chapter:
19
Factor Markets and
the Distribution of Income
1.
In 2010, national income in the United States was $11,722.6 billion. In the same
year, 139 million workers were employed, at an average wage of $57,348 per worker
per year.
a. How much compensation of employees was paid in the United States in 2010?
b. Analyze the factor distribution of income. What percentage of national income
was received in the form of compensation to employees in 2010?
c. Suppose that a huge wave of corporate downsizing leads many terminated employees to open their own businesses. What is the effect on the factor distribution of
income?
d. Suppose the supply of labor rises due to an increase in the retirement age. What
happens to the percentage of national income received in the form of compensation of employees?
1.
Solution
a. Since 139 million workers were employed at an average yearly wage of $57,348,
the total amount of compensation of employees was 139 million × $57,348 =
$7,791.4 billion.
b. Of a total of $11,722.6 billion, the amount received by workers was $7,791.4 billion.
In percentage terms, this is ($7,791.4 billion/$11,186.9 billion) × 100 = 68.0%.
c. The effect of this change is to diminish the share of income going to compensate
employees and increase the share going to proprietors’ income.
d. As the supply of labor increases, the equilibrium wage rate falls, but the equilibrium number of workers employed rises. So it is not clear whether more or less of
national income is paid to workers in the form of compensation.
2.
Marty’s Frozen Yogurt has the production function per day shown in the accompanying table. The equilibrium wage rate for a worker is $80 per day. Each cup of frozen
yogurt sells for $2.
Quantity of labor
Quantity of
frozen yogurt
(workers)
(cups)
0
0
1
110
2
200
3
270
4
300
5
320
6
330
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a. Calculate the marginal product of labor for each worker and the value of the marginal product of labor per worker.
b. How many workers should Marty employ?
2.
Solution
a. The accompanying table shows the marginal product of labor (MPL) and the value
of the marginal product of labor (VMPL) of each worker. Remember that VMPL =
P × MPL. Here that means that VMPL = $2 × MPL.
Quantity of labor
(workers)
Quantity of frozen
yogurt (cups)
0
0
1
110
2
200
3
270
4
300
5
320
6
330
MPL
VMPL
(cups per worker)
(per worker)
110
$220
90
180
70
140
30
60
20
40
10
20
b. Marty should employ 3 workers. The value of the marginal product of the third
worker ($140) is above the wage rate of $80: Marty should hire the third worker.
But the fourth worker’s value of the marginal product is only $60. This is less
than Marty would have to pay this worker, so Marty should not hire a fourth
worker.
3.
Patty’s Pizza Parlor has the production function per hour shown in the accompanying table. The hourly wage rate for each worker is $10. Each pizza sells for $2.
Quantity of labor
(workers)
Quantity of pizza
0
0
1
9
2
15
3
19
4
22
5
24
a. Calculate the marginal product of labor for each worker and the value of the marginal product of labor per worker.
b. Draw the value of the marginal product of labor curve. Use your diagram to determine how many workers Patty should employ.
c. Now the price of pizza increases to $4. Calculate the value of the marginal product of labor per worker, and draw the new value of the marginal product of labor
curve in your diagram. Use your diagram to determine how many workers Patty
should employ now.
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Solution
3.
a. The accompanying table shows the marginal product of labor (MPL) and the value
of the marginal product of labor (VMPL1).
Number of
workers
Quantity of
pizza
0
0
1
9
2
15
3
19
4
22
5
24
VMPL1 (per worker)
VMPL2 (per worker)
(pizzas per worker)
(price of
pizza = $2)
(price of
pizza = $4)
9
$18
$36
6
12
24
4
8
16
3
6
12
2
4
8
MPL
b. The accompanying diagram shows the value of the marginal product of labor
curve (VMPL1). The value of the marginal product of labor equals the wage rate at
2 workers. So Patty should employ 2 workers.
Wage
rate
$36
24
Wage
rate
18
16
12
10
6
4
0
VMPL2
VMPL1
1
2
3
4
5
Quantity of labor (workers)
c. The table shows the new value of the marginal product of labor (VMPL2). The
value of the marginal product of labor curve is labeled VMPL2 in the diagram. The
new value of the marginal product of labor equals the wage rate at 4 workers. So
Patty should employ 4 workers.
