# Coursework, Macro & Micro economics;ps3

Coursework, Macro & Micro economics;ps3

Project description

Problem Set #3

Contests

MAKE SURE TO PROVIDE EXPLANATIONS AND CALCULATIONS FOR YOUR ANSWERS!

1. Laverne and Shirley, two equally talented athletes, expect to compete for the county championship in the 400 meter hurdles in the up-coming season. Each

plans to train hard, putting in several hours per week. We will use the Tullock model to describe their behavior.

For each athlete winning is worth 40 hours per week; so we measure the prize as 40 hours. The cost of an hour of effort is, of course, one hour. The probability is

as described in the Tullock model.

a. Suppose that Laverne plans to train 25 hours per week, and that Shirley plans to train 15 hours. What is the probability that Shirley will be the county

champ?

P= 15/(25+15)=15/40=0.375=37.5%

b. What is Laverne’s payoff? (i.e. prob x prize – cost) Note: the payoff is measured in hours, not money.

c. Suppose that she decreases her training time to 20 hours per week. Does her payoff rise or fall? Explain.

d. Suppose that she increases her training time to 30 hours per week. Does her payoff rise or fall? Explain.

e. Is the allocation where Laverne trains 25 and Shirley trains 15an equilibrium? Why or why not?

f. Is the allocation where each athlete trains 10 hours per week as Nash equilibrium? (Hint: you can check to see if the payoff rises when, say, Laverne

increases to 11 and then when she reduces to 9. You don’t have to check for Shirley’s incentives because the situation is symmetric.)

Number of hours for Laverne Payoff for Laverne

(assuming that Shirley trains 10 hours.)

9 __________

10 __________

11 __________

g. Assume that the prize rises to 80 hours. Show that the 10 hours each allocation is no longer a Nash equilibrium. Hint: you only have to check that the payoff

is highest at 9 hours, 10 hours, or 11 hours for Laverne (again, holding Shirley at 10 hours.)

h. Finally, suppose that with the payoff back at 40 hours, a third athlete, Edna, now enters the race. Edna has the exact same ability,and the exact same payoff

of winning the race, as Laverne and Shirley. Is 10 hours training each still a Nash equilibrium? Hint: Do the same thing as before, that is hold both Shirley and Edna

at 10 hours of effort.

2. One of the predictions of contest theory is that effort is greater in symmetric contests, where ability is relatively equal as compared to asymmetric

contests, where ability is unequal. In “the incentive effects of leveling the playing field,” Franke tests this idea with data on amateur golf tournaments. The paper

is here.

He compares performance when the score uses unadjusted scores versus those that adjusts score by handicap. (Handicap scoring levels the playing field for the lower

ability golfer.) Here is the distribution of performance difference in tournaments that use gross (unadjusted) vs net (adjusted). (Performance is measured using the

Stabelford system. If there were no difference in performance, the distribution should be approximately binomial with a mean of zero.

a. Looking at the data, what is your guess about which type of tournament has higher (better) performance.

b. Is your answer to part a consistent with the predictions of contest theory? Why or why not?

The table shows regression coefficients (standard errors in parenthesis) for the independent variables. The dependent variable is score. (again, under the stabelford

system higher is better).

c. Type is a dummy variable with 1 for net score tournaments and 0 for gross score tournaments. Explain the meaning of the coefficient.

d. Is it significant at the 5% level? Explain.

e. What is the t-statistic? ________________

f. The variable “female” is a dummy variable with 1 for female tournaments and 0 for male tournaments. The coefficient is positive. Does this mean that women are

better golfers than men? Why or why not?

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