Introduction to Labor Markets and Discrimination
Spring 2010
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Relevant Readings
BFW Chapter 1 including Appendix 1A
KW Chapter 12
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Labor Markets and Discrimination
Outline
1
Labor Market Basics
Labor Demand
Labor Supply
Labor Market Equilibrium
Basic Model Issues
2
Discrimination
Definitions
3
Deviation from Market Equilibrium
Four Cases
Examples
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Labor Market Basics
Factors of Production
Labor is a factor of production
Factors of production are bought and sold in “factor markets” at “factor
prices”
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Labor Market Basics
Factors of Production
Factors of production differ from goods
Derived demand - demand for a factor of production is derived from
the firm’s output choice
Factor prices and derived demand determine how total income of
economy is divided - factor distribution of income
Roles are reversed from goods market:
Firms determine demand
Households determine supply
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Labor Market Basics
Factor Price: Wage
Wage is a common signal to both supply (HH) and demand (firm) side:
Demand-side: input price to production
Supply-side: income or source of purchasing power
Real wage: purchasing power of wage =
wage in current
price level
$
Price level is determined by a price index
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Labor Market Basics
Labor Demand
Labor Demand Basics
Firms decide how many workers to employ, given market wages and
technology
Firms pick the employment level that maximizes profit
Assume perfect competition: individual firm cannot influence output price
Output price takers
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Labor Market Basics
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Labor Demand
Labor Demand Basics
Marginal product of labor (MPL ): additional output from employing
one more worker
Diminishing marginal returns: MPL is decreasing as labor increases
(fixed capital)
Value of the marginal product of a factor (VMPL ): the monetary
value of the additional output from employing one more worker
VMPL = p ∗ MPL
where p is the price of the output sold by the employer
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Labor Market Basics
Labor Demand
Graphical Depiction of Total and Marginal Product
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Labor Market Basics
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Labor Demand
Optimal Labor Demand
Profits maximized when marginal benefit equals marginal cost
Marginal benefit of labor: VMPL
Marginal cost of labor: wage (w )
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Labor Market Basics
Labor Demand
Optimal Labor Demand
Intuition: Profit-maximizing and price-taking producer will hire additional
workers only if marginal value is greater than wage rate.
Hire until the value of the marginal product of the LAST employee is equal
to the wage rate
VMPL = w
Value of marginal product curve is the firms derived demand curve for labor
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Labor Market Basics
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Labor Demand
Optimal Labor Demand
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Labor Markets and Discrimination
Labor Market Basics
Labor Demand
Example
Handout 1: Derive the amount of labor that maximizes profits
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Labor Market Basics
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Labor Demand
Example
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Labor Market Basics
Labor Demand
Mathematical Derivation
Profit = π = Revenue - Cost
Revenue = price of output * output = p ∗ f (x)
p = market price of output
f (x) = production function
Production function: how much output you can produce for a given
level of inputs x
Cost = C = w1 x1 + w2 x2 + ... + wn xn = Σi wi xi
xi = factor i
wi = factor price for factor i
Suppose only factor is labor (L) then:
π = p ∗ f (L) − w ∗ L
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Labor Market Basics
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Labor Demand
Mathematical Derivation cont.
Goal: Find quantity of labor that maximizes profits
Calculus approach: Take derivative of profit with respect to L and set
equal to 0
p∗
∂f (L)
−w =0
∂L
p ∗ MPL = w
VMPL = w
Hire until wage equals value of marginal product of labor - same as
intuition provided earlier
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Labor Market Basics
Labor Supply
Labor Supply Basics
Workers decide how much and where to allocate their time given market
wages
Choose occupation and number of hours that maximizes utility
Workers evaluate marginal value of time
Value both consumption and leisure time
Work additional hour if marginal utility from consuming goods purchased
with hourly wage exceeds marginal utility of an additional hour of leisure
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Labor Market Basics
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Labor Supply
Labor Supply Basics cont.
