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Chapter 13
Labor
Markets
© 2004 Thomson Learning/South-Western
Marginal Productivity Theory of
Input Demand

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2
Input prices are also determined by the forces
of supply and demand.
The firms are on the demand side while the
supply comes from individuals.
The theory of input demand relies on Ricardo’s
theory of marginal productivity.
Profit-Maximizing Behavior and the
Hiring of Inputs
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A profit-maximizing firm will hire additional units
of any input up to the point at which the
additional revenue from hiring one more unit is
exactly equal to the cost of hiring that unit.
Let MEK and MEL denote the marginal expense
of hiring capital and labor, respectively.
Profit-Maximizing Behavior and the
Hiring of Inputs


Let MRK and MRL be the extra revenue that hiring more
units of capital and labor allows the firm to bring in.
Profit maximizing behavior requires:
ME K  MRK
MRL  MRL .
4
Price-Taking Behavior

If the firm is a price taker in the capital and labor
market then it can always hire an extra unit of capital at
the prevailing rate (v) and an extra unit of labor at the
wage rate (w).
v  ME K  MRK
w  ME L  MRL .
5
Marginal Revenue Product
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Marginal product is how much output the additional
input can produce.
Marginal revenue (MR) is the extra revenue obtained
from selling an additional unit of output.
Thus, the profit maximizing rules are:
v  ME K  MRK  MPK  MR
w  ME L  MRL  MPL  MR.
6
Marginal Revenue Product

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7
The marginal revenue product of labor and
capital are the extra revenue obtained from
selling the output produced by hiring an extra
worker or machine.
These show how much extra revenue is
brought in by hiring one more unit of an input.
A Special Case--Marginal Value
Product


If the firm is also a price taking in the goods market,
marginal revenue equals the price (P) at which the
output sells.
The profit maximizing conditions become
v  MPK  P
w  MPL  P
8
Marginal Value Product

The marginal value product (MVP) of capital and
labor, respectively, are special cases of marginal
revenue product in which the firm is a price taker for its
output.
v  MVPK
w  MVPL
9
APPLICATION 13.1: Hiring by
Nonprofit Firms
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Most hospitals in the U.S. operate on a not-forprofit basis.
In some cases hospitals are owned by public
corporations and presumably strive for
maximum profits.
Economists have found important differences
in the labor demand for these two types of
institutions.
APPLICATION 13.1: Hiring by
Nonprofit Firms
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Some of the differences may relate to a “quality bias”
for non-profit hospitals.
Such hospitals seem to hire more high-wage labor
(physicians) and less lower-wage labor (nurses) than
do for-profit hospitals.
One explanation for this result may be that nonprofit
hospitals are run by physicians who gain utility from
high-quality (high-cost) surroundings which the
managers of for-profit hospitals have a more “bottom
line” mentality.
APPLICATION 13.1: Hiring by
Nonprofit Firms
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Virtually all colleges and universities are
operated as nonprofit institutions.
It is not surprising that faculty hiring does not
follow the principles of profit maximization.
On most campuses, more than 50% of the
faculty has the rank of full professor but, on
average, full professors are paid nearly twice
as much as assistant professors and
instructors.
Responses to Changes in Input Prices:
Single Variable input Case
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Assume the firm has fixed capital and can only
vary its labor input in the short run.
Labor will exhibit diminishing marginal physical
productivity so labor’s MVP will decline as
more labor is hired.
In Figure 13.1, the profit maximizing firm will
hire L1 labor hours when the wage rate is w1.
FIGURE 13.1: Change in Labor Input When
Wage Falls: Single Variable Case
MVP
Wage
w1
w2
MVPL
14
0
L1
L2
Labor hours
Responses to Changes in Input
Prices: Single Variable input Case

