Ec 370 Valuing Cricketeers Using Hedonic Price Models

| June 14, 2018

Problem Set #4
Please be
careful to give calculations and explanations for you answers.

Ec
370 Summer,
2016

1.
A recent paper by AjitKarnik, entitled
“Valuing Cricketeers Using Hedonic Price Models,” studied the results of an
auction held by the Indian Premier League on February 20, 2008. The eight teams in the league bid on 75
players. The bids were wage offers, and
the team with the highest bid acquired the rights to the player and also was
required to pay that player a salary equal to the high bid.

In the study Karnik ran a regression to explain the
bid price for each player. The paper
reports the following results. Note that
p values (not standard errors or t statistics) are reported in parentheses.

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The meaning of the variables are as follows.

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Finally, AUS means that the player is of Australian
nationality and IND means that the player is of Indian nationality. The omitted category is all other nationalities.

a.
What is the dependent variable? __________________

b.
How
much does a player gain, in terms of salary, if he scores1% more of total runs
scored?
__________________

c.
Is
this coefficient significant? Explain.

d.
What kind of variable is AUS? What does its coefficient mean?

e.
Are salaries for younger players higher or
lower? Explain.

f.
What does the R2 number mean?

g.
An Indian player sues the league claiming that
Indian players are discriminated against relative to Australians. Does this study provide good evidence for his
claim?

h.
Consider
a 25 year old British cricketer with a strike rate of 70 who scored 1% of runs
and took 1% of wickets among the 75 cricketers considered (assume that RUNSAR =
0). According to the model, what will his salary be?

2.
You have achieved a dream job working for the
Toledo Mud Hens. Remembering what you
learned in Sports Economics, you managed to estimate the demand for general
admission tickets as follows.

Price Tickets
$27 0
$24 1,000
$21 2,000
$18 3,000
$15 4,000
$12 5,000
$9 6,000
$6 7,000

The
marginal (and average) cost of selling a ticket is $2. Other fixed costs per game equal $25,000. Finally, seating capacity is 7,000.

a.
What is the profit maximizing price? (Pick a multiple of $3.) _______________

b.
How many tickets will be sold at that price? _______________

c.
Compute
the profits. (revenues – costs) (costs =
$2 per ticket + fixed costs)

_______________

d.
Suppose that the East stands collapse, and
capacity falls to 3,000. What price do
you recommend?

e.
Now
suppose that the West stands are judged to be unsafe, and capacity shrinks to
1,000. What price do you recommend?

________________

3.
One of your duties for the Mud Hens is to
recommend contract incentives. You want
the manager to focus on developing talent for the Tigers. (Note:
The Detroit Tigers own the Mud Hens as a “farm team.” The best Mud Hen players move up to the
Tigers.)

a.
Suggest how the contract might motivate the
manager to focus on developing top talent.

b.
What else might the manager do with his time
besides developing top talent?

c.
If your friend were applying for the job of
Mud Hens manager, how might he credibly show that he both thought that he was
good at developing talent and that he will focus on it? (Cheap talk is not credible.)

4.
A
study of pay for goalies in hockey estimates the following equation.

Salary
= $1,500,000 + $1,200,000 x save percent

Save
percent is measure in decimals; i.e. a number between 0 and 1. The standard error on the estimate of the
coefficient is $140,000.

a.
Fred has a save percentage of 0.8. This study predicts that his salary is how
much?

______________

b.
The 95% confidence interval around this
prediction runs from

__________________ to __________________

c.
Fred makes $2,600,000. Give a statistical answer to the question,
“Is Fred underpaid?”

d.
On the diagram below show your answer to part
a. and Fred’s salary.

.wikipedia.org/wiki/File:Standard_deviation_diagram.svg”>.gif” alt=”http://upload.wikimedia.org/wikipedia/commons/thumb/8/8c/Standard_deviation_diagram.svg/325px-Standard_deviation_diagram.svg.png”>

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