# Differences in earnings and employment opportunities may arise

```Lecture 8: Labor Market Discrimination
Differences in earnings and employment opportunities may arise even among equally
skilled workers employed in the same job simply because of the workers’ race, gender,
national origin, sexual orientation, and other seemingly irrelevant characteristics. These
differences are often attributed to labor market discrimination.
1. The Discrimination Coefficient
Money, commonly used as a measuring rod, will also serve as a measure of
discrimination.
 If an individual has a &quot; taste for discrimination,&quot; he must act as if he were willing to
pay something, either directly or in the form of a reduced income, to be associated
with some persons instead of others.
 By using the concept of a discrimination coefficient (DC), it is possible to give a
definition of a &quot; taste for discrimination.&quot; It is parallel for different factors of
productions, employers, and consumers.
A DC represent a nonpecuniary element in certain kinds of transactions, and it is
positive or negative, depending on whether the nonpecuniary element is considered
 Discrimination is commonly associated with disutility caused by contract with some
individuals.
Money cost(return)
Employer
π
Employee
πj
Consumer
P
net cost(return)
π(1+di)
πj(1-dj)
P (1+dk)
Discrimation : di , dj ,dk &gt; 0
Nepotism : di , dj ,dk &lt; 0
(親戚主義，裙帶關係)
 This quantitative representation of a taste for discrimination provides the means for
empirically estimating the quantitative importance of discrimination.
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2. Employer Discrimination
There are two types of workers in the labor market: white workers and black
workers. We assume that black and white workers are perfect substitutes in production, so
that the production function can be written as:
(8-1)
q  f E w  E B 
Where q is the firm’s output, EW gives the number of white workers hired, and EB gives
the number of black workers hired.
A firm that does not discriminate will hire black workers up to the point where the
black wage equals the value of their marginal product, or:
(8-2)
WB  VMPE
Employment in a Discriminatory Firm
The employer acts as if the black wage is not WB, but is instead equal to WB  (1+d),
where d is the discrimination coefficient. The decision rule for an employer that
discriminates against blacks is:
Hire only blacks if WB  (1+d)&lt;WW
Hire only whites if WB  (1+d)&gt;WW
(8-3)
 As long as black and white workers are prefect substitutes, firms have a segregated
work force.
There are, therefore, two types of firms: “white firms,” and “black firms.”
Employers who have small discrimination coefficients will hire only blacks; employers
with large discrimination coefficients will hire only whites.
Dollars
Dollars
WB(1+d1)
WW
WB(1+d0)
WB
VMPE
EW*
VMPE
EB1
Employment
(a) White Firm
EB0
EB* Employment
(b) Black Firm
Figure 1. The Employment Decision of a Prejudiced Firm
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Discrimination and Profits
The relationship between the firm’s profits and the discrimination coefficient is
illustrated in Figure 2. The most profitable firm has a zero discrimination coefficient and
has profits of πmax dollars. This color-blind firm hires an all-black work force and EB*
workers. Firms with slightly positive discrimination coefficients still have an all-black
work force, but employ fewer black workers and earn lower profits. At some threshold
level of prejudice, given by the discrimination coefficient dW, the utility loss of hiring
blacks is too large and the firm hires only whites. As a result, profits take a dramatic
plunge (toπW dollars) because the firm is paying a much higher wage than it needs to.
Because all white firms hire the same number of white workers (or EW*) regardless of
their discrimination coefficient, all white firms earn the same profits.
Firms that discriminate lose on two counts: They are hiring the “wrong color” of
workers and/or they are hiring the wrong number of workers.
Dollars
πmax
πW
Black
Firms
0
White
Firms
dW
Discrimination
Coefficient
Figure 2. Profits and the Discrimination Coefficient
3. Employee Discrimination
The source of discrimination in the labor market need not be the employer, but might
instead be fellow workers. Suppose that whites dislike working alongside blacks and that
blacks are indifferent about the race of their coworkers. As we seen, white workers who
receive a wage of WW dollars will act as if their wage rate is only Ww  (1-d), where d is the
white worker’s discrimination coefficient.
A color-blind profit-maximizing employer would never have an integrated work
place. The employer would not hire both black and white workers because white workers
have to be paid a compensating wage differential, yet they have the same value of
marginal product as black. Hence, the employer will hire only whites if the white wage is
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below the black wage, and will hire only blacks if the black wage is below the white
wage.
Unlike employer discrimination, however, employee discrimination does not
generate a wage differential between equally skilled black and white workers.
Color-blind employers hire whichever labor is cheaper.
Note that employee discrimination does not affect the profitability of firms. Because
all firms pay the same price for an hour of labor, and because black and white workers
are perfect substitutes, there is no advantage to being either a black or a white firm.
4. Consumer Discrimination
If consumers have a taste for discrimination, their purchasing decisions are not based
on the actual price of the good, p, but on the utility-adjusted price, or p  (1+d),where d is
the discrimination coefficient.
As long as a firm can allocate a particular worker to one of many different positions
within the firm, consumer discrimination may not matter much.
If the firm cannot easily hide black workers from public view, however, consumer
discrimination can have an adverse impact on black wages. A firm employing a black
worker in a sales position will have to lower the price of the product so as to compensate
5. Statistical Discrimination
The concept of taste discrimination helps us understand how differences between
equally skilled blacks and whites (or men and women) can arise in the labor market. It
turns out that racial and gender differences will arise even in the absence of prejudice
when membership in a particular group (for example, being a black woman) carries
information about a person’s skills and productivity.
Statistical discrimination arises because the information gathered from the resume
and the interview does not predict perfectly the applicant’s true productivity. The
uncertainty encourages the employer to use statistics about the average performance of
the group (hence the name statistical discrimination) to predict a particular applicant’s
productivity. As a result, applicants from high-productivity groups benefit from their
membership in those groups, while applicants from low-productivity groups do not.
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6. Measuring Discrimination
How economists measure discrimination in the labor market. Suppose that we have
two groups of workers, say, male and female. The average male wage is given by W M,
while the average female wage is given by W F. One possible definition of discrimination
is given by the difference in mean wages, or:
(8-4)
W  W M  W F
A more appropriate definition of labor market discrimination compares the wages of
equally skilled workers. To simplify the exposition, suppose that only one variable,
schooling (which we denote by s), affects earnings. The earnings functions for each of the
two groups can then be written as:
Male earnings function: WM   M   M S M
Female earnings function: WF   F   F S F
(8-5)
The coefficient  M tell us by how much a man’s earnings increase if he gets 1 more year
of schooling, while the coefficient  F gives the same statistic for a woman.
The regression model implies that the raw wage differential can be written as:
W  W M  W F   M   M S M   F   F S F
(8-6)
The Oaxaca Decomposition
We can rewrite the raw wage differential as:

W   M   F    M   F S F   M S M  S F
Differential due to discrimination

(8-7)
Differential due to difference in skills
the second term in the equation arises because the two groups differ in their skills. The
first term in the equation arises because of this differential treatment of men and women
which is typically defined as discrimination.
 The raw wage differential can be decomposed into a portion due to differences in
characteristics between the two groups, and a portion that remains unexplained and
that we call discrimination.
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Dollars
Men’s Earnings Function
WM
W M*
Women’s Earnings Function
αM
WF
αF
SF
SM
Schooling
Figure 3. Measuring the Impact of Discrimination on the Wage
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