If the wage rate falls to w2 the firm hires
increased labor out to L2.
–
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15
If the firm continued to hire L1 it would not be
maximizing profit since labor would be capable of
producing more in additional revenue than hiring
additional labor would cost.
With one variable input, diminishing marginal
productivity results in a downward sloping
demand curve.
A Numerical Example
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Table 13.1 shows the productivity for
Hamburger Heaven when it uses four grills
The marginal product declines as more
workers are assigned to the grills
Marginal Revenue Product is simply price,
$1.00 times the marginal product.
At a wage of $5.00, the firm should hire four
workers.
TABLE 13.1: Hamburger Heaven’s ProfitMaximizing Hiring Decision
17
Labor
Input
per Hour
Hamburgers
Produced
per Hour
Marginal
Product
(Hamburger)
Marginal
Value Product
($1.00 per
Hamburger)
1
2
3
4
5
6
7
8
9
10
20.0
28.3
34.6
40.0
44.7
49.0
52.9
56.6
60.0
63.2
20.0
8.3
6.3
5.4
4.7
4.3
3.9
3.7
3.4
3.2
$20.00
8.30
6.30
5.40
4.70
4.30
3.90
3.70
3.40
3.20
The Substitution Effect
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The substitution effect, in the theory of
production, is the substitution of one input for
another while holding output constant in
response to a change in the input’s price.
In Figure 13.2(a), a fall in w will cause the firm
to change from input combination A to B to
equate RTS to the new w/v.
Diminishing RTS leads to more labor hired.
FIGURE 13.2: Substitution and Output
Effects of A Decrease in Price of Labor
Capital
per week
Price
MC
K1
A
P
K2
q1
0
L1
L2
Labor hours
per week
(a) Input Choice
19
0
q1
Output
per week
(b) Output Decision
FIGURE 13.2: Substitution and Output
Effects of A Decrease in Price of Labor
Price
Capital
per week
MC
K1
A
P
K2
B
0
L1
q1
L2
Labor hours
per week
(a) Input Choice
20
0
q1
Output
per week
(b) Output Decision
The Output Effect
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The output effect is the effect of an input price
change on the amount of the input that the firm
hires that results from a change in the firm;s
output level.
In Figure 13.2(b), the lower w causes the
marginal cost curve to shift to MC’.
The profit maximizing output raises to q2
resulting in more labor hired.
FIGURE 13.2: Substitution and Output
Effects of A Decrease in Price of Labor
Price
Capital
per week
MC
MC’
K1
A
P
K2
B
0
L1
q1
L2
Labor hours
per week
(a) Input Choice
22
0
q1 q2
Output
per week
(b) Output Decision
FIGURE 13.2: Substitution and Output
Effects of A Decrease in Price of Labor
Price
Capital
per week
MC
MC’
K1
A
C
K2
q2
B
0
L1
q1
L2
Labor hours
per week
(a) Input Choice
23
P
0
q1 q2
Output
per week
(b) Output Decision
Summary of Firm’s Demand for
Labor

A fall in the wage rate will cause the firm to hire
more labor for two reasons:
–
–
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The firm will substitute the now cheaper labor for
other inputs that are now relatively more expensive,
the substitution effect.
The decline in wages will lower marginal costs so
the profit maximizing firm will produce more output
which requires hiring more labor, the output effect.
Responsiveness of Input Demand
to Price Changes
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Ease of Substitution
–
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The size of the substitution effect will depend upon
how easy it is to substitute other factors of
production for labor.
The size of the substitution effect will also depend
upon the length of time as it becomes easier to find
substitutes in a longer period of time.
Costs and the Output Effect
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The size of the output effect will depend upon
–
–
–
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How large the increase in marginal costs brought
about by the wage rate increase is, and
How much quantity demanded will be reduced by
a rising price.
The first depend upon how important labor is in
production while the latter depends upon the price
elasticity of demand for the final product.
APPLICATION 13.2: Controversy over
the Minimum Wage
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The Fair Labor Standards Act of 1938
established a national minimum wage of $.25
per hour.
Each increase raises debate about whether
such increases are counterproductive
In Figure 1(a) the equilibrium wage is w1 with
l1 units of labor hired.
FIGURE 1: Effects of a Minimum Wage in a
Perfectly Competitive Labor Market
Wage
Capital
per week
S
w2
Wage = w1
w1
q1
D
q2
0
L2
Labor
per week
(a) The Market
28
0
l1
Labor
per week
(b) Typical Firm
APPLICATION 13.2: Controversy over
the Minimum Wage
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A minimum wage of w2 will cause firms to hire
less, l2, units of labor while more labor L3 will
be supplied
The imposition of a minimum wage will result
in an excess supply of labor over the demand
for labor of L3 - L2.
FIGURE 1: Effects of a Minimum Wage in a
Perfectly Competitive Labor Market
Wage
Capital
per week
S
w2
Wage= w2
Wage = w1
w1
q1
D
q2
0
L1 L2
L3 Labor
per week
(a) The Market
30
0
l2
l1
Labor
per week
(b) Typical Firm
Minimum Wages and Teenage
Unemployment

