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 non-discriminating 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 non-discriminating 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 non-French 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 non-discriminating 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) 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) 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) 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. BCS bowls generate greater revenue There are more non-BCS bowl games because of number of ‘bowl-eligible’ schools.
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.