Fall 2011 wikiHomework Solutions, Chapters 1-4
Professor John R. Crooker, Ph. D.
September 14, 2011
Instructions
Answer each of the following questions from chapter 1 material.
Chapter 1 Problems
1. Is the following statement made by a college athlete true or false? Explain
your reasoning. “I am attending college on a full athletic scholarship, so
the opportunity cost of attending college is zero for me.”
2. The term “figure skating” refers to the shapes that skaters used to trace
in the ice as part of skating competitions. In the 1970s, this aspect of
the sport was deemphasized and eventually eliminated. Use the theory
of comparative advantage to show why eliminating this part of the competition has led skaters to perform much more difficult and sophisticated
jumps and spins.
Chapter 1 Solutions
1. Is the following statement made by a college athlete true or false? Explain
your reasoning. “I am attending college on a full athletic scholarship, so
the opportunity cost of attending college is zero for me.”
False. All choices require an opporunity cost and the decision to attend
college on a full athletic scholarship or not is no different. There are several examples of prominent athletes who have skipped college even though
they would have received a full athletic scholarship to attend college. Notable examples include LeBron James, Kobe Bryant, and Bubba Starling
(2011 #1 draft pick by the Kansas City Royals). As these athletes received several millions of dollars to turn pro out of high school, clearly
a decision to go to college on a full athletic scholarship would have been
quite financially costly.
Even athletes who do not have opportunities in the professional sport’s
ranks still have an opportunity cost. Spending time at practices likely has
implications on available time to study or work and earn income. Practice
and game preparation also takes the athlete away from family and friends.
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Certainly, there are sacrificed opportunities when a student decides to accept a full athletic scholarship.
2. The term “figure skating” refers to the shapes that skaters used to trace
in the ice as part of skating competitions. In the 1970s, this aspect of
the sport was deemphasized and eventually eliminated. Use the theory
of comparative advantage to show why eliminating this part of the competition has led skaters to perform much more difficult and sophisticated
jumps and spins.
In competition, skaters would be expected to master and exhibit performances that score more points from the judges. A move that is perceived
to be more difficult and sophisticated and scored as such will invite skaters
to develop and refine this move. As skaters compete, those that excel in
events will have established a comparative advantage in executing the more
difficult and spohisticated moves. Skaters are then forced to practice the
more difficult moves so as to maintain or earn a comparative advantage
against others. To the extent that skating literal shapes and figures on the
ice is less complex or difficult, the elimination of these moves as worthy
of points has instigated the chase for enjoying comparative advantages in
more difficult maneuvers.
Chapter 2 Problems
1. Suppose the market demand for tickets to see a University of Tennessee
women’s basketball game is Qd = 40, 000−1, 000p, and the supply is Qs =
20, 000. Identify the equilibrium price and quantity of tickets exchanged.
What would happen to the market for tickets if the university set a price
ceiling on tickets of $10/ticket and if Tennessee had strict antiscalping
laws? What would happen if the price ceiling was $30/ticket instead?
2. The major North American sports leagues prohibit teams from locating
within a specfic distance of an existing team. Why do they have such a
rule?
3. Suppose the St. Louis Cardinals sign a star pitcher from Japan to a fiveyear $120 million contract. What is likely to happen to ticket prices in St.
Louis for Cardinal’s games? Why? Five years later, suppose the Cardinals
re-sign the pitcher to another five-year contract this time for $150 million.
What is likely to happen to ticket prices in St. Louis now? Why?
Chapter 2 Solutions
1. Suppose the market demand for tickets to see a University of Tennessee
women’s basketball game is Qd = 40, 000 − 1, 000p, and the supply is
Qs = 20, 000. Identify the equilibrium price and quantity of tickets exchanged. What would happen to the market for tickets if the university
set a price ceiling on tickets of $10/ticket and if Tennessee had strict antiscalping laws? What would happen if the price ceiling was $30/ticket
instead?
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The equilibrium quantity requires:
Qd = 40, 000 − 1, 000p = 20, 000 = Qs
Solving for p, we see p = 20. That is, at a price of $20 per ticket, 20,000
tickets will be exchanged for a University of Tennessee women’s basketball
game. The equilibrium price is $20 per ticket and the equlibrium quantity
is 20,000.
