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Chapter 5
The Demand for
Labor
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McGraw-Hill/Irwin
Copyright © 2008 by The McGraw-Hill Companies, Inc. All rights reserved.
5-2
1.Derived Demand
for Labor
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5-3
Derived Demand
 The demand for labor is a derived
demand.
 That is, it is derived from the demand
for the product or service that the labor
is helping produce.
 The demand for hamburgers leads to
the demand for hamburger workers.
 Demand for workers depends on:
 How the productive the workers are.
 The price of the product the workers
are helping produce
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5-4
2. A Firm’s Short-Run
Production Function
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5-5
Production Function
 A production function shows the
relationship between inputs and outputs.
 Assume that only two inputs are used to
make a product-- labor (L) and capital (K).
o firm is hiring homogeneous inputs of labor
 In the short run, at least one input is fixed.
 The total product for a firm in the short run
is:
 TPSR=f(K,L), where K is fixed.
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5-6
Definitions
 Total product (TP) is the total product
produced by each combination of
labor and the fixed amount of capital.
 Marginal product (MP) is the change
in total product associated with the
addition of one more unit of labor.
 Average product (AP) is the total
product divided by the number of units
of labor.
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5-7
The Law of
Diminishing Returns
 Definition
 As additional units of a
variable input are combined
with a fixed input, at some
point the additional output
(i.e., marginal product)
starts to diminish.
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• As5-8
units of variable input (labor) are
added to a fixed input, total product will
increase . . .
• First at an increasing rate . . .
• Then at a declining rate . . .
• Note that the Total Product curve is
smooth, indicating that labor can be
increased by amounts of less than a
single unit (it is a continuous function).
Units of
Variable
Resource
0
1
2
3
4
5
6
7
8
9
10
Total
Product
(Output)
0
8
20
34
46
56
64
70
74
75
73
Law of Diminishing Returns
Total
Product
Total
Product
80
70
60
Marginal Average 50
Product Product
40
30
20
10
1 2
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3
4 5 6 7 8 9 10
Quantity of Labor
• The5-9
Marginal Product curve will initially
increase (when TPC is increasing at an
increasing rate), reach a maximum, and
then decrease (as TPC increases at a
decreasing rate).
• The Average Product curve will have the
same general form except that its
maximum point will be at a higher
output level.
Units of
Variable
Resource
0
1
2
3
4
5
6
7
8
9
10
Total
Product
(Output)
0
8
20
34
46
56
64
70
74
75
73
Law of Diminishing Returns
Average and/or
Marginal Product
16
Marginal
Product
12
Average
Product
Marginal Average
Product Product
----8
12
14
12
10
8
6
4
1
-2
----8
10
11.3
11.5
11.2
10.7
10
9.3
8.3
7.3
8
4
Important Note :
MP always crosses AP
at its maximum point.
1 2
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3
4 5 6 7 8 9 10
Quantity of Labor
5-10
• Graphed together, one can see the
relationship between the TP, MP,
and AP curves more clearly.
TP
80
Law of
Diminishing Returns
AP & MP
Total
Product
16
Marginal
Product
70
12
60
50
Average
Product
8
40
30
4
20
10
1 2 3 4 5 6 7 8 9 10
Quantity
of Labor
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1 2 3 4 5 6 7 8 9 10
Quantity
of Labor
5-11
TP & MP in the Short Run
 If MP is positive
then TP is
increasing.
 If MP is negative
then TP is
decreasing.
 TP reaches a
maximum when
MP=0
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5-12
AP & MP in the Short Run
 If MP > AP then AP is
rising.
 If MP < AP then AP is
falling.
 MP=AP when AP is
maximized.
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5-13
The Law of Diminishing
Returns
 Reasons
• Increasing Returns
• Teamwork and Specialization
MP
Diminishing Returns Begins
Fewer opportunities for teamwork
and specialization
X
MP
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5-14
The Three Stages of
Production
 Stage I
 From zero units of the variable input
to where AP is maximized
 Stage II
 From the maximum AP to where
MP=0
 Stage III
 From where MP=0 on
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5-15
The Three Stages of
Production
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5-16
The Three Stages of
Production
 In the short run, rational firms should only be
operating in Stage II.
