BU EC 385 - PS#7: Labor Markets in Sports
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PS#7: Labor Markets in Sports (Chapters 8-10)I. Chapter 88.1 Suppose that the market demand for baseball players is perfectly inelastic (vertical) at 750 players. If the market supply increases due to an increase in the number of available international players, show using a graph how wages will change as a result.Answer: If the market demand is perfectly inelastic, an increase in supply will lead to a decrease in player wages. The quantity of labor remains constant at L*, but wages fall from w to w due to the increase in supply. See Figure 8.1A.Figure 8.1A8.2 Suppose that there are two types of players, good and medium. The team demand curve for top-quality players is Q  27  5w, and the market supply of top players is Q  4w, where w is the wage in millions of dollars how many top-quality players will the team hire? What will they be paid?Answer: To solve, set the quantity demanded equal to the quantity supplied.8.3 Use a graph similar to Figure 8.5 to show the effect on league salaries of(a) An increase in the number of players available.(b) A decrease in television revenues due to fan preferences for drama shows.(c) A minimum salary set above the equilibrium wage.Answers: For parts (a) and (b), the graph should show the appropriate shift in the supply or demand curve.(a) The supply curve shifts rightward, increasing quantity and decreasing the equilibrium wage.(b) The demand curve shifts to the left (due to the decrease in demand for output). The equilibrium quantity and wage both fall.(c) See Figure 8.2A. The wage increases, but employment decreases.Figure 8.2A8.4 Based on the following player statistics, compute the Wins Score values. Assuming the players have equal star power to attract fans and players are rewarded only based on Win Score values, which player deserves to be paid the most? Who should be paid the least? How would you answer change if players were only rewarded for scoring?Answer: Win score  points  rebounds  steals  1/2 blocked shots  1/2 assists  field goal attempts  1/2 free throw attempts  turnovers  1/2 personal fouls. For the four players the win scores are:By win score, Fred is the best player, but if players are paid by their scoring average, Bob gets paid the most despite being the worst player by win score.8.5 Go to the basketball-reference Web site http://www.basketball-reference.com and find the statistics and salary of your favorite NBA player. Use the equation for a player’s MRP to determine what this player is worth and compare it with his actual salary. Is he overpaid, underpaid, or accurately paid?Answer: Obviously this will all depend on what player you choose, but the technique is the same either way. The number of games a player is expected to win for his team is approximated by his win score  points  rebounds  steals  1/2 blocked shots  1/2 assists  field goal attempts  1/2 free throw attempts  turnovers  1/2 personal fouls. Then according to Berri, each win is worth $1.67 million to his team.Take Kevin Durant for example. In 2008-2009, Durant averaged 25.3 points, 6.5 rebounds, 1.3 steals, 0.7 blocks, 2.8 assists, 18.8 field goal attempts, 7.1 free throw attempts, 3.0 turnovers, and 1.8 personal fouls. His win score  25.3  6.5  1.3  (1/2) 0.7  (1/2) 2.8  18.8  (1/2) 7.1  3.0  (1/2) 1.8  8.6. At $1.67 million/game this results in a MRP of $14.4 million. Durant “only” earned $4.48 million during the season, however, suggesting that he was underpaid by about $10 million in the season. This should come as no surprise since Durant was only a second-year player and had not yet earned free-agency. Since the Supersonics/Thunder had exclusive rights to his services, they are able to underpay him for his work.8.6 Use a labor supply and labor demand graph to show why salaries in the NBA went down in 2009–2010. Explain why the curves moved the way they did.Answer: As the country fell into recession, the demand for NBA tickets, and hence the demand for NBA players fell. The demand curve shifted to the left, lowering price.8.7 Explain and show using a graph why, at any given wage, a monopoly firm will hire less labor than the total employment if the industry were competitive.Answer: See Figure 8.4 in text. Assume that output is a direct function of labor and that cost is a direct function of wage. Both monopolists and perfect competitors set MC (equal to wage here)  MR. For perfect competitors, however, MR  P while MR  P for monopolists. Therefore, a monopolist will always produce less output at a given MC than a perfect competitor. Since output is a function of labor, lower output means lower employment.8.8 Using a graph, show what happens to player effort in a tournament if the marginal cost-of-effort curve shifts upward.Answer: See Figure 8.4A. If the marginal cost of effort increases, the marginal revenue (prize difference between, for example, first and second) must also increase in order to get the player to elicit the same level of effort E*. With no increase in the reward, the player’s effort would fall to E.Figure 8.4A8.9 Show what would have happened to the Lorenz curve in Figure 8.11 if Serena Williams, Darina Safina, and Svetlana Kuznetsova had all lost in the first round of the U.S. Open in September 2009.Answer: The curve would be less bowed than before. These top players would have earned less money on the season by not performing well in a top-paying tournament. Lesser players would have received the earnings instead leading to a more even distribution of income and a less bowed Lorenz curve.8.10 Use the supply and demand model to explain why top athletes are paid less than top celebrities.Answer: Here are two possible reasons. First, celebrities could have a higher marginal revenue product than athletes. If Steven Spielberg’s movies sell more tickets than Roger Federer’s tennis matches then Spielberg is likely to have a higher income than Federer. A second reason would be that there is a larger supply of good athletes than celebrities. For example, Alex Rodriguez is paid well because he can hit the ball 400 feet, but there are reasonably large number of other players who can hit the ball nearly as well. Julia Robert is paid well because she is Julia Roberts. Therefore, it is arguable that Joe Mauer is a closer substitute for A-Rod than Scarlett Johansson is for Julia Roberts. Thus, with few available substitutes,

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