# Labor Demand

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```					Labor Demand

1
Labor Demand
• A firm’s decision about how much labor to use in production is
driven by the firm’s desire to maximize profits.
– Derived demand

• Firm’s thinking about whether to hire a worker
–   Each worker can produce a certain amount to output per hour
–   That output can be sold for money
–   Thus, each worker generates a certain amount of revenue per hour.
–   If that hourly revenue is greater than the hourly wage, then hire the
worker.

• Just another way of saying marginal benefit must be greater than
marginal cost

• Now let’s look at this formally.

2
Labor Demand
•   Production Function: q=f(E,K)

•   Some variable definitions
q = output
E = labor
K = capital

•   Example: q=E1/4K1/2

•   Marginal Product of Labor: Change in the physical output resulting
from a hiring an additional worker.
– MPE = Δq / ΔE
– For our example: MPE = 1/4(E-3/4K1/2)
– Note that the MPE is decreasing in labor
– Intuition

3
Labor Demand

q                MPE

E’       E         E’   E

4
Profit Maximization in a Perfectly
Competitive Market
•   Profits = pq-wE-rK
w = wage rate
r = price of capital
p = price of output

•   Labor demand in the short run (capital is fixed)

•   Marginal Revenue: Change in revenue resulting from a one-unit increase
in output.
– In a perfectly competitive market: MR=p

•   Value of the Marginal Product of Labor: The additional revenue a firm
– VMPE = p × MPE

5
Profit Maximization in a Perfectly
Competitive Market

•   Marginal Cost of Labor            VMPE
– MCE=w
VMPE=p×MPE
•   Decision making rule of profit
maximizing firm
– VMPE>w hire more               w*
– VMPE<w hire fewer
– VMPE=w stop

•   Labor demand curve in the short
run is the downward sloping
portion of the VMPE curve.                        E*   E

6
Example
Variables
• q = K1/3L1/2
• w=2
• p = 12
• K = 8 (fixed)

How many hours of labor should the firm employ?
• Capital is fixed so we can re-write the production function as:

q = (8)1/3E1/2 = 2 E1/2

•   MPE = E-1/2
•   VMPE=12E-1/2
•   Profit Maximization: VMPE=w
12E-1/2=2
E1/2=6
E*=36
7
Hey Wait
Econ 1   Econ 139
p = MC   VMPE = w
p × MPE = w

MPE = Δq / ΔE

Δq / ΔE : how much more output I can get from another unit
of labor.

ΔE / Δq: how much more labor I need to produce an

p × (Δq / ΔE) = w
p = w × (ΔE / Δq) = MC (So it’s exactly the same thing)

8
Labor Demand in the Long Run
•   Two factors of production: capital and labor.
•   Both capital and labor can be varied.
•   Labor demand curve downward sloping in the long run too.
•   Demand for labor more responsive to wage changes in the long run.
W

DLR
DSR
E                9
Elasticity of Labor Demand
How sensitive is the quantity of labor demanded to a change in wages?

w

D

E

E
% change in employment
                            E
% change in wage      w
w                           10
Diagram of Economy
Many markets influence the labor market

supply
Land
Capital
demand             supply
Consumers
Firms
demand
supply
Workers
demand

11
The Scale and Substitution Effects
•   How does a firm’s labor demand respond to changes in the price of labor?

•   Substitution effect: Describes how input demand changes as the relative
price of the inputs changes, holding output fixed.
– If labor becomes more expensive, you may want to substitute out of
labor and into capital.

•   Scale effect: Describes how input demand changes as output changes,
holding input prices fixed.
– If labor becomes more expensive, you may have to scale back
production.

12
Remember from Econ 1
MC2
\$                                               MC1

p

q
q2*   q1*

A wage increase will increase the marginal cost of producing an extra unit of
output. This will lead the firm to produce less.

13
Summary of Scale and Substitution
Effects

Increase in the Decrease in the
Price of Labor Price of Labor
Substitution   Quantity of labor   Quantity of labor
Effect         demanded            demanded
DECREASES           INCREASES
Scale Effect   Quantity of labor   Quantity of labor
demanded            demanded
DECREASES           INCREASES

14
Marshall’s Four Rules of Derived Demand

Own-wage elasticity is high when:

RULE 1: Relates to the output market. When the price elasticity of
demand for the product is high, the scale effect is big.

Output Market                          Output Market
Price Elasticity of                P   Price Elasticity of
P
Demand is High                         Demand is Low
S2                                     S2

S1                                         S1

D
D
Q2    Q1                       Q           Q2 Q1                       Q
15
Marshall’s Four Rules of Derived
Demand, Continued
RULE 2: Relates to the production technology. When the technology is such
that easy to substitute for labor in production, then the substitution effect is big.