 Why Stage II?
•Why not Stage III?
•Firm uses more variable inputs to produce less
output!
•Why not Stage I?
•Underutilizing fixed capacity.
•Can increase output per unit by increasing the
amount of the variable input.
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5-17
Optimal Level of Variable
Input Usage
 Consider the following short run production process.
Where
is
Stage
II?
Labor
Unit
(L)
0
1
2
3
4
5
6
7
8
Total
Product
(Q or TP)
0
10,000
25,000
45,000
60,000
70,000
75,000
78,000
80,000
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Average Marginal
Product Product
(AP)
(MP)
10,000
12,500
15,000
15,000
14,000
12,500
11,143
10,000
10,000
15,000
20,000
15,000
10,000
5,000
3,000
2,000
5-18
Optimal Level of Variable
Input Usage
Stage II
Labor
Total
Average Marginal
Unit
Product
Product Product
(X) (Q or TP)
(AP)
(MP)
0
0
1
10,000
10,000 10,000
2
25,000
12,500 15,000
3
45,000
15,000 20,000
4
60,000
15,000 15,000
5
70,000
14,000 10,000
6
75,000
12,500
5,000
7
78,000
11,143
3,000
8
80,000
10,000
2,000
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5-19
Optimal Level of Variable
Input Usage
 What level of input usage within
Stage II is best for the firm?
 The answer depends upon how
many units of output the firm can
sell, the price of the product, and
the monetary costs of employing
the variable input.
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5-20
3. Short-Run Demand for
Labor: The Perfectly
Competitive Seller
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5-21
Hiring Decision
 Profit-maximizing firms will hire
additional workers as long as each
worker adds more to revenue than she
costs.
 Marginal revenue product (MRP) is
the change in total revenue that results
from hiring of an additional worker.
 MRP= Marginal Revenue (MR) * MP
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5-22
Hiring Decision
 Marginal wage cost (MWC) is the
change in total wage cost of hiring
an additional worker.
 The Hiring Rule:
 Hire additional workers until
MRP = MWC.
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5-23
Optimal Use of the
Variable Input
•
How much labor or the variable
input should the firm use in order
to maximize profit.
• The firm should employ an
additional unit of labor as long as
the extra revenue genereted until
the extra revenue equals the
extra cost.
• Where MRP=MWC
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5-24
Value of Marginal Product
 The value of marginal product (VMP)
is the extra output in dollar terms that
society gains when an extra worker is
employed.
 VMP=Price * MP
 For a perfectly competitive seller,
MR=Price.
 As a result, VMP = MRP for such
firms.
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5-25
Optimal Use of the Variable
Input
Marginal Revenue
Product of Labor
MRPL = (MPL)(MR)
Marginal Wage Cost
(MWC)
Optimal Use of Labor
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TC
MRCL =
L
MRPL = MWCL
5-26
Short-Run Demand for
Perfectly Competitive Firm
• In the numerical example below, a computer company uses both
technology and data-entry operators to provide services in a perfectly
competitive market. For each unit processed the firm receives $200 (4).
• The Marginal Revenue Product schedule (6) indicates how hiring an
additional operator affects the total revenue of the firm.
OR MPR = 5*200
Units of
Labor (L)
(1)
0
1
2
3
4
5
6
7
Total
Product (TP)
(units per week)
(2)
0.0
5.0
9.0
12.0
14.0
15.5
16.5
17.0
MRP
MP
 TR
(Per Unit)
Total
Revenue
(3)
(4)
(5)
(6)
----5.0
4.0
3.0
2.0
1.5
1.0
0.5
$200
$200
$200
$200
$200
$200
$200
$200
$
0
$1,000
$1,800
$2,400
$2,800
$3,100
$3,300
$3,400
---1000
800
600
400
300
200
100
 TP
L
Sales Price
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L
5-27
Short-Run Labor Demand
Wage Rate
• Since a profit-maximizing firm
will only hire an additional worker 1000
only if the worker adds more to
revenues than she adds to wage
800
costs, the MRP curve is the firm’s
short run demand curve for labor.
