Homework 3 Solutions Guide

Economics of SportsFall 2013

Q1 (Chapter 7)

Suppose the demand for Cardinal’s World Series tickets is Qd=48,061-2.4P (for the purposes of this problem, we will suppose that fans do not care where they sit). The Cardinals play at Busch Stadium, which has a seating capacity of 46,861. The marginal cost of providing a seat to a fan is $0 for seats 0 through 46,861. At Qs=46,861, the marginal cost curve becomes a vertical line.

Q1 (a)

What would be the deadweight loss associated with a $20 tax on Cardinal’s World Series tickets?

If the Cardinal’s behaved as Price-Takers, we may identify the equilibrium quantity and price by setting Qs=Qd and solving for P.

46,861=48061-2.4PP=500

The equilibrium quantity is 46,861.

Q1 (a)Behaving as a Price Taker, the Cardinals are completely unresponsive to changes in ticket price. In this case, all $20 of the tax comes from the Cardinals. There is no deadweight loss to society as a result of the tax on World Series tickets.

The Cardinals do lose producer surplus (20*46,861), however, every penny lost by the Cardinals is received by Government. Hence, it’s not a social loss.

Q1 (b)

Define the Ramsey rule.The Ramsey rule is a tax that minimizes the deadweight loss imposed by the tax. Our text states specifically that the tax should be levied in inverse proportion to the price elasticity of demand for the good or service on which the government places the tax.

In our example, we see that we can achieve this “Ramsey” criterion of minimizing deadweight loss by levying a tax in inverse proportion to the price elasticity of supply as well if the firm was a price taker.

Q1 (c)

Based on the Ramsey rule, would this be a good product to tax?

Given the goal is to minimize deadweight loss, we know we cannot do better than taxing this good as there is zero deadweight loss.

Q1 (extension)If the Cardinals behave as a monopolist, the profit-maximizing price with no tax is:

20,025.42-0.83Q=0Q=24,030

At 24,030 tickets, fans are willing to pay $10,012.71 per ticket.

Consumer surplus with no tax is: 0.5*(20,025.42-10,012.71)*24,030= $120,302,710.65.

Producer surplus with no tax is:24,030(10,012.71)= $240,605,421.30.

Q1 (extension)With a $20 tax (let’s say paid by the Cardinals), the marginal cost curve shifts vertically higher to $20 over the range from 0 to 46,861 seats.

We see that MC=20 now for the Cardinals. Profit maximization occurs when20,025.42-0.83Q=20 orQ=24,006.

The corresponding ticket price is $10,022.92. (Ticket prices rise more than the tax amount).

Consumer Surplus is:0.5*(20,025.42-10,022.92)24,006=$120,060,007.50.

Producer Surplus is:(10,022.92-20)24,006=$240,130,097.52

Government Tax Revenue is:$20(24,006)=$480,120

Q1 (extension)ΔConsumer Surplus=120,060,007.50 -120,302,710.65=-$242,703.15.

ΔProducer Surplus=240,605,421.30-240,130,097.52=-$242,703.15.

ΔGovernment Tax Revenue=480,120-0=+$480,120.

Deadweight Loss:+$5,286.30.

A very small loss as a percentage of overall social welfare from this market.

Q2 (Chapter 8)

Page 261 of our text presents an equilibrium in the labor market for professional athletes in a particular sport (figure 8.5). On a similar graph, indicate the impact of the following effects:

Q2 (a)An increase in the number of players available.

An increase in the number of players available results in a rightward shift of the supply of players (more players at every salary level). The result according to the model is a lower equilibrium salary level for players and more players participating in the league.

Q2 (b)A decrease in television revenues due to fan preferences for reality tv shows.

A decline in interest in the league will result in a decrease in the demand for players. This results in a leftward shift of the demand for players. According to the model, this decline in demand will push player salaries down and result in fewer players participating in the league.

Q2 (c)A minimum salary set above the equilibrium wage.

The model predicts we will experience a perpetual surplus of players at the minimum salary. The Quantity supplied of players will exceed the Quantity demanded of players. There will be fewer players participating in the league as a result of the minimum salary rule.

Q3

Economists Berri, Schmidt and Brook estimated that a NBA playrs contribution to a team’s wins () is given by the equation below. AT the same time, the economists estimated the marginal revenue of a win is approximately $1.67 million. Given this information and table 1 below, answer the following questions (Chapter 8, “Measuring a player’s MRP” on page 258)

Q3 Table

Q3 (a)

Calculate each player’s marginal revenue product for their labor based on table 1 and the estimates identified above in the statement of the problem.

MRPL=MRwins(Δwins)

Q3 (b)

Suppose that the marginal revenue of a win rises to $2 million. Which player’s MRPL rises by the largest percentage?

Each player’s MRPL rises by the same amount when the MRwins increases to $2 million.

Q4

Chapter 9 of our textbook presents a discussion on arbitration. Based on this discussion, answer the following questions (Chapter 9, “Salary Arbitration” page 302).

Q4 (a)

Define binding arbitration

In binding arbitration, both parties agree (or are required) to abide by the decision of the arbitrator before the arbitrator reaches a decision.

Q4 (b)

Define final offer arbitration (FOA).

Each side of the negotiation submits a final offer to an independent arbitrator. The arbitrator may only select one of the two submitted final offers. No compromise is allowed.

Q4 (c)

Major League Baseball (MLB) has adopted FOA because it fears regular arbitration is addictive. In what way can binding arbitration be addictive?

If one or both sides submit unreasonable offers and the arbitrator desires to win approval from both parties, the arbitrator may select a middle ground. The side that is made better-off by this process would like to have the process repeated many times.