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.  We did this one for homework.

3.  We did this one for homework.

4.    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. 

5.    See above.

6.    We did this one in class.

7.    See Figure 8.4 on page 251 in the text. Of course, you'll have to add in a labor supply curve.

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

9.    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.

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

11.    This is for you to summarize.

12.    This is in the textbook.

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

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

15.    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.

16.    Think about the objectives of a labor union. What do they attempt to maximize? Wages? Employment? Total labor income (=WxL)?  If there is contraction, how will this affect the choice of W and L on the part of the union?

17.    MLB players may sue the League on antitrust grounds only if they decertify their labor union.

18.    This is in your notes.


20.    This is in your notes and the textbook.

21.    Google this study and see what bloggers are saying.

22.    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.

23.    We did this one as homework.

24.    Wage discrimination is defined as differences in pay, holding all productivity factors constant.  Thus, even though black players may earn more on average than white players, it could be that they should be paid even more if their productivity is higher compared to white players.

25.    Economists generally argue that compensation reflects the marginal revenue product of a worker.  If men and women tennis players generate differing MRPs, then there is no reason to expect that they be paid the same.  In principle, MRP could be measured through ticket sales, merchandise sales, and TV ratings.

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

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

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

29.    We did this one in class.

30.    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


University A

University B


Don’t Cheat


Recruit evenly
Both violate rules

B dominates

Don’t Cheat

A Dominates

Recruit evenly/Both
obey rules

31.    This is for you to ponder.

32.    (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.

33.    See #30 above for an example of the prisoner's dilemma.

34.    For you to ponder.

35.    Possible exam question.

36.    For the brave only.