600
• In the short-run, it will slope
downward because the marginal
product of labor falls as more of it 400
is used with a fixed amount of
capital.
200
MRP=DL
1
2
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3
4
5
6
7 Quantity of
Labor
5-28
Example 2
 In order to determine the optimal
input usage we assume that the
firm operates in a perfectly
competitive market for its input
and its output.
 Product price, P=$2
 Variable input price, w=$10,000
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5-29
Optimal Level of Variable
Input Usage
Labor Total
Unit Product
(X) (Q or TP)
0
0
1 10,000
2 25,000
3 45,000
4 60,000
5 70,000
6 75,000
7 78,000
8 80,000
Average Marginal
Product Product
(AP)
(MP)
10,000
12,500
15,000
15,000
14,000
12,500
11,143
10,000
10,000
15,000
20,000
15,000
10,000
5,000
3,000
2,000
Total
Revenue
Product
(TRP)
0
20,000
50,000
90,000
120,000
140,000
150,000
156,000
160,000
Marginal
Revenue
Product
(MRP)
20,000
30,000
40,000
30,000
20,000
10,000
6,000
4,000
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Total
Labor
Cost
(TLC)
0
10,000
20,000
30,000
40,000
50,000
60,000
70,000
80,000
Marginal
Labor
Cost TRP(MLC) TLC
0
10,000 10,000
10,000 30,000
10,000 60,000
10,000 80,000
10,000 90,000
10,000 90,000
10,000 86,000
10,000 80,000
MRPMLC
10,000
20,000
30,000
20,000
10,000
0
-4,000
-6,000
5-30
Optimal Level of Variable
Input Usage
Labor Total
Unit Product
(X) (Q or TP)
0
0
1
10,000
2
25,000
3
45,000
4
60,000
Stage 5 70,000
6
75,000
II
7
78,000
8
80,000
Average Marginal
Product Product
(AP)
(MP)
10,000
12,500
15,000
15,000
14,000
12,500
11,143
10,000
10,000
15,000
20,000
15,000
10,000
5,000
3,000
2,000
Total
Revenue
Product
(TRP)
0
20,000
50,000
90,000
120,000
140,000
150,000
156,000
160,000
Marginal
Revenue
Product
(MRP)
20,000
30,000
40,000
30,000
20,000
10,000
6,000
4,000
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Total
Labor
Cost
(TLC)
0
10,000
20,000
30,000
40,000
50,000
60,000
70,000
80,000
Marginal
Labor
Cost TRP(MLC) TLC
0
10,000 10,000
10,000 30,000
10,000 60,000
10,000 80,000
10,000 90,000
10,000 90,000
10,000 86,000
10,000 80,000
MRPMLC
10,000
20,000
30,000
20,000
10,000
0
-4,000
-6,000
5-31
Question for Thought
1. “Only that portion of the MP curve that lies below
AP constitutes the basis for a firm’s short-run
demand curve for labor.” Explain.
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5-32
4. Short-Run Demand for
Labor: The Imperfectly
Competitive Seller
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5-33
Short-Run Demand for
Imperfectly Competitive Firm
• In the numerical example below, the company uses both technology
and data-entry operators to provide services in an imperfectly
competitive market.
• Since it is in an imperfectly competitive market, the firm faces a
downward sloping product demand curve (4). That is, the product
price falls as the firm sells more units.
Units of
Labor (L)
(1)
0
1
2
3
4
5
6
7
Total
Product (TP)
(units per week)
(2)
0.0
5.0
9.0
12.0
14.0
15.5
16.5
17.0
MRP
MP
 TR
(Per Unit)
Total
Revenue
(3)
(4)
(5)
(6)
----5.0
4.0
3.0
2.0
1.5
1.0
0.5
$210
$200
$190
$180
$170
$160
$150
$140
$
0
$1,000
$1,710
$2,160
$2,380
$2,480
$2,475
$2,380
---1000
710
450
220
100
-5
-95
 TP
L
Sales Price
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L
5-34
Short-Run Labor Demand
• For imperfectly competitive
firms, the labor demand curve
will slope because of a falling
marginal product of labor and
because the firm must decrease
the price on all units of output as
more output is produced.