If we suppose that antiscalping laws prohibit any secondary market for
bsketball games, we expect the price to be $10/ticket. As the availability
of the tickets is likely limited by the capacity of the stadium at 20,000
seats, only 20,000 tickets will be sold. There would be a shortage of
10,000 tickets as the quantity demanded of tickets at $10 is 30,000. While
ticket prices may appear cheaper, fans would be forced to wait in lines for
tickets and possibly not get tickets. Thus, non-monetary costs of acquiring
tickets would go up.
If the price ceiling was $30/ticket, the price ceiling would not impact the
market. This is because the market reaches equlibrium below the price
ceiling.
2. The major North American sports leagues prohibit teams from locating
within a specfic distance of an existing team. Why do they have such a
rule?
This rule is designed to protect the market power of existing teams. If
teams in the same league are permitted to spring up within the limits of
an existing teams market, the team would create a substitute as multiple producers in the league compete for existing fan base. Without these
rules, the value of a franchise is reduced.
Formally, the monopoly pricing power of a league and subsequent profits
in a particular market is greater when the franchise has no close substitutes. If a substitute is introduced into the market, the demand curve
shifts to the left and becomes more elastic. As a result, the teams profits
are eroded. As teams become less profitable, the interest in owning a team
in the league wanes. As team owners can control this rule by participating
in the league, we would anticipate that they would collectively agree to
protect the markets of each other owner. This would ensure their own
profits as well.
3. Suppose the St. Louis Cardinals sign a star pitcher from Japan to a fiveyear $120 million contract. What is likely to happen to ticket prices in St.
Louis for Cardinal’s games? Why? Five years later, suppose the Cardinals
re-sign the pitcher to another five-year contract this time for $150 million.
What is likely to happen to ticket prices in St. Louis now? Why?
The knee-jerk reaction of most fans is that when a star player is signed,
the ticket prices will go up. This is not necessarily the case. It depends on
what happens to the demand for tickets. If the team is relatively loaded
with talent and another star player fails to generate more interest in attending the game in person (or subscribing to some satellite plan that
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enriches the owner), ticket prices would not rise. On the other hand, if
the star player generates more interest in the game, we would anticipate
the team would enjoy greater pricing power and raise ticket prices. If
five years later, the same concepts are relevant. If re-signing the same
star player causes new fans to come out to games more or existing fans
to come out more often, we would anticipate the team enjoying greater
pricing power. On the other hand, if re-signing the player will not cause
new fans to come out to games or induce existing fans to come out more
frequently, the re-signing will not have an impact on the ticket prices. Of
course, if the team fails to sign the player and existing fans come less frequently and new fans are not attracted, we would expect a loss in pricing
power and a subsequent reduction in ticket prices.
Chapter 3 Problems
1. Draw a graph (you can attach an image to your wikipage by clicking
the image icon in the toolbar that appears above when you begin editing
your page) that shows the demand for seats at an NFL stadium. Show
how demand for attendance at a given game would be affected if: a) The
prices of parking and food at the games increase but quality does not;
b) Televised games switch from free TV to pay-per-view only; c) A new
league forms with a team that plays nearby; d) The quality of the team
decreases dramatically; e) The length of the season is increased.
2. True or False; explain your answer: “If all teams are of equal quality, it
doesn’t matter whether they share gate receipts or not– revenue will be
the same for all teams.”
3. Suppose an owner pays $500 million to purchase a hockey team that earns
operating profits of $50 million per year. The new owner claims that $200
million of this prices is for the players, which he can depreciate using
straight-line depreciation in five years. If the team pays corporate profit
taxes of 40%, how much does the depreciation of the players save the
owner?
Chapter 3 Solutions
1. Draw a graph (you can attach an image to your wikipage by clicking the
image icon in the toolbar that appears above when you begin editing your
page) that shows the demand for seats at an NFL stadium. Show how
demand for attendance at a given game would be affected if: a) The prices
of parking and food at the games increase but quality does not; b) Televised games switch from free TV to pay-per-view only; c) A new league
forms with a team that plays nearby; d) The quality of the team decreases
dramatically; e) The length of the season is increased.
The effects of (a), (c), and (d) are all the same. Specifically, these effects will result in a decrease in demand. I have diagrammed a decrease
in demand below.
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200
150
100
Price
50
D0
60
80
0
<−−−−−−−−−−−−−
D1
0
20
40
100
Quantity
The original demand curve is labled D0 above. A decrease in demand is
depicted as a leftward shift. I have illustrated the decrease in demand as
a movement from D0 to D1.
