Fall 2011 Midterm 1 Answer Key
Economics of Sport
October 24, 2011
The examination consists of 3 open-ended questions with 4 subparts each.
Each subpart is equally weighted in the determination of your grade. Answer
the questions fully. Be sure to define any economic concept you use or refer to
in your answer.
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Tampa Bay Rays and Ticket Pricing
1.1
Statement of the Problem
An econometrician has estimated the demand function for Tickets to Rays game
as q = 500, 000 − 25, 000P , where P is the per game ticket price.
1. Use the information above to calculate the number of tickets sold when
P = $10.
2. Use the information above to calculate the number of tickets sold when
P = $12.
3. The Elasticity of Demand is calculated by ξ =
q1 −q0
q0
P1 −P0
P0
. Identify the Elas-
ticity of Demand at P = $10.
4. Given the marginal cost of admitting one more fan is zero, did the Rays
make a good decision regarding the increase in ticket price? Explain.
1.2
Solution
1. Use the information above to calculate the number of tickets sold when
P = $10.
Using the demand function for tickets at P = $10, we have q = 500, 000 −
25, 000(10) = 500, 000 − 250, 000 = 250, 000. That is, at a price of $10 per
ticket, when anticipate 250,000 tickets being sold. This raises $2.5 Million
in ticket revenue.
2. Use the information above to calculate the number of tickets sold when
P = $12.
Using the demand function for tickets at P = $12, we have q = 500, 000 −
25, 000(12) = 500, 000 − 300, 000 = 200, 000. That is, at a price of $12 per
ticket, when anticipate 200,000 tickets being sold. This raises $2.4 Million
in ticket revenue.
3. The Elasticity of Demand is calculated by ξ =
q1 −q0
q0
P1 −P0
P0
. Identify the Elas-
ticity of Demand at P = $10.
If we define q0 = 250, 000 with P0 = $10 and q1 = 200, 000 with Pq = $12,
we may use the supplied elasticity of demand formula to calculate:
ξ=
200,000−250,000
250,000
12−10
10
=
−1
5
1
5
= −1.
That is, at the price P = $10, demand is unitary elastic. Total Revenue
is maximized at the price where demand is unit elastic.
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4. Given the marginal cost of admitting one more fan is zero, did the Rays
make a good decision regarding the increase in ticket price? Explain.
Given the marginal cost of providing fans with the additional 50,000 seats
was zero, the Rays did not make a good decision raising ticket prices. In
fact, if we think that fans would have purchased more concessions and
parking (and these items are being sold at a profit), then we anticipate
the decision to raise ticket prices has caused the Rays to shrink profits.
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2
Washington Nationals and Winning in Major
League Baseball
2.1
Statement of the Problem
The Washington Nationals, one of the weakest teams in the National League
from a wins-losses perspective, is also one of the most profitable teams in baseball.
1. Explain what factors determine profitability of a team. In particular, why
might these profits be independent of wins and losses.
2. Is it possible that winning more games may actually hurt a team’s profitability? Explain.
3. If Major League Baseball teams are profit maximizers, what must be true
to encourage weak teams to win more games? Can you think of a league
policy that would be consistent with your observation? Explain.
4. Explain the law of diminishing marginal returns. If this concept applies
to Major League Baseball, explain how it may help support competitive
balance.
2.2
Solution
1. Explain what factors determine profitability of a team. In particular, why
might these profits be independent of wins and losses.
Team profits are the difference between revenues and costs. Revenues
for the team come from ticket sales, parking, concessions, advertising, and
television broadcasting rights. Team costs are largely driven by facility
charges and player contracts. Some teams in large markets, like the Nationals, draw from a very large metropolitan area. Also, there is a large
television market. As these revenue sources are less sensitive to wins and
losses, winning an extra game isn’t that valuable to the Nationals. Costs,
on the other hand, are quite sensitive to the quality of team assembled.
The team has an opportunity to field a poor team and not lose much revenue while driving costs down. This can boost profits.
