian labor market, average wages in
the civilian labor market would fall dramatically. Assume that the demand curve for civilian labor
does not shift when workers are released from the military. First, draw a simple diagram depicting
the effect of this influx of workers from the military. Next, using your knowledge of (i) the
definition of the own-wage elasticity of labor demand, (ii) the magnitude of this elasticity for the
economy as a whole, and
(iii) the size of civilian employment in comparison to this flood from the military, graph these events
and estimate the magnitude of the reduction in wages for civilian workers as a whole. Do you concur
with Professor Pessimist?
Answer:
Because you were asked about the effects on civilian wages as a whole, you will
probably not concur with Professor Pessimist. Own-wage elasticity of demand for
labor = %Δ(quantity demanded)/%Δ(wage) = (ΔLd/Ld)/(ΔW/W). In this case ΔLd = 1 million, Ld =
about 147 million employed workers, and the own-wage elasticity of demand for labor is
approximately −1. Thus, −1 = (1 million/147 million)/(ΔW/W), so ΔW/W will be very small–about
−1/147 (or −0.0068). This implies that wages will fall by 0.68%. However, the military recruits in a
very narrow segment of the labor market—mostly high school grads who do not attend college, and
who are between ages 17–21. Thus, downsizing would have the greatest effect on this segment of the
market. If there were only 13.5 million, say, in this age group, a labor demand elasticity of −1 would
yield a wage effect of the military downsizing of closer to −7.4% on this group of the population.
4.
The following table gives the demand for labor at Homer’s Hideaway, a motel in a small town.
Number of Hours
Wage
2
3
4
5
6
$10
8
6
4
2
a. Draw the demand for labor curve.
b. Calculate the wage elasticity of demand along the demand curve. Indicate whether the elasticity
is elastic, inelastic, or unitary elastic.
c. As you slide down along the demand curve, does the demand curve become more or less elastic?
Answer: a. Simple plot of tabular data.
b.
Number of Hours
Wage
Elasticity
2
3
4
5
6
$10
8
6
4
2
—
[(3 − 2)/2]/[(8 − 10)/10] = [1/2]/[−2/10] = −2.5
[(4 − 3)/3]/[(6 − 8)/8] = [1/3]/[−2/8] = −1.32
[(5 − 4)/4]/[(4 − 6)/6] = [1/4]/[−2/6] = −0.76
[(6 − 5)/5]/[(2 − 4)/4] = [1/5]/[−2/4] = −0.40
The demand curve is elastic at its upper end and inelastic at its lower end.
c. The demand curve becomes less elastic (or more inelastic) as you slide down along the
curve.
6.
Calculate the own-wage elasticity of demand for Occupations a, b, and c below. ED and W are the
original employment and wage. ED′ and W ′ are the new employment and wage. State whether the
demand is elastic, inelastic, or unitary elastic.
a. %ΔED = 5, %ΔW = −10
b. ED = 50, W = 7
ED′ = 40, W ′ = 8
c.
ED = 80, W = 8
ED′ = 100, W ′ = 6
Answer: a. ηD = %ΔED /%ΔW = 5/(−10) = −1/2 [inelastic]
b. [(40 − 50)/50]/[(8−7)/7] = (−0.20)/0.14 = −1.43 [elastic]
c. [(100 − 80)/80]/[(6 − 8)/8] = (20/80)/(−2/8) = −1 [unitary elastic].
Chapter 5
Review Questions
2. Why do upward-sloping labor supply curves to firms cause the marginal expense of labor to exceed
the wage rate?
Answer: With upward-sloping labor supply curves, firms wanting to increase their number of
employees must increase the wage offers for both their added workers and their existing
workers. Thus, the marginal expense of labor exceeds wages paid to the added workers.
4. “Minimum wage laws help low-wage workers because they simultaneously increase wages and
reduce the marginal expense of labor.” Analyze this statement.
Answer: This statement has two aspects. First, minimum wage laws can increase wages and reduce
the marginal expense of labor if the labor market is characterized by monopsonistic
conditions and the minimum wage increases are not “too large” (that is, they do not
impose a wage higher than the pre-existing marginal expense of labor). Second, however,
these changes can only help workers if the higher wage bills faced by employers do not
drive their employers out of business.
Problems
2.
Assume that the labor supply curve to a firm is the one given in Problem 1 above. If the firm’s
marginal revenue product of labor (MRPL) = 240 – 2E, what is the profit-maximizing level of
employment (E * ) and what is the wage level (W * ) the firm would have to pay to obtain E *
workers?