% change in K
Elasticity of substitution=                   L
% change in w
r

perfect                                                          perfect
complements                                                       substitutes
In most cases, inputs                elasticity of
elasticity of               are somewhere in the
substitution = 0                                                 substitution → ∞
middle

RULE 3: When the cost of employing labor is a large share of total costs.
16
Marshall’s Four Rules of Derived
Demand, Continued
RULE 4: When the supply of other factors of production is highly
elastic, then the substitution effect is big. Increases in the demand for
capital do not drive the price of capital up.

r               Capital
Market

S

D
K
17
Changes in the Demand for Labor
Wage

Decrease     Increase

in demand   in demand

D

Quantity

18
Three Factors that Affect Labor Demand

1.   Change in the price of output. For example, this could happen if there
were an increase in demand for the output.

w
Case of an increase in output prices.

VMPE=p2 × MPE

VMPE=p1 × MPE

E               19
Factors that Affect Labor Demand

2.   Firm’s technology choice. For example, the firm could switch to a
technology for which the marginal productivity in labor is higher.

w
Case of an increase in the MPE

VMPE=p × MPE’

VMPE=p × MPE

E            20
Factors that Affect Labor Demand

Capital Market
3. Change in the price of        \$               S2       S1
other inputs. For example,
this could happen if there                                       Supply decreases
were a change in the
supply of other inputs like                        D

capital and labor.                            K                                Output Market
S2
\$                        S1
Substitution effect
Example: Supply of                     (increases demand for labor)
capital decreases.
Ambiguous affect on                                                                                D
Labor Demand
the demand for labor.         \$
Q

Scale effect
(decreases demand for labor)
D

L

21
Gross Substitutes and Gross Complements

Labor demand         Labor demand
increases            decreases
r increases   Gross substitutes   Gross complements
(SE>SCE)             (SE<SCE)

Capital demand       Capital demand
increases           decreases
w increases    Gross substitutes   Gross complements
(SE>SCE)             (SE<SCE)

22
Labor Demand When the Labor
Market Is Not Perfectly Competitive
•    If a market is characterized by monopsony, it means that there are many

•    In the case of the labor market, it means that there’s only one firm that buys
labor.
– Prototypical example is a coal mine in a remote location.
– However, the most important feature of a monopsony is that if they want
to hire more workers, they can only do so by raising wages.

•    This could happen if there were a large number of employers but you also
– Mobility costs
– Firms may to pay workers higher and higher wages as the firm gets
bigger to prevent the workers from slacking off.

23
Differences in Labor Supply Curves Under
Perfectly Competition and Monopsony
Competitive
Monopsony
\$        Labor Market         \$
S

S=W

L                      L

Note: in this class, we will examine the case of a monopsonist who cannot
price discriminate. What does that mean?

It means that the monopsonist must pay all of it’s workers the same wage.
24
The Marginal Cost of Hiring For
Monopsonists
•   Intuitively, profit maximization is the same for a monopsonist as it is for a
perfectly competitive firm.

– Each firm’s profit maximizing demand for labor is the quantity of labor
such that: VMPE = MC of hiring a worker

•   However, the MC of hiring a worker will not be equal to w.
•   Why? Because when the monopsonist hires an additional unit of labor, it
must increase the wages.

•   Example:
– Labor supply curve: w=10+2E
– 10 workers, w = 30     Total Cost = 10 × 30 = 300
– 11 workers, w = 32     Total Cost = 11 × 32 = 352
– Marginal Cost of 11th worker = 52
– (=\$32 for 11th worker plus \$20 for extra \$2 paid to 10 original workers)

25
Graphically

w
MCE

S

E
26
Profit Maximization

w
MCE

How do you draw the
labor demand curve for
S       a monopsonist?

The monopsonist
simultaneously picks
w*                                 w* and E* so there is
no labor demand curve
for a monopsonist.
VMPE

E*                      E
VMPE = MCE                                  27
Comparison with Perfect
Competition
In a monopsony, fewer
w
MCE          people are hired than in a
perfectly competitive
market and wages are
lower.
S
This is because the
marginal cost of hiring an
w*                                   for a monopsonist than for
a perfectly competitive firm.

VMPE   Workers worse off relative
to perfectly competitive
E*   E*                 E   labor market.

VMPE = MCE                                 28
Monopsony in Professional Sports
• Sports owners are a small and interconnected group.

• Possibly can band together and act as monopsonists.

• Main issue here is that the owners can set wages—that is, wages
are not determined by perfect competition.

