R.E. McCormick, R.D. Tollison J. of Economic Behavior Org. 44 2001 201–219 213
discarding the mixed situation. We estimated the playing time equation to determine if there was a propensity for white coaches to favor white players or black coaches to favor black
players by including a dummy for the race match variable. In this specification, a player actually plays less, if he is the same race as his coach, but this result is not significant
the t ratio is −1.193 and the coefficient is small, less than half-a-minute per game. This result could be driven by the large portion of black players who play for white coaches.
Consequently we estimated this effect separately for black and white coaches. The basic result persists that black players play more, but there is no significant difference between
coaches in this regard. Both black and white coaches play black players more, other things the same.
6. A model of wage determination with racial discrimination by customers
Existing models of customer discrimination routinely employ an asymmetric approach. Some members of a majority group do not like members of a minority group. Here, we
develop a more complete model where both groups in the model are biased. Suppose that there is customer-driven racial discrimination in professional basketball. That is, some white
fans prefer to watch white players, and some black fans prefer to watch black players, other things the same. The remaining white and black fans are color blind. Furthermore, assume
that discrimination declines by both whites and blacks as the number of preferred players is hired by a team. That is, the whites who care about race care less at the margin when the
team is predominately white, and similarly for black fans. In this world, the actual impact of discrimination on hiring depends on the relative portions of black and white fans, assuming
that income, preferences specifically, discriminatory preferences, and other factors are constant across the two groups.
Consider a white fan attendance function A
w
= f G, W, P
w
1 where the number of white fans who attend A
w
, the function of quality of play games won G, the number of white players on the team W, and the number of potential white
fans in the area P
w
. Similarly, the black fan attendance function is A
b
= f G, B, P
b
2 where P
b
represents the black population in the community. We assume that white atten- dance increases with the number of white players, but at a decreasing rate.
23
That is, ∂A
w
∂W 0 and ∂
2
A
w
∂W
2
0. And similarly for blacks, attendance increases as the number of black players increase, but at a decreasing rate.
Both attendance equations are positive functions of the respective populations in Fig. 1. As the white or black population in the area increases, the relevant attendance function
shifts up. The original white attendance function is drawn with population equal to P. When
23
We employ a continuous characterization of the model under the presumption that a team can alter the number of whites and blacks over the course of a season to approximate a continuous process. That is, the twelfth player
on a team can be white for some portion of the season and then be replaced with a black player.
214 R.E. McCormick, R.D. Tollison J. of Economic Behavior Org. 44 2001 201–219
Fig. 1. Attendance, racial composition, and population.
the white population in the relevant market increases to P
′
, the attendance function shifts up.
The NBA restricts roster size by fiat. The number of blacks on the team, B, plus the number of whites, W, sums to a constant, k. Total attendance, A
t
, is the sum of white and black attendance, A
t
= A
w
+ A
b
. The derivative of total attendance with respect to white players on the team is: ∂A
t
∂W = ∂A
w
·∂W − ∂A
b
·∂B . Naturally, attendance is
maximized when the slopes of the two attendance functions are equal see Fig. 2. This point obviously depends on the relative proportions of whites and blacks in the community
Fig. 2. Attendance and racial composition.
R.E. McCormick, R.D. Tollison J. of Economic Behavior Org. 44 2001 201–219 215
Fig. 3. Wage gap between black and white players.
and their respective attitudes toward each other. The optimal racial composition of the team is a function of the racial composition of the community.
24
Consider Fig. 2. In general, the derived demand for black and white players of comparable skills will not be the same. Suppose the team is all black. Switching a white player for any
black player induces an increase in white attendance that is not completely offset by a loss of black customers. The value of the marginal product of white players is greater up to the
point where w
∗
of them are hired. After that point, the increase in white attendance from switching a white player for a black player reduces total attendance as the increase in white
attendance is dominated by the loss of black fans. Now consider Fig. 3. Here, we have drawn the wage gap as the racial composition changes
from an all-black team to an all-white team. The hypothetical gap between the wage paid to a white player of certain skills lies above the wage that the firm would be willing to pay
to a black player of similar skills, but that gap decreases as the whiteblack population ratio decreases towards one. As the ratio of white-biased fans increases relative to the number of
black-biased fans, w
∗
and the point of no wage gap moves to the right.
25
The critical point is that the wage gap vanishes at the attendance maximizing number of white players, w
∗
. When there are both black and white fans who are racially biased, the profit-maximizing
team erases the gap between races by adjusting the proportions of white and black players. Accordingly, while we believe that racial prejudice can affect team composition, so long
as the team is neither all white or all black, there can be no wage differential at the margin between players of equal abilities based on skin color. On these grounds, we are inclined
to reject the racial discrimination explanation for any wage differentials between black and white players. Put another way, when the team has attained the correct racial composition,
the owner is indifferent about the skin color of two players of similar abilities.
26
24
Of course, it is revenues and not attendance that matter, but absent a ticket price discrimination scheme across races, revenues are a monotone function of attendance.
25
There is no theoretical reason that w
∗
must lie to the left of k, and hence we cannot conceptually argue that we should observe no wage gap based on racial discrimination.
26
Our model should not be interpreted to mean that fans only care about player skin color. Of course, they also enjoy performance and winning. Thus, we are speaking about adjustments at the racial margin. The question of
average levels of black and white players depends on many other things including their relative supply in the economy.
216 R.E. McCormick, R.D. Tollison J. of Economic Behavior Org. 44 2001 201–219
7. Odds and ends
