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Homework 3 Solutions Guide
Economics of Sports
Fall 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=48061-2.4P
P=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=0
Q=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
when
20,025.42-0.83Q=20 or
Q=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.
Government Tax Revenue is:
$20(24,006)=$480,120
Producer Surplus is:
(10,022.92-20)24,006=
$240,130,097.52
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.
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