Problem Set #4
Please be careful to give calculations and explanations for you answers.
- A recent paper by Ajit Karnik, 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.
The meaning of the variables are as follows.
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.
- What is the dependent variable? __________________
- How much does a player gain, in terms of salary, if he scores 1% more of total runs scored?
- Is this coefficient significant?
- What kind of variable is AUS? What does its coefficient mean?
- Are salaries for younger players higher or lower?
- What does the R2 number mean?
- 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?
- Consider a 24 year old South African cricketer with a strike rate of 60 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?
- 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.
The marginal (and average) cost of selling a ticket is $4. Other fixed costs per game equal $15,000. Finally, seating capacity is 3500.
- What is the profit maximizing price? (Pick a multiple of $4.)
- How many tickets will be sold at that price? _______________
- Compute the profit at this price. Profit = Revenue – cost. (Cost = $4 per ticket + fixed costs)
- Suppose that the East stands collapse, and capacity falls to 3,000. What price do you recommend?
- Now suppose that the West stands are judged to be unsafe, and capacity shrinks to 1,000. What price do you recommend?
- The city of Toledo now requires the stands to be inspected before every game, to ensure that there will not be a collapse when fans are present. This inspection costs $5000 per game. How many tickets will the Mud Hens sell now?
- 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.)
- Suggest how the contract might motivate the manager to focus on developing top talent.
- What else might the manager do with his time besides developing top talent?
- 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.)
- A study of pay for goalies in hockey estimates the following equation.
Salary = $2,000,000 + $1,000,000 x save percent
Save percentage is measure in decimals; i.e. a number between 0 and 1. The standard error on the estimate of the coefficient is $240,000.
- Fred has a save percentage of 0.9. This study predicts that his salary is how much?
- The 95% confidence interval around this prediction runs from
__________________ to __________________
- Fred makes $2,400,000. Give a statistical answer to the question, “Is Fred underpaid?”
- On the diagram below show your answer to part a. and Fred’s salary.