Teenagers are most likely to be affected by
minimum wage laws because their skills are
usually at the lower end of the spectrum.
–
–
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While many factors are at play, a major study in the
1970s found that a 1-percent increase resulted in a
0.3 percent reduction in teenage employment.
Minority group members have rates that exceed 30
percent.
Recent Disputes over the Evidence
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A 1994 study by Card and Krueger challenged
the belief that minimum wages reduced
employment opportunities.
–
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Their study of fast-food restaurants in New Jersey
and Pennsylvania found no negative effects on
employment.
However, an analysis of different data from these
states found negative employment effects
Input Supply

Resources come from three major sources:
–
–
–
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33
Labor is provided by individuals.
Capital equipment is produced which other firms
can buy outright or rent.
Natural resources are extracted from land and can
be used outright or sold to other firms.
As shown in earlier chapters, capital and
natural resources have upward sloping
supply curves.
Labor Supply and Wages
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Wages represent the opportunity cost of not
working at a paying job for individuals.
For purposes of this analysis, wages should be
interpreted to include all forms of
compensation.
Individuals will balance the monetary rewards
from working against the psychic benefits of
other, nonpaid activities.
Labor Supply and Wages
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Labor supply curves will differ based upon
individual preferences.
–
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It is likely that an increase in the wage will
result in more labor supplied to the market.
–
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Noneconomic factors such as pleasant working
conditions will affect the location of the supply
curve.
Graphically, the market labor supply curve is likely
to be positively sloped.
Equilibrium Input Price
Determination
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In Figure 13.3, the market demand for labor is
labeled D, and the market supply of labor is
labeled S.
The equilibrium wage and quantity is where
quantity demanded equals quantity supplied,
[w*, L*].
Other things equal, this equilibrium will tend to
persist from period to period.
FIGURE 13.3: Equilibrium in an
Input Market
Wage
S
w*
D
37
0
L*
Labor hours
per week
Shifts in Demand and Supply
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Any factor that shifts the firms’ underlying
production function will shift its input demand
curve.
Since the demand for an input is derived from
the demand for the output, changes in the
prices of the output will shift input demand
curves
Shifts in Demand and Supply
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39
In Figure 13.3, the demand curve shifts to D’
which reduces equilibrium wages from w* to w’
and equilibrium employment from L* to L’.
The various factors that shift input demand and
supply curves are summarized in Table 13.2.
FIGURE 13.3: Equilibrium in an
Input Market
Wage
S
w*
w’
D
D’
40
0
L’
L*
Labor hours
per week
TABLE 13.2: Factors That Shift Input
Demand and Supply Curves
Demand
Demand Shifts Outward
Rise in output price
Increase in marginal
productivity
Demand Shifts Inward
Fall in output price
Decrease in marginal
productivity
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Labor Supply
Capital Supply
Supply Shifts Outward
Decreased preference
Fall in input costs of
for Leisure
equipment makers
Increased desirability
Technical progress in
of job
making equipment
Supply Shifts Inward
Increased preference
Rise in input costs of
for Leisure
equipment makers
Decreased desirability
of job
APPLICATION 13.3: Why is Wage
Inequality Increasing?
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Wage inequality has a long history, but seems
to have increased recently.
Measuring Wage Inequality
–
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To control for differences in hours, researchers look
at “full-time, year-round” workers.
Usually, they concentrate on one gender and try to
include total wages including fringe benefits.
A common approach is to compare workers in the
90th to workers in the 10th percentile.
APPLICATION 13.3: Why is Wage
Inequality Increasing?
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U.S. studies for the 1965-1995 period find
–
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The 90/10 ratio in 1965 stood at about 4.3 for
male, full-time, year round workers.
By 1995, this 90/10 ratio had increased to 5.4.
European countries have also experienced
an increase in inequality although only the
United Kingdom has had increases similar to
the U.S.
APPLICATION 13.3: Why is Wage
Inequality Increasing?
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Factors that increase the supply of low-wage
workers or increase the demand for high-wage
workers would help to explain these trends.
Two Important Trends
–
44
A sharp increase in the relative demand for
technically skilled workers which partially explains
the rising wages of college graduates.
APPLICATION 13.3: Why is Wage
Inequality Increasing?
–
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Two reasons for the decline
–
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The second factor, which explains less of the trend,
is that there has also been a decline in the demand
for low-wage workers.
A decline in the importance of manufacturing
industries in the overall economy, and
Sustained increases in imports of goods that are
produced primarily with unskilled labor
APPLICATION 13.3: Why is Wage
Inequality Increasing?

