QUESTION 2:
Suppose there is a risk-neutral farmer whose output is either ½ or 1. The probability that the farmer gets an output of one is e , where e is a number between zero and one that represents the effort level chosen by the farmer. The probability of getting an output of ½ is thus 1 – e.
The farmer’s cost of providing effort e is given by
2
.
A) Suppose that the farmer enters into a sharecropping contract in which she keeps a fraction s of the output. What effort level will she choose? (10 points)
B) There are two contractual options for the tenant to choose from:
1) Rental contract: Keep all of the output, pay fixed rent of ¼
2) Sharecropping contract: Keep ½ of the output (no additional rent)
Suppose that there is no possibility of default and that the tenant has zero nonlabor income. Which option will this risk-neutral tenant prefer? Carefully justify your answer by finding the tenant’s utility under each contract. (10 points)

C) Would your answer to part C) change if the tenant was risk-averse rather than riskneutral? Consider a more realistic environment in which the probability of the harvest being a success is not entirely determined by the tenant’s effort. (5 points)
D) Discuss a specific example from the articles you’ve read that gives an example of an institution that could help lead a tenant to choose the efficient contract by helping her to cope with risk. (10 points)

QUESTION 3:
There is a culture of corruption in Bribeland. New government officials see others taking bribes and so they also take bribes. Bribeland’s government wants to reduce corruption.
Suppose that the benefits of spending x dollars on a program to reduce corruption is
A x , where A is a constant. The cost of the program is x .
Also suppose that the government estimates the severity of corruption in a few different places. The program involves spending money on auditors in places where the government estimates that corruption is particularly high.
A) The government wants to maximize the benefits of the program minus the cost. Solve for the optimal level of spending for the government to choose. (5 points)
B) You are a government official who has to decide how beneficial the program is by figuring out what A really is. A year after implementing the program, the government estimates the severity of corruption in areas that received the program and in some neighboring areas. The government observes that measured corruption falls more in places that received the program than in places that did not. If this evidence is enough to show that the program has a positive effect, explain why. If this evidence is insufficient, describe in detail how you could design a different program that would make it possible to test the program’s effectiveness in reducing corruption. (10 points)
C) If there was only a probability p
H
that the program would bring down corruption by
A x and a 1 p
H
probability that the program would reduce corruption by only half that much, how much would you spend on the program? (5 points)

D) Suppose that the program does bring corruption down, but that the government runs out of money and cannot pay to support the auditors anymore. Would we necessarily expect that corruption would return to its previous level? Use the concept of equilibrium to justify your answer. (5 points)
E) Suppose that in a different country, corruption currently amounts to $500,000 per year.
If the country spends $1,000,000 on corruption prevention this year, it can completely eliminate the corruption this year. In all future years, because behavior has changed, corruption will fall to $400,000 even though no funds are being spent on stopping corruption any more.
Assume that there is a discount factor of .95 for future periods. In other words, we assign a weight of 1 to this year, .95 to next year, .95
2
to two years from now, and so on.
Should the government decide to spend the $1,000,000 on corruption prevention this year? Or would it make more sense to not spend the money on the anti-corruption program? Show all work. (10 points)