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1

Labor Demand

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Labor Demand• A firm’s decision about how much labor to use in production is

driven by the firm’s desire to maximize profits.

• Firm’s thinking about whether to hire a worker– Each worker produces a certain amount to output per hour– That output can be sold for money– So, 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

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Output• Production Function: q=f(E,K)

• Some variable definitions:

• Example:

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The marginal product of labor• Marginal Product of Labor: Change in output resulting

from a hiring an additional worker. – MPE = ∆q / ∆E

• For our example:

– Note that the MPE is decreasing in labor– Intuition

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5

q MPE

EE’ E

Output and the marginal product of labor

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The value of the marginal product of labor

• Value of the marginal product of labor: the dollar increase in revenue generated by an additional worker.

• VMPE = p × MPE

E

VMP ($)

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Labor Demand in the Short Run• Profits = pq(E,K)-wE-rK

w = wage rate r = price of capitalp = price of output

• In the short run, capital is fixed.

• Value of the Marginal Product of Labor– VMPE = p × MPE

• Marginal Cost of Labor– MCE = w

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Profit Maximization

Decision making rule:

VMPE > w

VMPE < w

VMPE = w

VMPE

E

VMPE = p×MPE

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9

ExampleVariables• q = K1/3E1/2

• w = 2• r=1• p = 12• K = 8 (fixed)

Capital is fixed, so we can re-write the production function as:

• MPE = E-1/2

• VMPE = 12E-1/2

• Profit Maximization: VMPE=w

ProfitΠ=pq(E,K)-wE-rK

Profit maximization in the short-run:VMPE=w -> p×MPE=w

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Reconciling Different Conditions for Profit Maximization

Econ 1p = MC

Econ 139VMPE = wp × MPE = w

MPE = ∆q / ∆E

∆q / ∆E : how much more output firm gets from additional unit of labor.

∆E / ∆q: how much more labor firms needs to produce an additional unit of output.

p × (∆q / ∆E) = wp = w × (∆E / ∆q) = MC

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Labor Demand in the Long Run• Two conditions must hold in the long run:

– VMPE =w -> p×MPE=w– VMPK=r -> p×MPK=r

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ExampleVariables• q = K1/3E1/2

• w = 2• r=1• p = 12

Profit Maximization:• MPE=(1/2)K1/3E-1/2

• MPK=(1/3)K-1/3E1/2

• 6K1/3E-1/2 =2• 4K-1/3E1/2 =1

ProfitΠ=pq(E,K)-wE-rK

Profit maximization in the long run:p×MPE = w p×MPK = r

Solve for K and E.

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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.

E

W

DSR

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Why does the labor demand curve slope downward?

• Substitution effect: Describes how input demand changes as the relative price of the inputs changes, holding output fixed.– If wages increase, firms may want to substitute out of labor

and into other inputs such as capital.

• Scale effect: Describes how input demand changes as output changes, holding the relative price of inputs fixed. – If wages increase, firms may want to scale back production

(see next slide).

• Both of these effects cause the quantity of labor demanded to drop.

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Why wage changes lead to a scale effect:

q

MC1$

p

q1*

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

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Effect of Wage Change on the Quantity of Labor Demanded

Increase in the Price of Labor

Scale Effect

Substitution Effect

Decrease in the Price of Labor

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Elasticity of Labor DemandHow sensitive is the quantity of labor demanded to a change

in wages?

E

w

D

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Why do we care about the elasticity of labor demand?

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In order to understand the elasticity of labor demand, you have to understand

many other markets

Firms Households

Labor

Land Capital

supply

supply

supply demand

demand

demand

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Marshall’s Four Rules of Derived DemandOwn-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.

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Marshall’s Four Rules of Derived Demand, Continued

RULE 2: Relates to the production technology. When the technology is such that it’s easy to substitute for labor in production, then the substitution effect is big.

perfectcomplementselasticity of

substitution = 0

perfectsubstituteselasticity of

substitution → ∞

RULE 3: When the cost of employing labor is a large share of total costs.

In most cases, inputs are somewhere in the

middle

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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.

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Changes in the Demand for Labor

Wage

E

D

Decrease

Increase

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Factors that Affect Labor Demand

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

VMPE=p1 × MPE

E

w An increase in output prices.

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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.

VMPE=p × MPE

E

w An increase in the MPE

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KD

$

D

$

$

E

QLabor Market

Capital Market

Output Market

Substitution Effect (SE)increases the demand for

labor

Scale Effect (SCE)decreases the demand for

laborD

S1Supply decreases

??

S23. Change in the price of other inputs.

Example: Supply of capital decreases, leading to an increase in the price of capital.

S2

S1

Factors that Affect Labor Demand

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Gross Substitutes and Gross Complements

r increases

Labor demand decreases

Labor demand increases

w increases

Capital demand decreases

Capital demand increases

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Labor Demand When the Labor Market Is Not Perfectly Competitive

• If a market is characterized by monopsony, it means that there are many sellers and only one buyer.

• In the case of the labor market, it means that there’s only one firm that buys labor. – Prototypical example: a coal mine in a remote location.

• However, the most important feature of a monopsony is that if a firm wants to hire more workers, it must raise wages.

• This could happen if there are – Mobility costs– Firms have to pay workers higher and higher wages as the

firm gets bigger to prevent the workers from shirking.

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Differences in Labor Supply Curves Under Perfectly Competition and Monopsony

S

S=W

Competitive Labor Market

Monopsony

L L

$ $

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

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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 = MCE.

• However, the MC of hiring a worker does not equal w.

• Why? Because when the monopsonist hires an additional unit of labor, it must increase the wages it pays to all workers.