Maximize utility (U) which is represented by an indifference curve
“Map” of consumer preferences
All combinations of goods or time allocations that make a person
equally better off
Time allocation budget line: tradeoff between leisure and income used
for consumption of goods
Given the time allocation budget line, household will choose leisure and
work levels that maximize utility (i.e. highest indifference curve)
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Labor Market Basics
Labor Supply
Time Allocation Example
Suppose wage rate is $8 per hour and have 80 hours a week to allocate
between work and leisure.
If devote all time to work get $640 in income to purchase
consumption goods and 0 hours of leisure
If devote all time to leisure get no income for consumption
Optimal leisure and labor time determined by tangency of time allocation
budget line and utility curve.
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Labor Market Basics
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Labor Supply
Time Allocation Budget Line
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Labor Market Basics
Labor Supply
MRS
Marginal rate of substitution (MRS): the rate at which a consumer is
willing to give up one good in exchange for another good while
maintaining the same level of satisfaction
Slope of the indifference curve
MRS12 =
MU1
MU2
=
∂U
∂z1
∂U
∂z2
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Labor Market Basics
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Labor Supply
Utility Maximization
From the graph we can see that utility is maximized when the utility curve
is tangent to the time allocation line
Slope of utility = slope of time allocation line
MRS12 =
MU1
MU2
=w
MRS equal to the wage rate
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Labor Market Basics
Labor Supply
Labor Supply and Wage Increase
A wage increase does not necessarily increase hours of work
Two conflicting effects:
Substitution effect:
Change in the opportunity cost of leisure in terms of other goods
Relative cost of leisure increases when wage increases
Decreased leisure time and increased labor time
Income effect:
Consumer richer for each hour of work
Leisure is a normal good - increased consumption with income
Increased leisure and decreased labor
→ Total affect on hours of work indeterminant
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Labor Market Basics
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Labor Supply
Labor Supply and Wage Increase to $10
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Labor Markets and Discrimination
Labor Market Basics
Labor Supply
Labor Supply Curves
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Labor Market Basics
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Labor Market Equilibrium
Market Demand and Supply
Market demand for labor is the aggregate of individual firm demands at
each wage
As price increases for an input, the firm demands less of that input as
they substitute to a relatively cheaper input
As wage increases, substitute machines for labor
Market supply for labor is the aggregate of household labor supplies at
each wage
As wage increases, more potential workers enter the market and total
supply will increase
Typically do not have backward-bending market supply curves
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Labor Market Basics
Labor Market Equilibrium
Equilibrium: Supply = Demand
At w*, last worker paid the value of their leisure time, others paid
more than reservation wage
No unemployment at w*
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Labor Market Basics
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Labor Market Equilibrium
Potential Shifters
Demand Shifters
price of product (↑)
price of substitutes (↑)
MP of workers (education, experience) (↑)
demand for product (↑)
price of complementary inputs (↓)
Supply Shifters
population (↑)
taste for leisure (↓)
taste for home time (↓)
wages elsewhere (↓)
bad non-pecuniary aspects of job (↓)
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Labor Markets and Discrimination
Labor Market Basics
Labor Market Equilibrium
Curve Shifts and Equilibrium Effects
Demand shifts out → wage ↑ and labor ↑
Supply shifts out → wage ↓ and labor ↑
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Labor Market Basics
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Labor Market Equilibrium
Wage Determination Model
Using the demand and supply shift effects, we can predict how various
factors effect wages
Wage = f[output price (+), productivity (+), substitute output price (+),
complement price (-), good job attributes(-), bad job attributes (+),
competition (-), wages in other jobs(+)]
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Labor Market Basics
Labor Market Equilibrium
Stable Equilibrium
All persons willing to work at going rate are able to find employment and
all employers willing to hire someone at going rate are able to find workers
Since firms who maximize profits set VMPL equal to the wage rate,
equally productive individuals should earn the same wage
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Labor Market Basics
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Labor Market Equilibrium
Underlying Assumptions
1
People have rational preferences among outcomes that can be
identified and associated with a value
2
Individuals maximize utility and firms maximize profits
3
People act independently on the basis of full and relevant information
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Labor Market Basics
Basic Model Issues
Violations of Underlying Assumptions
People do not always behave rationally
People do not always make choices that maximize utility or profits
Lack of full information
Uncertainty
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Labor Market Basics
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Basic Model Issues
Violations of Underlying Assumptions cont.