Prices of parking and food at the game increasing without any improvement in quality are likely to impact the demand for game attendance
because these items are complement goods. That is, these goods are used
together with game attendance. When the price of complement goods
rise, the demand for the related complement good declines.
If a new league forms nearby, we would anticipate a decrease in the demand for games for the incumbent team. This is because a new league
with a team would constitute a substitute good. As the price of a substitute goes down, the demand for the related substitute good declines.
So, given the new league has a team viewed by fans in the market as a
substitute game experience, the demand would decrease.
A loss of team quality would also cause demand to decrease. Provided fans
enjoy the quality of play, a decrease in quality holding all else constant
is going to result in less fan interest– and fewer fans willing to pay the
same price for the same number of games attended. Thus, a decrease in
demand.
Part (b) supposes the impact of switching televsied games from free TV to
pay-per-view. As watching the games on TV is a substitute for attending
the game, making the substitute price more expensive is likely to increase
the demand for game attendance. Thus, we anticipate a rightward shift
of the demand curve as illustrated here.
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200
150
100
50
Price
D1
0
D0
0
20
40
60
80
100
Quantity
The original demand curve is denoted D0 in the graph above. As a result
of the change, demand increases to D1.
Let’s consider part (e). If the length of the season is increased, this is likely
equivalent to an increase in the supply of games. We would anticipate that
more opportunities to go out to a game results in a smaller demand for
tickets on any particular game day. For the picture I have illustrated below, the increase in the length of season will likely cause ticket prices to
fall. As ticket prices go down, we anticipated the quantity demanded of
tickets rising.
2. True or False; explain your answer: “If all teams are of equal quality, it
doesn’t matter whether they share gate receipts or not– revenue will be
the same for all teams.”
False. While teams may be of equal quality, the problem does not state
that all markets are the same. We know that some markets are bigger
than others and some markets may have a different collection of entertainment options for people in that market. As the availability of other
substitutes may differ across teams, the pricing power and subsequent revenue and profits are also likely to be heterogeneous even if the teams were
homogeneous in quality.
3. Suppose an owner pays $500 million to purchase a hockey team that earns
operating profits of $50 million per year. The new owner claims that $200
million of this prices is for the players, which he can depreciate using
straight-line depreciation in five years. If the team pays corporate profit
taxes of 40%, how much does the depreciation of the players save the
owner?
By claiming $200 million of the $500 million the owner paid for the hockey
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team is for the players, the owner may subtract 1/5 of the amount in one
year a depreciation expense. In this case, the depreciation expense is $40
million. As depreciation expense is a deductible expense, the owner will
pay taxes on $50 million - $40 million, or $10 million. This means a tax
bill of $4 million with the depreciation expense. Without depreciation
for the players, the owner must presumably pay taxes on the entire $50
million in operating profit. Thus, the owner would pay $20 million in
taxes if depreciation is not allowed. Thus, the owner saves $16 million in
taxes per year if he is allowed to depreciate players.
Chapter 4 Problems
1. An athletic director was once quoted as saying that he felt his school spent
too much on athletics but that it could not afford to stop. Use game theory
to model his dilemma.
2. Suppose that the demand curve for tickets to see a football team is given
by Q = 100, 000 − 100p and marginal cost is zero. a) How many tickets
would the team be able to sell (ignoring capacity constraints) if it behaved competitively and set price equal to marginal cost? b) How many
tickets would it sell– and what price would it charge– if it behaved like
a monopoly? (HINT: In this case the marginal revenue curve is given by
M R = 1, 000 − 0.2Q).
3. Suppose the typical Buffalo Bills fan has the demand curve for Bills football games: p = 120 − 10G, where G is the number of games the fan
attends. a) If the Bills want to sell the fan a ticket to all eight home
games, what price must they charge? What are their revenues? b) Suppose the Bills have the chance to offer a season ticket that is good for
all eight home games, a partial season ticket that is good for four home
games, and tickets to individual games. What price should they charge?
What is their revenue?
Chapter 4 Solutions
1. An athletic director was once quoted as saying that he felt his school spent
too much on athletics but that it could not afford to stop. Use game theory to model his dilemma.
The game embodied in the table below represents a two-player simultaneous move game. The players are ’My U’ and ’Arch Rival.’ Each player
may play the “Spend Too Much” strategy or “Spend Little” strategy. The
pay-outs are listed with the row player’s pay-out first followed by the column player’s pay out.