Trends in labor supply have exacerbated the
demand effects.
–
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Large (legal and illegal) immigrations in the 1990s
may have increased the supply of low-wage
workers.
The increase in labor supply of women has probably
had its greatest impact on low-wage men.
Monopsony
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47
If the firm is not a price taker in the input
market, it may have to offer a higher wage to
attract more employees.
A monopsony is the condition in which one
firm is the only hirer in a particular input
market.
If the firm is a monopsony, it faces the entire
market supply curve for the input.
Marginal Expense

The marginal expense of an input is the cost
of hiring one more unit of an input.
–
–
48
The firm has to offer a higher wage to the hired
worker and to the workers already employed.
The marginal expense of labor (MEL) will exceed
the price of the input if the firm faces an upwardsloping supply curve for the input.
A Numerical Illustration
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Suppose the Yellowstone Park Company is the
only hirer of bear wardens.
The number of people willing to take this job
(L) is given by
1
L w
2
This relationship is shown in Table 13.3
TABLE 13.3: Labor Costs of Hiring Bear
Wardens in Yellowstone Park
Hourly
Wage
$2
4
6
8
10
12
14
50
Workers
Supplied
per Hour
1
2
3
4
5
6
7
Total Labor
Cost per
Hour
$2
8
18
32
50
72
98
Marginal
Expense
$2
6
10
14
18
22
26
A Numerical Illustration
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51
Total labor costs (w·L) is shown in the third
column and the marginal expense of hiring
each warden is shown in the fourth column.
Since the new warden and the existing
wardens receive the wage increase, the
marginal expense exceeds the wage rate.
A Numerical Illustration

Figure 13.4 shows the supply curve (S) for
wardens.
–
–
52
If Yellowstone wishes to hire three wardens it must
pay $6 per hour with total outlays of $18 (point A on
the graph).
The wage must be increased to $8 to get a fourth
warden (point B) which results in total outlays of
$32.
FIGURE 13.4: Marginal Expense of
Hiring Bear Wardens
Hourly
wage
S
B
$8
A
6
0
53
3
4
Bear wardens
per hour
A Numerical Illustration

The marginal expense of the fourth warden,
$14 is reflected in the graph.
–
–
–
54
The hourly wage ($8) is shown in gray.
The extra outlay to the three previous workers ($8
per hour versus $6 per hour previously) is shown in
color.
Total outlays exceed the amount for three wardens
by the sum of these two areas.
FIGURE 13.4: Marginal Expense of
Hiring Bear Wardens
Hourly
wage
S
B
$8
A
6
0
55
3
4
Bear wardens
per hour
Monopsonist’s Input Choice

The profit-maximizing monopsonist will hire up to the
point where the additional revenue equals the
additional cost of hiring one more unit of input.
For labor this requires:

Only if the firm is a price taker will MEL = w.

