Problem Set #4

ProblemSet #4

Pleasebe careful to give calculations and explanations for you answers.

Ec370 Summer, 2014

Michigan StateUniversity W. Melnik/L. Martin

  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 foreach player. The paper reports the following results. Note that pvalues (not standard errors or t statistics) are reported inparentheses.

The meaning of the variables are as follows.

Finally, AUS means that the player is of Australian nationality andIND means that the player is of Indian nationality. The omittedcategory is all other nationalities.

  1. What is the dependent variable? —Bid Price

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

—$ 60.01 more

  1. Is this coefficient significant? Explain.

This coefficient may or may not be significant depending on valuesthat may be obtained from other intermediate variables in the model

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

This is anintermediate variable. Its coefficient will mean that the player iseither Austrian or not but not both.

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

The salaries foryounger players are higher because the age as a multiplying factorwill be low. This will give a lower value which will be subtractedin the model resulting in a higher salary for the younger player

  1. What does the R2 number mean?

This number givesthe coefficient of determination which gives the percentage ofvariation that can be explained by the regression model

  1. 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?

The model actuallyprovided good evidence that Indian players are favored againstAustrian players. They have a higher multiplying factor than theAustrians. Indians have 311320 while Austrians have 200370

  1. 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?

The salary will be

560900 + 60010 x0.01 + 40227 x 0.01 – 15965 x 25 + 1178.3 x 70 + 0 + 0 + 0

= 252008.37.

  1. 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 (andaverage) cost of selling a ticket is $2. Other fixed costs per gameequal $25,000. Finally, seating capacity is 7,000.

  1. What is the profit maximizing price? (Pick a multiple of $3.) $15

  1. How many tickets will be sold at that price? 4000 tickets

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

Profit = 15 x 4000–(4000 x 2 + 25000) = 27000

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

I would recommend aprice of $19.33 so as to get the same profit margin

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

$ 54 will be theprice recommended to be paid so as to realize the same profit marginof $27000

  1. 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.)

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

A competitive paypackage for the contract that will consider several variables will bemotivating. Some of the variables to be considered should includehigh level skills in talent which can easily make the player move upto the Tigers.

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

The manager shoulddevote his time also in acquiring new game skills that wouldchallenge competitors in the game.

  1. 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.)

Testimonials andrelevant credentials should be produced to support the claims. Myfriend should also be ready to demonstrate the skills practically

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

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

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

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

Predictions for hissalary will be 1500000 + 1200000 x 0.8 = 2460000

  1. The 95% confidence interval around this prediction runs from -1.96 to 1.96

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

At 95% confidence level, the limits for the salary using a standarderror of 140000 are 1774400 for the upper salary and 1226000 for thelower salary. Getting a salary of 2600000 therefore means that he isoverpaid.

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

122600 1500000 1774400 2600000