Problem 3 - Moral Hazard: You are a landlord (principal) who owns a piece of land. Because you do not want to harvest, writing contracts with a farmer collective (agent). You have three choices:

You can employ the farmer collective at a fixed wage of w = 400 (and you keep the harvest);

You can rent the land to the collective at a fixed fee of rent = 400 (and the collective keeps

the harvest); or you can adopt a sharecropping contract in which you and the collective share the harvest H in equal parts.

The harvest can be either good or bad. The value of the harvest is affected by both the level of effort expended on cultivation and by chance (nature plays after the farmer collective).

The farmer collective can put much or little effort into cultivation. When the effort is high, the collective endures a cost equal to 100. If they put in a high effort, the probability of having a good harvest is equal to .75. The probability of having a bad harvest is equal to .25. If the collective puts in a low effort, the harvest is good with probability .25 and bad with probability .75. When the harvest is good, its value is 1,000; when the harvest is bad, its value is 400.

Both you and the collective are risk-neutral.

a) Consider the employment contract. What is the collective's expected payoff if they choose high

effort? What is their expected payoff if they choose low effort? Which of the two strategies will the farmer collective choose? What is your expected payoff from the employment choice?

b) Consider the rent contract. What is the collective's expected payoff if they choose high effort? What is their expected payoff if they choose low effort? Which of the two strategies will the collective choose? What is your expected payoff from the rent choice?

c) Consider the sharecropping contract. What is the collective's expected payoff if they choose high effort? What is their expected payoff if they choose low effort? Which of the two strategies will the collective choose? What is your expected payoff from the sharecropping action?

d) Which contract will you choose? If you were risk-averse, would you choose the same action? Can you give an unambiguous answer to this question? Explain and discuss the problem graphically on a utility diagram.