• The MRP (=MR *MP) for
imperfect competitors is less than
the VMP (=P*MP) at all levels of
output past the first unit.
• The labor demand curve for an
imperfectly competitive firm
(MRP) is less elastic than that for
a perfectly competitive firm
(VMP). As a result, they will hire
fewer workers other things equal.
Wage Rate
1000
800
600
400
200
0
VMP
1
2
3
4
5
6
7 Quantity of
Labor
MRP=DL
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5-35
5. Long-Run Demand
for Labor
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5-36
Long-Run Labor Demand
 In the long run, both labor and capital
are variable.
 The total product for a firm in the long
run is:
 TPLR=f(K,L)
 The long-run labor demand curve is
downward sloping because a wage
decline has both an output and
substitution effect.
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5-37
Output Effect
 The output effect (also called the scale effect) is
the change in employment resulting solely
from the effect of a wage on the employer’s
costs of production.
 Normally, a decline in the wage rate shift a
firm’s marginal cost curve downward, as
from MC1 to MC2.
 This means that marginal revenue exceeds
marginal costs.
 Adhering to MC profit-maximizing rule, the
firm will now find it profitable to increase
its output from Q1 to Q2 units.
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5-38
Output Effect
Price
• A decline in the wage rate will
reduce the marginal cost (MC1 to
MC2) to and increase the profit
maximizing level of output (40 to
70).
• To produce the higher output
level, the firm will have to hire
more workers.
• This output effect is present in the
short run.
MC1
10
MC2
8
MR
6
4
2
10 20
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30 40 50 60 70 Quantity of
Output
5-39
Substitution Effect
 The substitution effect is the change in
employment resulting from a change in the
relative price of labor, output being held
constant.
 If a decline in the wage rate occurs, firms
will substitute labor for the now relatively
more expensive capital.
 Since capital is fixed in the short run, this
effect can’t occur in the short run.
 The long-run demand for labor will be more
elastic than the short-run demand curve.
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5-40
Long-Run Labor Demand
Wage Rate
• A wage decrease from $800 per
week to $600 increases the shortrun quantity of labor from 3 to 4
(A to B). This is the output effect.
1000
A
800
• In the long-run, the firm also
substitutes labor for capital,
resulting in a substitution effect
of 2 units (B to C).
• The long-run demand curve
results from both effects and is
found by connecting points A
and C.
B
600
C
DLR
400
DS
200
R
1
2 3
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4
5
6
7 Quantity of
Labor
5-41
Other Factors
1. Product demand
 Product demand is more elastic in the
long run than in the short run, making
labor demand more elastic the longer
the period.
2. Labor-Capital interaction
 If the wage rate falls, the short-run
quantity demanded of labor rises.
 This will increase the MP of capital
and thus the MRP of capital.
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5-42
Other Factors
 The higher MRP of capital, will
increase the quantity of capital and
thus the MP and MRP of labor.
 As a result, the long-run response will
be greater than the short-run response.
3. Technology
 If the wage rate falls, technology
innovators will try to reduce the use of
relatively more expensive capitals and
increase the use of labor.
 The long run response will be greater
than the short-run response.
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5-43
Question for Thought
1. Referring to the output and substitution effects,
explain why an increase in the wage rate for
autoworkers will generate more of a negative
employment response in the long run than in the
short run. Assume there is no productivity
increase and no change in the price of nonlabor
resources.
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5-44
6. Market Demand for
Labor
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5-45
Market Labor Demand
Wage Rate
• The market demand curve for labor
is less elastic than a horizontal
summation of the demand curves
of individual firms (D).
1000
A
800
• A lower wage induces all firms to
hire more labor and produce more
output, causing the supply of the
product to increase.
• The resulting decline in the
product price shifts the firms’
labor demand to left.
• As a result, total employment
B
600
C
D
400
DMARKET
200
rises to A to B rather than from
A to C.
10 20 30
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40 50 60 70 Quantity of
Labor
5-46
7. Elasticity of Labor
Demand
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5-47
Wage Elasticity Coefficient
 The wage elasticity coefficient
measures the responsiveness of the
quantity demanded of labor to the
wage rate.
