CHAPTER 3
“The laborer is worth his
hire.”
-The Gospel of St. Luke
McGraw-Hill/Irwin
Copyright © 2013 by The McGraw-Hill Companies, Inc. All rights reserved.
Introduction
• Firms hire workers because consumers want to
purchase a variety of goods and services.
• Demand for workers is derived from the wants and
desires of consumers.
• Central questions: how many workers are hired and what
are they paid?
3-2
The Firm’s Production
Function
• Describes the technology that the firm uses to produce
goods and services.
• The firm’s output can be produced by a variety of capital–
labor combinations.
• The marginal product of labor is the change in output
resulting from hiring an additional worker, holding constant
the quantities of other inputs.
• The marginal product of capital is the change in output
resulting from employing one additional unit of capital,
holding constant the quantities of other inputs.
3-3
The Total Product, the Marginal Product,
and the Average Product Curves
The total product curve gives the relationship between output and the number of workers hired by
the firm (holding capital fixed). The marginal product curve shows the output produced by each
additional worker, and the average product curve shows output per worker.
3-4
Profit Maximization
• Objective of the firm is to maximize profits.
• The profit function is:
o Profits = pq – wE – rK
• Total Revenue = pq
• Total Costs = (wE + rk)
• Perfectly competitive firms cannot
influence prices of output or inputs.
3-5
Short Run Hiring Decision
• Value of Marginal Product of Employment (VMPE) is the
marginal product of labor times the dollar value of the
output.
• VMPE indicates the dollar benefit derived from hiring an
additional worker, holding capital constant.
• Value of Average Product of Employment is the dollar
value of output per worker.
3-6
The Firm's Hiring Decision
in the Short-Run
A profit-maximizing
firm hires workers
up to the point
where the wage
rate equals the
value of marginal
product of labor. If
the wage is $22,
the firm hires eight
workers.
3-7
Labor Demand Curve
• The demand curve for labor indicates how many workers
the firm hires for each possible wage, holding capital
constant.
• The labor demand curve is downward sloping. This
reflects the fact that additional workers are costly and
alter average production due to the Law of Diminishing
Returns.
3-8
The Short-Run Demand Curve
for Labor
Because marginal
product eventually
declines, the short-run
demand curve for labor is
downward sloping. A
drop in the wage from
$22 to $18 increases the
firm’s employment. An
increase in the price of
the output shifts the
value of marginal product
curve upward (to the
right), and increases
employment.
3-9
Maximizing Profits:
Two Rules
• The profit maximizing firm should produce up to the point
where the cost of producing an additional unit of output
(marginal cost) is equal to the revenue obtained from
selling that output (marginal revenue).
• Marginal Productivity Condition: hire labor up to the point
where the value of marginal product equals the added
cost of hiring the worker (i.e., the wage).
3-10
The Mathematics of Marginal
Productivity Theory
• The cost of producing an extra unit of output:
o MC = w x (1 / MPe)
• The condition: produce to the point where MC = P (for
the competitive firm, P = MR)
o W x (1 / MPe) = P
3-11
Critiques of Marginal
Productivity Theory
• A common criticism is that the theory bears little
relation to the way that employers make hiring
decisions.
• Another criticism is that the assumptions of the
theory are not very realistic.
• However, employers act as if they know the
implications of marginal productivity theory
(hence, they try to make profits and remain in
business).
3-12
The Short-Run Demand Curve
for the Industry
Wage
Wage
T
D
20
20
10
10
D
T
15
Firm
28
30
Employment
30
56
60
Employment
Industry
3-13
The Firm's Output
Decision
Dollars
MC
p
Output Price
q*
A profit-maximizing
firm produces up to
the point where the
output price equals
the marginal cost of
production.
Output
3-14
The Employment Decision
in the Long Run
• In the long run, the firm maximizes profits by choosing
how many workers to hire AND how much plant and
equipment to invest in.
• Isoquant curves describe the possible combinations of
labor and capital that produce the same level of output.
3-15
Isoquant Curves
All capital-labor
combinations that lie on a
single isoquant produce
the same level of output.
The input combinations
at points X and Y
produce q0 units of
output. Combinations of
input bundles that lie on
higher isoquants must
produce more output.
Capital
X
K
Y
q1
q0
E
Employment
3-16
Isocost Lines
• The isocost line indicates all labor–capital bundles
that exhaust a specified budget for the firm.
• Isocost lines indicate equally costly combinations of
inputs.
• Higher isocost lines indicate higher costs.