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Example of why MC increasing• 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 =

• (=$32 for 11th worker plus $20 for extra $2 paid to 10 original workers)

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Graphically

E

w

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Profit Maximization

E

w

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

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

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Comparison with Perfect Competition

E

w

S

MCE

VMPE

E*VMPE = MCE

w*

Fewer people are hired than in a perfectly competitive market and wages are lower.

This is because the marginal cost of hiring an additional worker is higher for a monopsonist than for a perfectly competitive firm.

Workers worse off relative to perfectly competitive labor market.

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Supplemental Reading 3Kahn, Lawrence,

“The Sports Business as a Labor Market Laboratory”, p76-p83.

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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– The greater is a league’s monopsony power, the lower will be

player salaries.– Players will be paid below their VMPE.

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Salaries of Major League Baseball Players, 1876-1920

1876: Start of NationalBaseball League

1879: Reserve Clause

1882: Start ofAmerican

Association

1891: American Association Ends

1901: Start of American League

1903: Start of Major League

1913: Startof Federal League

1915 Endof Federal

League

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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)– VMPE = p × MPE

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

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Labor Demand Application: Minimum Wage Laws

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Minimum Wage Laws

• Basic Facts• Federal minimum wage is $5.15/hour.• California minimum wage is $6.75/hour.• 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.

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The Real and Nominal Value of the Federal Minimum Wage, 1970-2000

$0.00$1.00$2.00$3.00$4.00$5.00$6.00

1970 1975 1980 1985 1990 1995 2000

Year

1982

Dol

lars

Nominal Min.WageReal Min Wage

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Theoretical Effect of Minimum Wage Laws

Perfect Competition:

• Minimum wages are a type of price floor.

• Effectively change supply curve.

• Decrease employment.

• Extent to which demand drops depends on the elasticity of labor demand.

$

E

D

S

w*

E*

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Monopsony and Minimum Wages

Employment

$ MCE

S

VMPE

E*

w*

When minimum wage laws are implemented in a monopsonistic market, then employment may actually increase.

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Criticisms of the Minimum Wage

• It only helps teenagers.• It causes unemployment.

• Are these criticisms valid?

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Who Earns the Minimum Wage?(Age Groups)

One third are teenagers.

Almost one half are over the age of 25.

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Who Earns the Minimum Wage?(Relationship in Household)

About 25% are heads of a households.

About 35% are children.

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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”.

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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

misleading.

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What is the Effect of the Minimum Wage on Employment

3. Other changes in the economy also affect employment.

D

Sw

EE*

w0

min wage

Emin50

Need Variation!Sources of Minimum Wage Variation:

State to state variation in the nominal and real value of the minimum wage. Can relate state variation in real value of minimum wage to state variation in employment rates.

Time series variation in nominal and real minimum wage. Can relate variation over time in the real value of the minimum wagewith variation over time in employment rates.

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State variation in minimum wage?

Two problems:1. States with high minimum wage laws might be states with

strong economies and, thus, low unemployment rates.2. Many states have minimum wages that are the same as the

Federal minimum wage.52

Time Series VariationReal Value of Minimum Wage and Average Wages

of Manufacturing Production Workers

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Teenage Employment Rate With Dates of Minimum Wage Changes

Problem: Employment fluctuations large compared to employment fluctuations that you would expect from minimum wage increases.

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Study DesignRandomized Experiment

• What would be the ideal way to study the effect an increase in minimum wage on employment?

• How might a doctor test the effectiveness of a new drug?

• Why would the doctor have a control group?

• How would you design a randomized experiment to study the effect of a minimum wage?

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Study by Card and Krueger• Can’t conduct a randomized experiment.

• Alternatively, use “natural experiments”. Prior to April 1992, the minimum wage in NJ and PA is $4.25/hourApril 1, 1992 NJ raises its minimum wage to $5.05/hourThe minimum wage in PA doesn’t change.

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Study by Card and KruegerData Collection

• Survey 400 fast food establishmentsBurger King, Roy Rogers, KFC, Wendy’s etc.New Jersey and Pennsylvania

• Asked them number of full-time and part-time employees

• Before: March, 1992• After: December, 1992

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Difference-in-Difference Estimation

Difference

21.2(D)

23.3(C)

PA

21.0(B)

20.4(A)

NJDifferenceAfterBefore

Number of Full-Time Equivalent Non-supervisory Employees

Suggests that employment increased! 58

Implications of Card and Krueger Study

• Suggests that the labor demand curve is upward sloping.

• Monopsony?

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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

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What are we to make of minimum wage laws?

• Theoretically, they can reduce employment rates.

• But, not a lot of empirical evidence that increases in the minimum wage lead to lower employment rates.

• Still, not clear that increases in the minimum wage are the best means of fighting poverty.

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Living Wage Campaigns Currently Very Active

A total of 130 places have living wage ordinances and living wage campaigns are underway in another 119 cities, counties and universities.

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Selected Cities with Living Wages

CITY Living Wage Living Wage WithNo Health Benefits

Sacramento CA 9.33 10.87 Sebastopol CA 11.70 13.20 Port Hueneme CA 9.00 11.50 Lansing MI 12.09 12.09Orlando FL 8.50 11.20 Dayton OH 9.30 11.16 Arlington VA 11.20 11.20Prince George's County MD 10.80 10.80 Santa Fe NM 8.50 8.50

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Impact of Living Wage Law• Theoretical effects are complex because living wages only cover a

relatively small number of companies.– Covered sector– Non-covered sector

• Not a lot of evidence that living wage ordinances decrease employment.• Some evidence that they reduce poverty.

• Who really pays for living wage ordinance? Unknown.• To what extent might employers cut back on other benefits? Unknown.

• Still an area of active research.