4.
The production function for Patty’s Pizza Parlor is given in the table in Problem 3.
The price of pizza is $2, but the hourly wage rate rises from $10 to $15. Use a diagram to determine how Patty’s demand for workers responds as a result of this wage
rate increase.
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Solution
4.
The accompanying diagram shows the value of the marginal product of labor curve
and the wage rates of $10 and $15. As the wage rate increases from $10 to $15,
Patty’s demand for workers decreases from 2 workers to 1 worker. So, as the wage
rate increases, Patty should hire fewer workers.
Wage
rate
$18
New wage
rate
Old wage
rate
15
12
10
8
6
4
0
5.
VMPL
1
2
3
4
5
Quantity of labor (workers)
Patty’s Pizza Parlor initially had the production function given in the table in
Problem 3. A worker’s hourly wage rate was $10, and pizza sold for $2. Now Patty
buys a new high-tech pizza oven that allows her workers to become twice as productive as before. That is, the first worker now produces 18 pizzas per hour instead of 9,
and so on.
a. Calculate the new marginal product of labor and the new value of the marginal
product of labor.
b. Use a diagram to determine how Patty’s hiring decision responds to this increase
in the productivity of her workforce.
Solution
5.
a. The accompanying table shows the new production function for Patty’s Pizza
Parlor, the new marginal product of labor (MPL3), and the new value of the marginal product of labor (VMPL3).
KrugWellsECPS3e_Micro_CH19.indd S-264
Quantity of labor
(workers)
Quantity of pizza
0
0
1
18
2
30
3
38
4
44
5
48
MPL3 (pizzas
per worker)
VMPL3 (per
worker)
18
$36
12
24
8
16
6
12
4
8
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b. The accompanying diagram shows the original value of the marginal product of
labor curve from Problem 3 (VMPL1) and the new value of the marginal product
of labor curve (VMPL3). The value of the marginal product of labor now equals
the wage rate at 4 workers. So Patty should employ 4 workers. As the value of the
marginal product of labor increases—in this case as a result of a technological
innovation (the new pizza oven)—Patty should hire more workers.
Wage
rate
$36
24
18
16
12
10
6
4
Wage
rate
0
VMPL3
VMPL1
1
2
3
4
5
Quantity of labor (workers)
6.
Jameel runs a driver education school. The more driving instructors he hires, the
more driving lessons he can sell. But because he owns a limited number of training
automobiles, each additional driving instructor adds less to Jameel’s output of driving lessons. The accompanying table shows Jameel’s production function per day.
Each driving lesson can be sold at $35 per hour.
Quantity of labor
Quantity of
driving lessons
(driving instructors)
(hours)
0
0
1
8
2
15
3
21
4
26
5
30
6
33
Determine Jameel’s labor demand schedule (his demand schedule for driving instructors) for each of the following daily wage rates for driving instructors: $160, $180,
$200, $220, $240, and $260.
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Solution
6.
The accompanying table calculates the marginal product of labor (MPL) and the
value of the marginal product of labor (VMPL).
Quantity of labor
(driving
instructors)
Quantity of driving
lessons (hours)
0
0
1
8
2
15
3
21
4
26
5
30
6
33
MPL
VMPL
(hours per
driving
instructor)
(per
driving
instructor)
8
$280
7
245
6
210
5
175
4
140
3
105
If the daily wage rate of driving instructors is $160, Jameel should hire 4 instructors:
the fourth instructor has a value of the marginal product of $175, which is greater
than the wage rate; but the fifth instructor would have a value of the marginal product
of only $140, which is less than the wage rate. By similar reasoning for the other wage
rates, Jameel’s demand schedule for labor is as shown in the accompanying table.
Quantity of labor
demanded (driving
7.
Daily wage rate
instructors)
$160
4
180
3
200
3
220
2
240
2
260
1
Dale and Dana work at a self-service gas station and convenience store. Dale opens
up every day, and Dana arrives later to help stock the store. They are both paid the
current market wage of $9.50 per hour. But Dale feels he should be paid much more
because the revenue generated from the gas pumps he turns on every morning is
much higher than the revenue generated by the items that Dana stocks. Assess this
argument.