3-17
Isocost Lines
Capital
C1/r
C0/r
Isocost with Cost Outlay C1
Isocost with Cost Outlay C0
C0/w
C1/w
All capital-labor
combinations that lie on a
single isocost curve are
equally costly. Capitallabor combinations that
lie on a higher isocost
curve are more costly.
The slope of an isoquant
equals the ratio of input
prices (-w/r).
Employment
3-18
The Firm's Optimal
Combination of Inputs
Capital
C1/r
A
C0/r
P
175
B
q0
100
Employment
A firm minimizes the cost
of producing q0 units of
output by using the
capital-labor combination
at point P, where the
isoquant is tangent to the
isocost. All other capitallabor combinations (such
as those given by points A
and B) lie on a higher
isocost curve.
3-19
Cost Minimization
• Profit maximization implies cost minimization.
• The firm chooses the least-cost combination of
capital and labor.
• This least-cost choice is where the isocost line is
tangent to the isoquant.
• Marginal rate of substitution equals the ratio of
input prices, w / r, at the least-cost choice.
3-20
Long Run Demand for
Labor
• When the wage drops, two effects arise.
o The firm takes advantage of the lower price of labor by
expanding production (the scale effect).
o The firm takes advantage of the wage change by
rearranging its mix of inputs, by employing more labor and
less of other inputs, even if holding output constant (the
substitution effect)
3-21
The Impact of a Wage Reduction
Holding Costs Constant
Capital
C0/r
R
P
75
q0

q0
Wage is w0
25
Wage is w1
A wage reduction flattens the
isocost curve. If the firm were
to hold the initial cost outlay
constant at C0 dollars, the
isocost would rotate around
C0 and the firm would move
from point P to point R. A
profit-maximizing firm,
however, will not generally
want to hold the cost outlay
constant when the wage
changes.
40
3-22
The Impact of a Wage Reduction on the Output and
Employment of a Profit-Maximizing Firm
Dollars
Capital
MC0
MC1
p
R
P
150
100
100
150
Output
25
50
Employment
•A wage cut reduces the marginal cost of production and encourages the firm to
expand (from producing 100 to 150 units).
•The firm moves from point P to point R, increasing the number of workers hired
from 25 to 50.
3-23
Substitution and Scale
Effects
Capital
D
C1/r
Q
C0/r
R
P
200
D
100
Wage is w1
Wage is w0
25
40
50
A wage cut generates
substitution and scale
effects. The scale effect
(from P to Q) encourages
the firm to expand,
increasing the firm’s
employment. The
substitution effect (from
Q to R) encourages the
firm to use a more laborintensive method of
production, further
increasing employment.
Employment
3-24
Two Special Cases of
Isoquants
Capital
Capital
100
q 0 Isoquant
q 0 Isoquant
5
200 Employment
20
Employment
Capital and labor are perfect substitutes if the isoquant is linear (so that two workers
can always be substituted for one machine). The two inputs are perfect
complements if the isoquant is right-angled. The firm then gets the same output
when it hires 5 machines and 20 workers as when it hires 5 machines and 25
workers.
3-25
Elasticity of Substitution
• The elasticity of substitution is the percentage
change in the capital to labor ratio given a
percentage change in the price ratio (wages to
real interest).
o Formula: %∆(K/L)  %∆(w/r).
o Interpret a particular elasticity of substitution number as the percentage
change in the capital–labor ratio given a 1% change in the relative price
of labor to capital
3-26
Elasticity of Substitution
• Example:
If the elasticity of substitution is 5, then a 10% increase
in the ratio of wages to the price of capital would result
in the firm increasing its capital-to-labor ratio by 50%.
3-27
Long Run Demand Curve
for Labor
Dollars
The long-run demand curve
for labor gives the firm’s
employment at a given wage
and is downward sloping.
w0
w1
DLR
25
50
Employment
3-28
The Short- and Long-Run Demand
Curves for Labor
Dollars
Short-Run
Demand Curve
Long-Run
Demand Curve
In the long run, the firm
can take full advantage of
the economic
opportunities introduced
by a change in the wage.
As a result, the long-run
demand curve is more
elastic than the short-run
demand curve.
Employment
3-29
Application
• Affirmative action and production costs:
o A firm is “color blind” if race does not enter the hiring decision.
o Discrimination shifts the hiring decision away from the cost
minimization tangency point on the isoquant.
3-30
Affirmative Action
Black Labor
Q
P
q*
White Labor
The discriminatory firm
chooses the input mix at
point P, ignoring the costminimizing rule that the
isoquant be tangent to the
isocost. An affirmative
action program can force
the firm to move to point Q,
resulting in more efficient
production and lower costs.