• Two implications

29
Salaries of Major League Baseball
Players, 1876-1920

30
Evidence on the Degree of
Monopsonistic Exploitation
• If an employer is a monopsony, then workers are paid less than their
marginal product

• How does a player’s marginal revenue product (or value of marginal
product of labor) compare with that player’s salary?

• Two steps
– Calculate how various measures of player performance affect a team’s
winning percentage (MPE)
– Calculate how a team’s winning percentage affects revenue (p)

• Estimates
– Late 1960s: players paid 15-20% of VMPE.
– Late 1980s: players paid 29-45% of VMPE.
– Reserve clause effectively ends in 1976.

31
Labor Demand Application:
Minimum Wage Laws

32
Minimum Wage Laws
Basic Facts
 Federal minimum wage is.
 California minimum wage is
 Not all sectors are covered.
 Farmworkers employed on small farms
 Employees of season recreational establishments
 Salespeople at automobile dealerships
 In 2001, 3.1 percent of workers earned at or below the Federal
minimum wage, and 71 percent of those workers earned below
\$5.15 per hour.

33
Value of the Federal Miniumum Wage
(1970-2000)
Nominal Min. Wage        Real Min Wage

6.00
5.00
4.00
3.00
2.00
1.00
0.00
70

74

78

82

86

90

94

98
19

19

19

19

19

19

19

19
Year

34
Minimum Wage Laws
Perfect Competition:                w

Minimum wages are a type
of price floor.
S
Effectively change supply
curve.                   min w

Decrease employment.          wC

D

Emin EC           E
35
Monopsony and Minimum Wages

\$       New MCE     MCE

S

Note that when minimum
wage laws are implemented in
a monopsonistic market, then

wmin
w*

VMPE

E* Emin    Employment
36
Criticisms of the Minimum Wage
• It causes unemployment.
• It only helps teenagers.

• Are these criticisms valid?

37
Who Earns the Minimum Wage?
(Age Groups)
 One third are
teenagers.

 Almost one half
are over the
age of 25.

38
Who Earns the Minimum Wage?
(Relationship in Household)
households.

children.

39
Who Earns the Minimum Wage?
(Race and Gender)

Mostly women.
 63.7% of minimum wage earners are women.

Mostly White.
 80% of minimum wage earners are ―white‖.

40
What is the Effect of the Minimum
Wage on Employment
Issues to consider:
1.    We observe employment and the timing of minimum wage
increases.
2.    Looking at what happens in a small number of firms can be

McDonald’s                 KFC

S                        S

WMIN

W

D                         D
41
E                            E
What is the Effect of the Minimum
Wage on Employment
3.    Other changes in the economy also affect employment.

w
S

min wage

w0

D

D

E
Emin      E* E’
42
Need Variation!
Sources of Minimum Wage Variation:

            variation in the nominal and real value of the minimum wage

            variation in nominal and real minimum wage

43
Time Series Variation
Real Value of Minimum Wage and Average Wages of
Manufacturing Production Workers

44
Teenage Employment Rate With
Dates of Minimum Wage Changes

Problem:

45
Study by Card and Krueger
Study Design
Natural Experiment
• Ideally, we would randomize.

• Alternatively, we can look for ―natural experiments‖.
 Prior to April 1992, the minimum wage in NJ and PA is
\$4.25/hour
 April 1, 1992 NJ raises its minimum wage to \$5.05/hour
 Other states nearby didn’t (for example, PA)

46
Study by Card and Krueger
Data Collection

• Survey
 Burger King, Roy Rogers, KFC, Wendy’s etc.
 New Jersey and Pennsylvania
• Asked them number of full-time and part-time employees
• Before:
• After:

47
Difference-in-Difference
Estimation
Number of Full-Time Equivalent       Non-
supervisory Employees

NJ        PA       Difference
March 1992     20.4      23.3
(A)       (B)
December 1992   21.0      21.2
(C)       (D)
Difference

48
Difference-in-Difference
Estimation
Number of Full-Time Equivalent         Non-
supervisory Employees
Before     After   Difference
NJ            20.4      21.0        .6
(A)      (B)       (B-A)
PA            23.3      21.2       -2.1
(C)       (D)       (D-C)
Difference       2.9        .02
(C-A)      (D-B)

49
Suggests that employment
Implications of Card and Krueger
Study
• Suggests that the labor demand curve is upward sloping.

• Monopsony?

50
Criticisms of the Card and Krueger
Study
•   No attempt to collect data on hours worked.
•   Big drop in employment in PA over 8 month time period.
•   Overall increase masks huge variation in both directions.
•   Hungry teenager theory

51

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