Free markets operate in a frictionless market and have have no
discrimination
→ Discrimination is a market failure
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Discrimination
Discrimination
Discrimination is a departure from a freely functioning labor market
equilibrium
Wage no longer equals marginal productivity
Wage differentials does not imply discrimination
Compensating differentials (cover later)
Human capital differences (education, experience, etc.)
Discrimination can function on either side of the market:
Demand side: depressed output price or restricted marginal
productivity
Supply side: job rationing
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Discrimination
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Definitions
Discrimination Definitions
Websters Dictionary:
To make a distinction; to use good judgment
To make a difference in treatment or favor on a basis other than
individual merit
Discrimination, in this definition, can be viewed as positive or negative
Positive connotation - A discriminating person is someone who has
more information and uses this information to make their decision
Negative connotation - A discriminating person is someone who
knows less about the ability of individuals and uses information on
group characteristics to make decision
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Discrimination
Definitions
Discrimination Definitions
Dictionary.com:
Treatment or consideration of, or making a distinction in favor of or
against, a person or thing based on the group, class, or category to
which that person or thing belongs rather than on individual merit
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Discrimination
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Definitions
Discrimination Definitions
Economic Definitions
To offer different transaction terms to individuals based on
Group membership or attribute (antagonism, BFW pg 203)
Accurate knowledge of group differences (statistical)
Subjectively held opinions regarding relevant criteria (institutional or
unconscious)
When two equally qualified individuals are treated differently solely on
their group identity (gender, race, age, disability, etc.)
When two individuals with identical observed characteristics besides
group membership have systematically different outcomes
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Discrimination
Definitions
Sources of Discrimination
Access to skills and training
Segregation in schools
Barriers to entry (ex: cost)
Output price
Access to inputs
USDA withheld extension services to black farmers
Restriction of job entry
Unions
Occupational licensing restrictions
Quality of equipment
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Discrimination
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Definitions
Circumstance can be unfair, but NOT discrimination unless it has a group
dimension
Undervaluing a group, NOT an individual
Examples?
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Discrimination
Definitions
Discrimination versus Prejudice
Discrimination - Treating people differently based on innate
characteristics (discriminatory outcomes)
Prejudice - Dislike, distaste, or misperception based on innate
characteristics (discriminatory attitudes/feelings)
Prejudice may or may not cause discrimination
Discrimination may not be a result of prejudice
Examples?
Contrary to many legal matters, it is not the intent that matters, it is
the outcome that matters
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Discrimination
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Definitions
Profiling
Profiling - the use of specific characteristics, as race or age, to make
generalizations about a person, as whether he or she may be engaged in
illegal activity
Type of discrimination
Blacks more likely to be stopped, questioned or searched – racial
profiling
Profiling can occur without prejudice
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Discrimination
Definitions
Segregation
Segregation - separation of people on the basis of race
Discrimination can occur without segregation
Segregation can occur without discrimination
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Discrimination
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Definitions
Labor Market Discrimination
Wage discrimination - prices paid by employers for given productive
characteristics are systematically different for different demographic
groups
Occupational discrimination - members of specific group with the
same education and productive potential are forced in lower-paying
occupations or levels of responsibilities by employers who reserve the
higher-paying jobs for members of a different group
Occupational segregation does not imply occupational discrimination
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Deviation from Market Equilibrium
Deviation from Market Equilibrium
What factors would lead to wage differences across markets, groups, or
jobs?
Are wage differences evidence of discrimination?
When market is away from equilibrium, discriminatory job rationing is
possible.
Cases:
1
Wage setting union
2
Cyclical downturns
3
Compensating Differentials
4
Skill Differences
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Labor Markets and Discrimination
Deviation from Market Equilibrium
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Four Cases
1. Wage Setting Union
Union sets w > w ∗
H’ = notional demand
H” = notional supply
Demand side is constraining
the equilibrium
00
Unemployment rate = (H H−H
00
= fraction wanting to supply
labor at market wage but do
not have a job
0)
Only discrimination if access
to rationed jobs is preferential
for or against a group
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Deviation from Market Equilibrium
Four Cases
2. Cyclical Downturn
In recession, labor demand
falls to H’ at current wages
Reluctance to reduce nominal
wages (unions, contracts)
Who loses jobs?