Answer: Total labor costs to the firm (C) equal WE, which, expressed in terms of E, are as follows:
C = E × E /5 = 0.2 E 2
To maximize profit, the firm’s marginal revenue product of labor, 240 – 2E, must equal
the marginal expense of labor: dC/dE = 0.4E
Thus, for profit-maximization the following must hold: 240 – 2E = 0.4E
Solving the above equation for E yields E * = 100. Plugging E = 100 into the labor supply
equation (E = 5W ) and solving for W yields W * = $20.
6.
Teddy’s Treats, the dog biscuit company in Problem 5, has the following marginal revenue product
of labor (MRPL):
Number of Hours
MRPL
18
29
19
27
20
25
21
23
22
21
a. Add the marginal revenue product curve to the drawing in Problem 5.
b. If Teddy’s Treats is maximizing profits, how many hours of labor will be hired? What wage
will be offered?
Answer: a.
b. The profit-maximizing number of hours is 20 and Teddy’s Treats will offer a wage of
$6 per hour.
Chapter 6
Review Questions
2. Evaluate the following quote: “Higher take-home wages for any group should increase the
labor force participation rate for that group.”
Answer: This quotation is correct, because for labor force participation decisions, the
substitution effect dominates the income effect. The strength of the income effect
is relatively weaker when the initial hours of work are smaller. When initial hours
of work are zero—as is the case when a person is out of the labor force—then the
income effect is zero if leisure is a normal good (increased resources cannot induce
one to increase the consumption of leisure, since leisure hours are already at their
maximum).
8. The Tax Reform Act of 1986 was designed to reduce the marginal tax rate (the tax rate on
the last dollars earned) while eliminating enough deductions and loopholes so that total
revenues collected by the government could remain constant. Analyze the work incentive
effects of tax reforms that lower marginal tax rates while keeping total tax revenues
constant.
Answer: Reducing the marginal tax rate has the effect of increasing the wage rate, because
workers are allowed to keep more from any extra hours worked. Keeping tax
revenues constant suggests that workers’ after-tax incomes also remain constant.
Thus, the Tax Reform Act tended to increase the wage while keeping workers’
incomes constant—creating a pure substitution effect that tended to increase hours
of work.
Problems
4. The federal minimum wage was increased on July 24, 2007 to $5.85 from $5.15. If 16 hours
per day are available for work and leisure, draw the daily budget constraint for a worker
who was earning the minimum wage rate of $5.15 and the new budget constraint after the
increase.
Answer:
6.
Stella can work up to 16 hours per day at her job. Her wage rate is $8.00 per hour
for the first 8 hours. If she works more than 8 hours, her employer pays “time and
a half.” Draw Stella’s daily budget constraint.
Answer:
Stella’s earnings are equal to the following:
[Number of hours (within first 8 hours) × $8]
hours) × $12].
[Number of hours (among next 8
The budget constraint for the first 8 hours of work is the segment to the right of the
dotted vertical line at 8 hours. The budget constraint for subsequent hours of work
is the segment to the left of the dotted vertical line at 8 hours.
Chapter 8
Review Questions
4. Suppose that someone claims that low-wage jobs lack the healthcare and pension benefits
enjoyed by higher-wage employees Assuming this claim to be true, does this fact contradict
the theory of compensating wage differentials? Explain.
Answer: The theory of compensating differentials predicts that, other things equal, jobs with
low non-wage benefits would have to pay higher wages. This statement is
implicitly comparing those in low-skilled jobs with those in high-skilled jobs,
where clearly “other things” are not comparable. Thus, the facts in this statement do
not contradict the theory of compensating wage differentials.
Chapter 9
Problems
4.
Prepaid college tuition plans, also known as Prepaid Education Arrangements (PEAs), allow
you to prepay college tuition at present-day prices. The value of the investment is
guaranteed by the state to cover college tuition, regardless of its future cost. You are
considering the purchase of an education certificate for $25,000, which will cover the future
tuition costs of your 8-year old daughter. You expect the tuition cost of your daughter’s
bachelor’s degree to be $50,000 in 10 years. What would your personal discount rate need to
be in order for it to be worthwhile for you to make the investment and purchase the
certificate?
Answer: For a PEA to be worthwhile, its present value to you now must be at least $25,000.
In 10 years, the PEA will be worth $50,000, and its present value to you now is
$50,000/(1 r)10, where r is your personal discount rate. Thus,
$50,000 /(1 + r )10 = $25,000, or
$50,000 / $25,000 = (1 + r )10
2 = (1 + r )10
(1 + r ) = (2)1/10
(1 + r ) = 1.0718
r = 0.0718
Your personal discount rate needs to be 7.18% or less for the PEA to be worth
investing in.