Solution
7.
Dale’s argument is incorrect because the owner of the business will hire workers
until the hourly value of the marginal product of the last person hired equals $9.50.
This implies that all other workers hired will have an hourly value of the marginal
product higher than $9.50 but will be paid a wage of $9.50. Or to put it a slightly
different way, any worker who opens the station, regardless of whether it is Dale or
Dana, will have a higher value of the marginal product than the second person to
report for work.
8.
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A New York Times article published in 2007 observed that the wage of farmworkers in Mexico was $11 an hour but the wage of immigrant Mexican farmworkers in
California was $9 an hour.
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a. Assume that the output sells for the same price in the two countries. Does this
imply that the marginal product of labor of farmworkers is higher in Mexico or
in California? Explain your answer, and illustrate with a diagram that shows the
demand and supply curves for labor in the respective markets. In your diagram,
assume that the quantity supplied of labor for any given wage rate is the same for
Mexican farmworkers as it is for immigrant Mexican farmworkers in California.
b. Now suppose that farmwork in Mexico is more arduous and more dangerous than
farmwork in California. As a result, the quantity supplied of labor for any given
wage rate is not the same for Mexican farmworkers as it is for immigrant Mexican
farmworkers in California. How does this change your answer to part a? What
concept best accounts for the difference between wage rates for Mexican farmworkers and immigrant Mexican farmworkers in California?
c. Illustrate your answer to part b with a diagram. In this diagram, assume that
the quantity of labor demanded for any given wage rate is the same for Mexican
employers as it is for Californian employers.
Solution
8.
a. We know that farmworkers are employed up to the point where the value of the
marginal product of labor is just equal to the wage: VMPL = P × MPL = W. In
Mexico, this means that P × MPLMexico = $11 and in California P × MPLCalifornia =
$9. Since the price, P, is the same in Mexico and in California, this means that
the marginal product of labor in Mexico has to be higher than in California.
Assuming that the quantity supplied for any given wage rate is the same for
Mexican farmworkers as it is for immigrant Mexican farmworkers in California
implies that the two groups have equivalent supply curves. Therefore, one supply
curve can be drawn to illustrate the supply responses of both types of workers. The
different wage rates received by the two groups of workers is a result of differences
in the demand curves for labor. Because Mexican farmworkers have a higher marginal product of labor, the demand curve for their labor lies above and to the right
of the demand curve for their peers in California, as shown in the accompanying
diagram.
Supply
Wage
$11
9
Demand for Mexican
farmworkers in Mexico
Higher MPL of Mexican
farmworkers in Mexico
0
Demand for immigrant
Mexican farmworkers
in California
Quantity of labor
b. Because farmwork in Mexico is more arduous and dangerous than farmwork in
California, we can no longer infer that the higher wages paid to Mexican farmworkers is evidence that they have a higher marginal product of labor than their
peers in California. Rather, the difference in wages is a compensating differential
that compensates Mexican farmworkers for the greater difficulty and danger they
face.
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c. Assuming that the quantity of labor demanded for any given wage rate is the
same for the two groups means that one demand curve can be drawn to represent
employers’ demand responses in both markets. The compensating differential that
Mexican farmworkers demand relative to their peers in California is illustrated by
their supply curve of labor in the accompanying diagram, which lies above and to
the left of the supply curve of their Californian peers.
Wage
Labor supply of Mexican
farmworkers in Mexico
Labor supply of
immigrant Mexican
farmworkers in
California
$11
9
Compensating
differential
0
9.
Demand
Quantity of labor
Kendra is the owner of Wholesome Farms, a commercial dairy. Kendra employs
labor, land, and capital. In her operations, Kendra can substitute between the
amount of labor she employs and the amount of capital she employs. That is, to produce the same quantity of output she can use more labor and less land; similarly, to
produce the same quantity of output she can use less labor and more land. However,
if she uses more land, she must use more of both labor and capital; if she uses less
land, she can use less of both labor and capital. Let w* represent the annual cost of
labor in the market, let r*L represent the annual cost of a unit of land in the market,
and let r*
K represent the annual cost of a unit of capital in the market.
a. Suppose that Kendra can maximize her profits by employing less labor and more
capital than she is currently using but the same amount of land. What three conditions must now hold for Kendra’s operations (involving her value of the marginal product of labor, land, and capital) for this to be true?
b. Kendra believes that she can increase her profits by renting and using more land.