Upon examining the pay-out matrix, we see each University has a dominant strategy to “Spend Too Much.” That is, “Spend Too Much” always
does better than “Spend Little.” If the Arch Rival “Spends Too Much,”
My U does better by also choosing “Spend Too Much.” If the Arch Rival
chooses “Spend Little,” My U does better by choosing “Spend Too Little.”
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My U
Spend Too Much
Spend Little
Arch Rival
Spend Too Much
(-10, - 10)
(-20, +20)
Spend Little
(+20, -20)
(0, 0)
In fact, this is the favorite outcome for My U. Unfortunately, we anticipate
each University adopting the dominant strategy of “Spend Too Much.” As
a result, each University experiences a -10 outcome. The dilemma is that
we see that both schools do strictly better-off by both adopting a “Spend
Little” approach. This outcome is not sustainable, however. If somehow
the schools found themselves in this situation, both schools would have an
incentive to switch to the “Spend Too Much” strategy. In the language
of Game Theory, we would say that the “Spend Too Much”-“Spend Too
Much” outcome is a Nash Equilibrium.
2. Suppose that the demand curve for tickets to see a football team is given
by Q = 100, 000 − 100p and marginal cost is zero. a) How many tickets
would the team be able to sell (ignoring capacity constraints) if it behaved competitively and set price equal to marginal cost? b) How many
tickets would it sell– and what price would it charge– if it behaved like
a monopoly? (HINT: In this case the marginal revenue curve is given by
M R = 1, 000 − 0.2Q).
If the team priced competitively and set price equal to marginal cost ($0),
the number of tickets demanded with a price of $0 is 100,000. This would
generate $0 in revenue. If the team, instead, behaved like a monopolist,
the team would set:
M R = 1, 000 − 0.2Q = 0 = M C.
Solving for Q, we see:
Q = 5, 000.
We can identify the required ticket price by solving:
5000 = 100, 000 − 100p
or
p = $950.00.
Charging $950/ticket for 5,000 tickets generates $4,750,000.
3. Suppose the typical Buffalo Bills fan has the demand curve for Bills football games: p = 120 − 10G, where G is the number of games the fan
attends. a) If the Bills want to sell the fan a ticket to all eight home
games, what price must they charge? What are their revenues? b) Suppose the Bills have the chance to offer a season ticket that is good for
all eight home games, a partial season ticket that is good for four home
games, and tickets to individual games. What price should they charge?
What is their revenue?
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If the Bills must charge a single game ticket price and use the ticket price
for all games, the Bills must charge $40/ticket or less to induce the fan to
purchase tickets to all eight games. A price of $40/ticket generates $320
in ticket revenue for the Bills from this fan.
20
40
60
Price
80
100
120
If we want to sell the fan a ticket all eight home games, we should calculate the individual’s maximum willingness-to-pay for 8 games. This
corresponds to the area under the demand curve from 0 to 8 Games. This
region can be broken down into a triangle and a rectangle. The triangle
has a height of $80/Game and a width of 8 games. The rectangle has a
height of $40/Game with a width of 8 games.
0
2
4
6
8
10
Games
Thus, the indivdiual’s maximum willingness-to-pay for 8 games is $320 +
$320 = $640. Thus, selling a season ticket for all 8 games for just under
$640 would entice the individual to purchase a season-ticket if he or she had
no other alternatives. The individual has a maximum willingness-to-pay
of $400 for a partial season ticket of 4 games. A single game revenue maximizing price would be $60/Game. Recall that the marginal revenue curve
will have the same vertical axis intercept as the demand curve but with
twice the slope. Thus, given p = 120 − 10G, we know M R = 120 − 20G.
Hence, the revenue maximizing single game price is M R = 120 − 20G = 0
imples G = 6. The highest price the consumer would pay per game is
p = 120 − 10(6) = 60. The fan would purchase 6 tickets spending $360
total.
The Bills would do best by charging $639.99 for a season ticket to all 8
gmaes. Pricing the partial season ticket (4 games) at $400 or more would
dissuade the individual to purchase a partial season ticket to 4 games.
Finally, charging $115 or more for a single game ticket would keep the fan
from purchasing single game tickets. In this example and perhaps in the
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limit, the fan is better-off by $0.01 by purchasing a full season ticket for
$639.99. This is the greatest revenue the Bills can raise from the fan.
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