% Change in
% Q
Wage Elasticity quantity demanded
Coefficient = % Change in Wage = % W
(Q0  Q1 ) (Q0 Q1 )
- or put simply (W0  W1 ) (W0  W1 )
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5-48
Determinants of Elasticity
 Elasticity of product demand
 The greater the price elasticity of
product demand, the greater the
elasticity of labor demand.
 Firms with market power tend to more
inelastic product demand, and thus a
more inelastic labor demand
 Product demand tends to be more
elastic in the long run and thus labor
demand is more elastic in the long run.
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5-49
Determinants of Elasticity
 Ratio of labor costs to total costs
 The larger the share of labor costs in
total costs, the greater will be the
elasticity of labor demand.
 A 10% wage rise if labor accounts for
10% of total costs, will raise total costs
by 1%.
 A 10% rise in wages when labor costs
for 50% of total costs will raise total
costs by 5%.
 If costs rise more, the price rise must be
greater and thus decrease quantity more.
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5-50
Determinants of Elasticity
 Substitutability of other inputs
 The greater the substitutability of other
inputs for labor, the greater will be the
elasticity of labor demand.
 Supply elasticity of other inputs
 The greater the elasticity of supply of
other inputs for labor, the greater will
be the elasticity of labor demand
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5-51
Estimates of Elasticity
 Most estimates of elasticity indicates
the overall long-run elasticity of
demand is about -1.0.
 A 1% rise in the wage rate will lower
the quantity demanded of labor by 1%.
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5-52
Significance of Elasticity
 Labor unions.
 Unions can achieve greater wage gains
when the labor demand curve is more
inelastic.
 Minimum wage
 The employment decline of a hike in
the minimum wage will be larger
when the labor demand curve for
affected worker is more elastic.
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5-53
8. Determinants of Demand
for Labor
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5-54
Determinants of Labor
Demand
 Product demand
 A change in product demand, will shift
labor demand in the same direction.
 Productivity
 Assuming that it does not cause an
offsetting decrease in the product
price, a change in marginal product
will shift labor demand in the same
direction.
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5-55
Determinants of Labor
Demand
 Number of employers
 Other things equal, a change in the
number of firms employing a
particular type of labor will change
labor demand in the same direction.
 Prices of other resources
 Normally labor and capital are
substitutes in production.
 One can substitute labor for capital
and vice versa in the production
process.
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5-56
Determinants of Labor
Demand
 Gross substitutes
 Gross substitutes are inputs such that
when the price of one changes, the
demand for the other changes in the
same direction.
 Implies substitution effect outweighs
the output effect.
 Example: the decline in the price of
security equipment used by businesses
has decreased the demand for night
guards.
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5-57
Determinants of Labor
Demand
 Gross complements
 Gross complements are inputs such
that when the price of one changes, the
demand for the other changes in the
opposite direction.
 Implies output effect outweighs the
substitution effect.
 Example: the decline in the price of
telephone switching equipment has
increased the demand for
communications workers.
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5-58
Determinants of Labor
Demand
 Pure complements
 Pure complements in production are
inputs that are used in direct
proportion to each other.
 Since no substitution effect occurs, the
inputs must be gross complements.
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5-59
Question for Thought
1. Use the concepts of (a) substitutes in production
versus pure complements in production and (b)
gross substitutes versus gross complements to
assess the likely impact of the rapid decline in the
price of computers and related office equipment
on the labor demand for secretaries.
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5-60
9. Real World Applications
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5-61
Employment in Textiles
and Apparel
2
1.5
1
0.5
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00
20
97
19
94
19
91
19
88
19
85
19
82
19
79
19
76
19
19
73
0
70
• Robots and assembly-line
labor are gross substitutes.
The price of robots has
fallen and so labor
demand has fallen.
2.5
19
• Employment in the textile
and apparel industries has
fallen in one-half since
1973.
• Demand for American
textile and apparel workers
has fallen because the
share of sales due to
imports has risen from 5%
in 1970 to 40% now.
Employment (millions)
3
5-62
End
Chapter 5
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