What three conditions must hold (involving her value of the marginal product of
labor, land, and capital) for this to be true?
9.
Solution
a. The three conditions are: (1) Kendra’s current value of the marginal product of
land = r*.
Only if this is satisfied should Kendra leave the amount of land she
L
employs unchanged. (2) Kendra’s current value of the marginal product of labor
< w*. Only if this is satisfied should Kendra reduce the amount of labor she
employs. (3) Kendra’s current value of the marginal product of capital > r*.
Only
K
if this is satisfied should Kendra increase the amount of capital she uses.
b. The three conditions are: (1) Kendra’s current value of the marginal product of
land > r*.
Only if this is satisfied should Kendra increase the amount of land
L
she employs. (2) Kendra’s current value of the marginal product of labor > w*.
Kendra must hire more labor if she employs more land. Thus, only if this condition is satisfied should Kendra increase the amount of labor she employs along
with the amount of land. (3) Kendra’s current value of the marginal product of
capital > r*.
Kendra must use more capital if she employs more land. Thus, only if
K
this condition is satisfied should Kendra increase the amount of capital she uses
along with the amount of land.
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FA C T O R M A R K E T S A N D T H E D I S T R I B U T I O N O F I N C O M E
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For each of the following situations in which similar workers are paid different
wages, give the most likely explanation for these wage differences.
a. Test pilots for new jet aircraft earn higher wages than airline pilots.
b. College graduates usually have higher earnings in their first year on the job than
workers without college degrees have in their first year on the job.
c. Full professors command higher salaries than assistant professors for teaching the
same class.
d. Unionized workers are generally better paid than non-unionized workers.
Solution
10.
a. This is most likely because being a test pilot for a new aircraft design is more dangerous than flying a commercial airliner. So the most likely explanation is that of
compensating differentials.
b. This is probably due to differences in human capital. More education gives a
worker greater amounts of human capital. So more education usually translates
into greater earnings.
c. This is also probably due to differences in human capital. Because full professors
have been teaching longer than assistant professors, their greater on-the-job experience has given them greater human capital. And greater human capital translates into higher salaries.
d. Unions exercise considerable bargaining power in negotiating wages for their
members. This results in higher wages and therefore wage differences that are not
explained by marginal productivity theory.
11.
Research consistently finds that despite nondiscrimination policies, African-American
workers on average receive lower wages than White workers do. What are the possible
reasons for this? Are these reasons consistent with marginal productivity theory?
Solution
11.
One possible reason is that this is the result of discrimination in the workplace. And,
as you know, discrimination is not consistent with marginal productivity theory. But
another possible reason for this income disparity is that it may be a result of past discrimination, which is consistent with marginal productivity theory. In the past, because
of overt discrimination, the educational opportunities for African-American children
were severely limited. These children are today’s workers, and if their educational attainment is lower, they embody less human capital and are therefore paid a lower wage. So
the current income disparity may imply past discrimination but be consistent with marginal productivity theory. But even if this is true, keep in mind that marginal productivity theory does not give moral justification to the current distribution of income.
12.
Greta is an enthusiastic amateur gardener and spends a lot of her free time working in
her yard. She also has a demanding and well-paid job as a freelance advertising consultant. Because the advertising business is going through a difficult time, the hourly
consulting fee Greta can charge falls. Greta decides to spend more time gardening and
less time consulting. Explain her decision in terms of income and substitution effects.
Solution
12.
As Greta’s hourly consulting fee falls, the opportunity cost of leisure—time spent
working in her yard—also falls. So the substitution effect will push Greta toward
spending more time gardening and less time consulting. However, the income effect
of a fall in the consulting fee makes Greta poorer and—since leisure is a normal
good—less inclined to consume leisure. That is, the income effect will push Greta
toward working more. If, overall, Greta decides to work less, the substitution effect
must have dominated the income effect.
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13.
