Problem Set 3 Answers

1.    Are there position-specific stats that you can use?  Are there any "off-the-field" measures of popularity that would want to add?

2.    In conducting any sort of statistical test of a hypothesis, scientists that focus on the impact of X on Y will want to hold constant any other variable, such as Z, that may have an effect on Y also.  Thus, in trying to determine whether 2nd basemen earn more than shortstops, you would want to hold constant as many other variables as possible that might affect the earnings of these players. 

3.    See above.

4.    We did this one in class.

5.    See Figure 8.7 on page 260 in the text.

6.    Player salaries would decrease; team profits would increase; competitive balance would be unaffected; the length of player contracts would be reduced.

7.    The player should stay in college for an extra year if his income grows at a rate that exceeds the interest rate. When his income goes from $500,000 to $600,000, the rate of change in income is 0.20 (or 20%).  Because a 20 percent return exceeds the 8 percent interest rate, the player should stay in college.

If there is a 50 percent chance that the player would make $500,000 rather than $600,000, then the expected earnings would be $550,000.  This translates into g = 10%.  Because 10 percent exceeds 8 percent, it still pays for the player to remain in school.

8.   Use the tournament model of labor markets to explain the similarities.

9.    This is for you to summarize.

10.    This is in the textbook.

11.    By some estimates, FOA has done more to contribute to escalating player salaries than free agency.  Can you explain why?

12.    When demand for the sport falls, the demand for labor falls as well. With a constant wage and falling demand, the magnitude of the deadweight loss increases. See Figure 9.2 below. The original deadweight loss is the area efg. The new deadweight loss is area abc.

13.    Highly unlikely.  What would be the benefits from unionization for individual players?  What would be the costs?

14.    The McNeil decision increased the players bargaining power because it gave the players a significant legal victory over owners’ attempts to limit player movement. Thus, the players’ minimum acceptable offer should shift to the right. To the extent that the owners recognize the decision as a defeat and reduction in their own bargaining power, it should shift their maximum acceptable wage to the right as well. Thus the contract zone should occur at higher wages.

15.    Check your notes and the textbook.

16.    For you to ponder.

17.    This is in your notes.

18.    False, even under the proportionality standard, if men and women are not represented equally in the broader student body, then proportional spending would not result in equal spending.

19.    We did this one as homework.

20.    The NCAA acts as the cartel enforcer.  By issuing penalties for rules violations, the NCAA can keep member schools, and conferences, in line.

21.    Consider the decision to use steroids as an example of the prisoner's dilemma.

22.    If pecuniary compensation is legalized, how would other forms of educational remuneration be affected?

23.    The supply of potential college players available to each division would not change, but the quantity supplied likely would. Prohibitions against scholarships act as a price ceiling. Allowing payments to Division III players would have the same effect as the removal of a price ceiling. If many Division III schools felt compelled to offer generous bonuses to recruits it could result in a prisoners’ dilemma. That is, each school would fear that if it did not offer bonuses, it would suffer in recruiting. Thus, all schools may be forced to offer the bonuses, increasing payments to players at the Division III level overall, but leaving the relative quality between Division III schools unchanged.

24.    If each school is afraid that the other school may commit a violation, it will have an incentive to violate NCAA rules as well or risk losing the recruit

25.    This is for you to ponder.

26.    (a) An increased risk of a career ending injury should shift the student’s incentives away from investing in athletics towards increased investment in academics. For those who continue to seek a professional career, it will increase the likelihood of turning pro before finishing college, thereby diminishing both forms of training.

(b)  As the probability of success in professional athletics increases, the expected returns from an investment in athletic training also increase. This would lead to greater investment in athletics and less investment in academics.

(c)  An increase in the cost of college tuition would increase the probability that an athlete may seek athletic training outside the collegiate ranks, such as in a minor league if the individual must pay some or all of the tuition. If the student still attends college, and receives a scholarship that pays full tuition, there is no incentive to change his or her behavior.

(d)  An increase in the demand for professional sports increases the equilibrium quantity and salary of professional athletes, thereby increasing the probability and profitability of a professional career. Thus the expected gains from investing in athletics increases, and the student would shift their efforts away from academics towards sports.

27.    See #24 above for an example of the prisoner's dilemma.

28.    For you to ponder.

29.    For the brave only.