56
MEL  MVPL
A Graphical Demonstration
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57
The demand curve in Figure 13.5 is D.
Since marginal expense (MEL) exceeds the
wage, the marginal expense curve is above the
supply curve (S).
L1 is the profit maximizing choice while the
marginal value product is MVP1 and the wage
is w1.
FIGURE 13.5: Pricing in a
Monopsonistic Labor Market
Wage
ME
S
D
58
0
Labor hours
per week
FIGURE 13.5: Pricing in a
Monopsonistic Labor Market
ME
Wage
S
MVP1
D
59
0
L1
Labor hours
per week
FIGURE 13.5: Pricing in a
Monopsonistic Labor Market
ME
Wage
S
MVP1
w1
60
0
D
L1
Labor hours
per week
A Graphical Demonstration
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61
L1 is less than L*, the amount hired with perfect
competition.
As with a monopoly, the “demand curve” for a
monopolist actually consists of the single point
given by L1, w1.
FIGURE 13.5: Pricing in a
Monopsonistic Labor Market
ME
Wage
S
MVP1
w*
w1
62
0
D
L1
L*
Labor hours
per week
Monopsonists and Resource
Allocation

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
63
Since the monopsonist restrict its input use, it
pays an input less than its marginal value
product (w1 < MVP1).
Total output could be increased by drawing
more labor into the market.
The more inelastic the labor supply, the more
the monopsonists can benefit from this profit
opportunity.
Causes of Monopsony

If competition for inputs is lacking, monopsony
may exit.
–
–
–
64
The input may have high opportunity costs of
moving to another input market.
The input may be so specialized that there is only
one firm that hires that input.
Firms may join together to form a cartel in the input
market.
APPLICATION 13.4: Monopsony in the
Market for Sports Stars
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65
Because players marginal revenue products
are more easily measured and correlated with
spectator attendance, sports provides a good
market for study.
The “reserve clause” in professional baseball
found layers to teams that first signed them
giving teams monopsony power.
Monopsony in Major League Baseball

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66
In a famous 1974 study, G.W. Scully examined
the correlation between a team’s winning
percentage and its attendance.
Next, he analyzed what aspects of an
individual’s performance most closely related
to a team’s overall performance.
He used this information to estimate the MRPs
of the players.
Monopsony in Major League Baseball


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67
He found the MRPs greatly exceeded players
salaries.
A players strike in 1972 and other legal actions
led to the adoption of the free-agent provisions
that partially replaced the reserve-clause.
This has severely limited the monopsony
power of major league teams.
Basketball and Michael Jordan

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68
While it did not have a reserve clause, the
National Basketball Association (NBA) has
exercised some monopsony power.
Early stars probably were most affected, but
Michael Jorden’s multimillion dollar salary was
millions of dollars less than what he was worth
to the NBA in terms of higher television ratings
when he played.
Bilateral Monopoly

A bilateral monopoly is a market in which
both suppliers and demanders have monopoly
power.
–

69
Pricing is indeterminate in such markets.
In Figure 13.6, “supply” and “demand” intersect
at P*, Q*, but this is not equilibrium since
neither player is a price taker.
FIGURE 13.6: Bilateral Monopoly
ME
Input
price
S
D
MR
70
0
Quantity per
period
Bilateral Monopoly

71
The monopoly supplier will operate on its
marginal revenue curve (MR) and prefer pricequantity combination P1, Q1.
FIGURE 13.6: Bilateral Monopoly
ME
Input
price
S
P1
D
MR
72
0
Q1
Quantity per
period
Bilateral Monopoly


73
The monopoly supplier will operate on its
marginal revenue curve (MR) and prefer pricequantity combination P1, Q1.
The monopsonistic will operate on its marginal
expense curve (ME) and prefer combination
P2, Q2.
FIGURE 13.6: Bilateral Monopoly
ME
Input
price
S
P*
P2
D
MR
74
0
Q2
Quantity per
period
Bilateral Monopoly



75
The monopoly supplier will operate on its
marginal revenue curve (MR) and prefer pricequantity combination P1, Q1.
The monopsonistic will operate on its marginal
expense curve (ME) and prefer combination
P2, Q2.
The final outcome, after bargaining, will lie
between these two combinations.
FIGURE 13.6: Bilateral Monopoly
ME
Input
price
S
P1
P*
P2
D
MR
76
0
Q2 Q1
Q*
Quantity per
period