2. Is it possible that winning more games may actually hurt a team’s profitability? Explain.
If Team Revenues are not sensitive to wins and costs are highly sensitive to wins, we can see that mathematically winning more games can
shrink a team’s profits. For simplicity, let’s suppose that the Nationals
only get revenue from tickets and have a 50,000 seat stadium and charge
$50 per ticket. Thus, each game the Nationals generate $2.5 million in
revenue. We’ll also suppose that this revenue does not depend on how the
team is performing as the Washington D.C. market is so big and incomes
are so high. With 80 home games per season, this generates $200 million
in ticket revenue.
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Now, the Nationals could build a competitive team and spend $150 million on player contracts. This would leave profits of $50 million per year.
On the other hand, if the Nationals do not build a competitive team and
spend only $75 million on player contracts (losing many more games), the
team would geenrate profits of $125 million per year. Clearly in this example, winning more games causes the Nationals to lose profits. Again,
this is if team revenues are somewhat insensitive to the team’s on the field
success.
3. If Major League Baseball teams are profit maximizers, what must be true
to encourage weak teams to win more games? Can you think of a league
policy that would be consistent with your observation? Explain.
To encourage MLB teams to win more games given they are profit maximizers, the league must design profit incentives to weak teams to win
more games. Gate sharing for away teams may be a part of this initiative. When weak teams visit fairly strong teams, attendance tends to be
down even for the strong team. If the weak teams can share in the gate,
they have a much larger incentive to field a more competitive team because
they would generate stronger gate revenue even when they go on the road.
4. Explain the law of diminishing marginal returns. If this concept applies
to Major League Baseball, explain how it may help support competitive
balance.
The law of diminishing marginal returns suggests that after some point,
the returns necessarily get smaller. This may support competitive balance
because this may keep superstar players spread out through the league
rather than consolidated on a single team. If we suppose there are 10 superstars, the marginal return of the first superstar is quite high. However,
eventually, as a single team got more than say 3 or 4 superstars, another
team may value the next superstar more highly than the team that has 3
or 4 signed. This keeps the league more balanced than a situation where
all 10 superstars played for the same team.
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3
The Arizona Cardinals and Price Discrimination
3.1
Statement of the Problem
The typical Arizonal Cardinals fan has the demand curve for Cardinals football
games: p = 120 − 15G, where G is the number of games attended and p is the
price per game.
1. If the Cardinals want to seel the fan a ticket to all eight home games, what
price must they charge? What are their revenues?
2. What is the typical fans benefit (total willingness-to-pay) for eight games?
3. What is the typcial fans benefit (total willingness-to-pay) for four games?
4. Suppose the Cardinals can sell a season-ticket (good for all 8 home games),
a partial season-ticket (good for 4 home games), or single game tickets.
Given the information you have calculated in this problem, what pricing
structure would you suggest to maximize the revenues of the Cardinals?
3.2
Solution
1. If the Cardinals want to seel the fan a ticket to all eight home games, what
price must they charge? What are their revenues?
Charging a single game price, we want to know the price such that G = 8.
Using the information above, we see: p = 120 − 15(8) = 0. That is, we
must give the tickets away for free if want our typical fan to attend all 8
home games. This will generate $0 in ticket revenues.
2. What is the typical fans benefit (total willingness-to-pay) for eight games?
The area under the demand curve between 0 and 8 games captures the
dollar value of the fans total willingness-to-pay for all eight games. This
is calculated as:
T W T P8 =
1
(120 − 0)(8) = $480.
2
That is, our typical Cardinals fan values all eight home games at $480.
3. What is the typcial fans benefit (total willingness-to-pay) for four games?
The height of the demand curve at G = 4 is $60. Thus, the typical
fan’s total willingness-to-pay for 4 games is given by:
T W T P4 =
1
(120 − 60)(4) + 4(60) = $360.
2
That is, the fan derives benefit of $360 from attending 4 games.
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4. Suppose the Cardinals can sell a season-ticket (good for all 8 home games),
a partial season-ticket (good for 4 home games), or single game tickets.
Given the information you have calculated in this problem, what pricing
structure would you suggest to maximize the revenues of the Cardinals?
The Arizona Cardinals could sell a season ticket for $479.99 to all eight
home games and maximize the amount of revenue extracted from Cardinal
fans. Selling a partial season ticket for $361 and a single game ticket for
$116 would also force Cardinal fans to purchase the season ticket.
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