Discrimination if layoffs are
based on favoritism or
preferential treatment of a
group
Discrimination more
prevalent in downturns and
less in upturns
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Deviation from Market Equilibrium
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Four Cases
3. Compensating Wage Differentials
Compensating differential: wage required to compensate a worker for
accepting a bad job attribute or the wage reduction a worker would accept
to get a good job attribute
Dangerous jobs
Undesirable jobs
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Deviation from Market Equilibrium
117
99
79
75
70
62
62
55
54
Four Cases
Nonfatal work related injuries
Most Injurious
Production Assistants
0.7
Data/sales workers
0.7
Structural metalworkers
0.7
Non-construction Laborers
0.6
Public transportation
0.6
attendants
Machine feeders and
0.5
off-bearers
Construction and extractive 0.4
trades helpers
Punching and stamping
0.4
machine operators
Construction laborers
0.4
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per 1000 workers
Least Injurious
Typists
Education administrators
Economist
Library clerks
Data processing
equipment repairers
Management analysts
Child care workers
Correctional institution
officers
Securities and financial
services salespeople
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Deviation from Market Equilibrium
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Four Cases
3. Compensating Differentials
2 occupations where one has preferable attributes
Workers in risky job need compensation → supply curve shifts
S = initial supply (wages equal)
S’ = supply with risk rating
Displaced workers from risky job obtain non-risky job at lower wage
Wage difference: w 00 − w 0 → does not necessarily imply discrimination
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Deviation from Market Equilibrium
Four Cases
4. Skill Differences
Human Capital: Skills embodied in the worker that improves labor
Examples: education, on-the-job training, knowledge
Suppose there are 2 jobs, one of which requires more schooling (ex:
business versus construction)
Worker will need to be compensated for additional schooling
Supply of business workers falls (shifts left)
Some workers shift to construction → supply shifts right
Additional skills raises workers’ marginal productivity so demand for
skilled workers also increases
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Deviation from Market Equilibrium
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Four Cases
4. Skill Differences
Wage differential = w 00 − w 0
Reflects differences in cost of skill acquisition and productivity
Discrimination only if unequal access to education or training
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Deviation from Market Equilibrium
Examples
Taxi Cab Situation
Consider a taxi driver driving down a one-way street late at night in a
dangerous part of town. Two people hail the cab at the same time but on
different sides of the street. Since it is a one-way street, their is no
difference to the cab-driver which side of the street a person in on. On the
left-hand side a little old lady hails the cab driver. On the right-hand side
a tall African American teenage boy wearing a hood hails the cab driver.
The taxi driver unhesitatingly picks up the little old lady.
Did the cab driver discriminate? Did the cab driver engage in racial
profiling?
Does it make a difference if the cab driver was a women or a man?
What if the cab driver had more information (neighborhood, recent
crime, knew one of the potential customers, etc.)?
What would you do?
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Deviation from Market Equilibrium
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Examples
Video Game Store
Suppose you are a cop in a large metropolitan area. You get a report that
a a video game store has been robbed. Witnesses saw someone leaving the
scene wearing a black baseball cap and heading towards the local grocery
store. You are in the immediate area and the grocery store agrees to lock
down the doors. You find four people wearing a black baseball cap:
Teenage girl
Teenage boy
Middle-aged man
Middle-aged woman
Suppose the optimal interrogation technique is to interview from least
innocent to most guilty. What order would you interview the four people
and why?
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Deviation from Market Equilibrium
Examples
Video Game Store cont.
Did you make your decision based on age or sex?
Would you consider it profiling if the police used age or sex as a
determinant of interview order?
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Deviation from Market Equilibrium
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Examples
Sells Representative
Handout 2 - Sales Representative Example
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Deviation from Market Equilibrium
Examples
Readings for Next Lecture
Regression Analysis:
BFW Appendix 7A (pgs 250-255)
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