Wendy works at a fast-food restaurant. When her wage rate was $5 per hour, she
worked 30 hours per week. When her wage rate rose to $6 per hour, she decided to work
40 hours. But when her wage rate rose further to $7, she decided to work only 35 hours.
a. Draw Wendy’s individual labor supply curve.
b. Is Wendy’s behavior irrational, or can you find a rational explanation? Explain
your answer.
Solution
13.
a. Wendy’s individual labor supply curve has the backward-bending shape shown in
the accompanying diagram.
Wage
rate
$7
Individual labor
supply curve
6
5
0
30
35
40
Quantity of labor (hours)
b. Wendy’s behavior has a perfectly rational explanation. As the wage rate increases,
the opportunity cost of leisure increases. So the substitution effect says to consume less leisure and work more. At the same time, an increase in the wage rate
makes Wendy richer in a real sense. And since leisure is a normal good, the
income effect says to consume more leisure and work less. Income and substitution effects work in opposite directions. As Wendy’s wage rate rises from $5 to $6,
the substitution effect dominates the income effect. As her wage rate rises further
to $7, the income effect dominates the substitution effect.
14.
You are the governor’s economic policy adviser. The governor wants to put in place
policies that encourage employed people to work more hours at their jobs and that
encourage unemployed people to find and take jobs. Assess each of the following policies in terms of reaching that goal. Explain your reasoning in terms of income and
substitution effects, and indicate when the impact of the policy may be ambiguous.
a. The state income tax rate is lowered, which has the effect of increasing workers’
after-tax wage rate.
b. The state income tax rate is increased, which has the effect of decreasing workers’
after-tax wage rate.
c. The state property tax rate is increased, which reduces workers’ after-tax income.
Solution
14.
a. The effect of this policy on the incentive to work is ambiguous. A lower income
tax rate has the effect of raising workers’ wages in a real sense. The substitution
effect will induce people to work more, but the income effect will induce them to
work less. So this is an effective policy only if the substitution effect is stronger
than the income effect.
b. The effect of this policy on the incentive to work is also ambiguous. A higher
income tax rate has the effect of reducing workers’ wages in a real sense. The substitution effect will induce people to work less, but the income effect will induce
them to work more. So this is an effective policy only if the income effect is
stronger than the substitution effect.
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c. This policy will unambiguously encourage people to work more. The increase in
the property tax rate makes people feel poorer, and as a result, they will consume
less of all normal goods. Since leisure is a normal good, people will consume less
leisure and work more. This policy influences how much labor is supplied only
through the income effect. There is no substitution effect on the quantity of labor
supplied in this case since the opportunity cost of leisure has not changed.
15.
A study by economists at the Federal Reserve Bank of Boston found that between 1965
and 2003 the average American’s leisure time increased by between 4 and 8 hours a
week. The study claims that this increase is primarily driven by a rise in wage rates.
a. Use the income and substitution effects to describe the labor supply for the average American. Which effect dominates?
b. The study also finds an increase in female labor force participation—more women
are choosing to hold jobs rather than exclusively perform household tasks. For the
average woman who has newly entered the labor force, which effect dominates?
c. Draw typical individual labor supply curves that illustrate your answers to part a
and part b above.
Solution
15.
a. As wage rates rise, the substitution effect says to consume less leisure, because
leisure has just become relatively more expensive. However, the income effect says
to consume more leisure, because a wage rate increase makes consumers richer
and leisure is a normal good. Since the overall effect has been for leisure time to
increase as a result of the wage rate increase, the income effect must have been
stronger than the substitution effect.
b. As wage rates rise, income and substitution effects work in the same ways as in
part a. However, since female labor force participation has increased, the substitution effect must have been stronger for new female workers. (Why is this? For
individuals who are not participating in the labor market, an increase in the wage
rate has only a substitution effect, leading them to consume less leisure since its
opportunity cost has risen—that is, leading them to work more. Since they are not
earning income from work, an increase in the wage rate has no income effect.)
c. The accompanying diagram shows a typical labor supply curve for all workers in
panel (a) and for new female workers in panel (b).
(a) All Workers
Wage
rate
Quantity of labor
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(b) New Female Workers
Wage
rate
Quantity of labor
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