3-31
Affirmative Action
Black Labor
A color-blind firm is at point
P, hiring relatively more
whites because of the
shape of the isoquants. An
affirmative action program
will increase this firm’s
costs if it must further
increase its amount of black
labor.
Q
P
q*
White Labor
3-32
Marshall’s Rules
• Labor Demand is more elastic when:
o The elasticity of substitution is greater.
o The elasticity of demand for the firm’s output is
greater.
o Labor’s share in total costs of production is greater.
o The elasticity of supply of other factors of production
such as capital is greater.
3-33
Factor Demands When There
are Several Inputs
• There are many different inputs.
o Skilled and unskilled labor
o Old and young
o Old and new machines
• Cross-elasticity of factor demand.
o %∆xi%∆wj
o If cross-elasticity is positive, the two inputs are said to
be substitutes in production.
3-34
The Demand Curve for a Factor of Production
is Affected by the Prices of Other Inputs
Price of
input i
(a)
D0
Price of
input i
(b)
D0
D1
Employment of
input i
D1
Employment of
input i
The labor demand curve for input i shifts when the price of another input
changes. (a) If the price of a substitutable input rises, the demand curve for
input i shifts up. (b) If the price of a complement rises, the demand curve for
input i shifts down.
3-35
Labor Market Equilibrium
Dollars
Supply
whigh
w*
wlow
Demand
ED
E*
ES
In a competitive labor
market, equilibrium is
attained at the point
where supply equals
demand. The marketclearing wage is w* at
which E* workers are
employed.
Employment
3-36
Application: The
Employment Effects of
Minimum Wages
• The unemployment rate is higher the higher the
minimum wage and the more elastic are the labor supply
and demand curves.
• The benefits of the minimum wage accrue mostly to
workers who are not at the bottom of the distribution of
permanent income.
3-37
The Impact of the Minimum Wage
on Employment
Dollars
S
w
w*
D
E
E*
ES
A minimum wage set at w
results in employers
cutting employment from
E* to E. The higher wage
also encourages ES – E*
workers to enter the
market. Thus, under a
minimum wage, ES – E–
workers are unemployed.
Employment
3-38
Minimum Wages in the United States,
1938-2010
8
0.6
7
6
0.5
Ratio
5
4
0.4
3
2
0.3
Nominal Wage
1
0
0.2
1938
1944
1950
1956
1962
1968
1974
1980
1986
1992
1998
2004
2010
Year
3-39
The Impact of Minimum Wages on the
Covered and Uncovered Sectors
Dollars
Dollars
SU
SC
(If workers migrate to
covered sector)
SU
w
SU
(If workers migrate to
uncovered sector)
w*
w*
DU
DC
E
EC
(a) Covered Sector
Employment
EU
EU
EU
Employment
(b) Uncovered Sector
If the minimum wage applies only to jobs in the covered sector, the displaced workers might
move to the uncovered sector, shifting the supply curve to the right and reducing the
uncovered sector’s wage. If it is easy to get a minimum wage job, workers in the uncovered
sector might quit their jobs and wait in the covered sector until a job opens up, shifting the
supply curve in the uncovered sector to the left and raising the uncovered sector’s wage.
3-40
Asymmetric Variable
Adjustment Costs
Variable
Adjustment Costs
C0
-25
0
+50
Change in
Employment
Changing employment quickly is costly, and these costs increase at
an increasing rate. If government policies prevent firms from firing
workers, the costs of trimming the workforce will rise even faster than
the costs of expanding the firm.
3-41
Slow Transition to a New
Labor Equilibrium
Employment
150
B
100
50
A
C
Variable adjustment costs
encourage the firm to
adjust the employment
level slowly. The
expansion from 100 to
150 workers might occur
more rapidly than the
contraction from 100 to
50 workers if government
policies “tax” firms that
cut employment.
Time
3-42
Estimating Labor Demand
• One can identify the slope of the labor demand curve,
which can be used to calculate the elasticity of labor
demand, when the supply curve shifts.
• Problem: Must make sure the labor demand curve is not
also changing.
3-43
Problems with Estimating Labor
Demand
S0
Dollars
S1
Z
P
w0
R
w2
Z
Q
w1
D1
D0
E0
E1
E2
Employment
3-44
The Impact of Wartime Mobilization
of Men on Female Labor Supply
3-45
The Impact of Wartime Mobilization
of Men on Female Wages
3-46