Homework 4 Solutions Guide
Economics of Sports
Fall 2013
Q1 (a)
Suppose that the supply of both Hispanic and
white pitchers (of equal quality) were perfectly
elastic. Using supply and demand graphs, show
the number of each player type hired by an
owner with a taste for discrimination against
Hispanics and those hired by a nondiscriminating owner.
Q1 (a)
We must first identify
equilibrium in the white pitcher
market. As supply of white
pitchers is perfectly elastic, it is a
horizontal line with a slope of
zero. The height of this line
determines the salary of white
pitchers. I have indicated the
equilibrium white pitcher salary
as P* and the equilibrium
quantity as Q*.
Q1 (a)
The Hispanic pitcher market is
diagrammed here. I have
assumed that the Hispanic
pitcher supply is perfectly
elastic at the same salary as
equally qualified white
pitchers. The demand curve
for non-discriminating owners
is labeled “Dn” while the
demand curve for
discriminating owners is
labeled “Dd.” The
discriminating owners are not
willing to pay P* to a Hispanic
pitcher. This implies all
Hispanic pitchers are
employed by nondiscriminating owners (Q*H)
who pay P*. All remaining
pitchers are white and are
hired by both owner types at
P*.
Q1 (b)
Use Becker’s model to explain why sponsors
who discriminate will likely experience lower
profits for doing so.
Becker’s “taste for discrimination” model
suggest that as people who discriminate
maximize utility, their willingness to pay in order
to indulge their tastes has an impact on markets.
Q1 (b)
Suppose we have owners that
discriminate against nonFrench speaking players. This
taste for discrimination results
in greater demand for French
speaking players– and
subsequently a higher
equilibrium wage. I have
identified this wage as PF.
Q1 (b)
As not all owners are
interested in hiring non-French
speaking players, the demand
curve for the non-French
speaking players is shifted in to
the left relative to the demand
for French speaking players.
The market result is a lower
salary (Pn) for the non-French
speaking players relative to the
French speaking player salary
of PF.
The result is that owners who
have a taste for discrimination
will end-up with higher costs to
operate. Greater production
costs will result in lower profits
for the same level of
production as nondiscriminating owners.
Q1 (c)
Suppose the competitive salary in independent
league baseball is $3,500,000 per season. One
team owner has a taste for discrimination
against all nonwhite players. Her coefficient of
discrimination against Latinos is 0.2, and her
coefficient of discrimination against blacks is
0.18. What would she consider the salaries of
people who are members of these two groups
to be? If the supply of players were perfectly
elastic, how many of each group will be hired?
Q1 (c)
Employer Type
Latino Equivalent Salary
Black Equivalent Salary
Non-Discriminating
Employer
$3,500,000
$3,500,000
Discriminating Employer
$4,200,000
$4,130,000
Given the supply of players from each group is perfectly elastic (at $3,500,000), the
employer indulging in discrimination will hire zero Latino and Black players. This is
because the Latino Equivalent Salary and Black Equivalent Salary exceeds the
$3,500,000 salary of players from other groups. Non-discriminating employers would
be indifferent and hire players from all groups.
Q1 (d)
Use what you know about the prisoner’s
dilemma to explain why the English Premier
League teams such as Arsenal have so many
foreign players even when, as a group, the
Premier League teams agree that they want to
limit the number of foreign-born players.
Q1 (d)
Arsenal Rival (R)
Hire Foreign
Exclude Foreign
Hire Foreign
A: -10
R: -10
A: 40
R: -50
Exclude Foreign
A: -50
R: 40
A: 10
R: 10
Arsenal (A)
In the prisoner’s dilemma game represented in the table above, we see that the
Arsenal always does better by hiring foreign born players. [The Arsenal earns -10
(better than -50) by selecting the ‘Hire Foreign’ strategy when the rival selects ‘Hire
Foreign.’ The Arsenal earns 40 (better than 10) by selecting the ‘Hire Foreign’
strategy when the rival selects ‘Exclude Foreign.’] The corollary is also true for the
Arsenal Rival. The nash equilibrium is for both teams to select the ‘Hire Foreign’
strategy. The ‘dilemma’ aspect is that both teams would be strictly better-off in
another outcome of this game (specifically, the outcome where both teams play
‘Exclude Foreign’); however, the strictly better outcome is not sustainable.
Q2 (a)
Use MC and MR curves to show why the BCS
schools claimed a larger share of bowl and TV
revenues than non-BCS schools. NOTE:
Submitted answers without graphs will receive 0
points no matter how well-written or described.
Q2 (a)
BCS bowls generate
greater revenue
There are more non-BCS bowl games
because of number of ‘bowl-eligible’
schools.
The BCS is limited to 6
games. So, the MCBCS
becomes a vertical line at
6 bowls.
The BCS commands higher
pay-outs to participating
teams, as the bowls
involve the schools with
the best performance
throughout the season.
Thus, the MCBCS is strictly
higher than the MCOther.
MRBCS is greater than
MROther at every quantity
of bowl games because
there is a greater demand
for the top-rated teams.
Q2 (b)
Use human capital theory to explain why colleges
might not pay students their full marginal product.
Human capital theory posits that human capital
refers to the set of skills that contribute to a
person’s productivity. Individuals can enhance their
productivity by expanding their stock of skills and
knowledge. These stocks can be increased by
investments in (1) general training; and (2) specific
training.
Q2 (b)
While college athletes have significantly restricted
money wages, the human capital theory suggests
that they have the opportunity to significantly
enhance their stock of skills and knowledge through
formal coursework. Additionally, development in
the athlete’s sport may make the athlete attractive
to professional sports teams. Thus, the college
need not pay the athlete his or her entire marginal
product in money wages as the athlete is willing to
attend the college for the human capital
investment.
Q2 (C)
How might failing to graduate from college be an optimal
investment in one’s human capital?
As suggested in the previous question subpart, human
capital includes both general and specific skill sets. If a
student has had the opportunity to expand his or her
skillset enough through specific training before earning a
degree, this skillset may be so valuable to employers that
a wage high enough is offered to induce the student to
forgo the remainder of his or her academic studies. It
could be very expensive to remain in school if the student
must surrender this high potential wage.
Q2 (d)
Use human capital theory to explain why
graduation rates for women’s basketball players
are so much higher than those for men’s
basketball players.
Men have significantly expanded opportunities to participate in professional
basketball leagues relative to women. This suggests that college basketball affords
men the opportunity to develop skillsets that are attractive to professional teams.
Once they demonstrate these high abilities, professional teams are willing to pay the
male players significant salaries. Given this is not true for women, the general
training women receive during college is much more valuable. As the women tend
not to become professionals in their sport but in their classroom training, the degree
becomes a larger prize for them. As a result, greater rates of women earn degrees as
greater rates of men become professional basketball players.