YOU are in as a farmer. You are facing a risky income that is $160,000 with good luck (probability 0.5) and $40,000 with bad luck (probability 0.5). Hence, you have substantial income variability and are not very happy about this because you are averse to risk. Your utility function is u(x)=x, where x is any given non-negative monetary amount.

Consider the situation where your and your neighbor's risks are perfectly negatively corre- lated. Think about any potential risk-sharing arrangements that you and your neighbor can agree on. Let us assume that there are no incentive issues and these arrangements will be enforced by pressure from the island community. Let us formalize these arrangements as the following contract (x, y)such that If you have good luck you pay your neighbor an amount x, and if you have bad luck, you receive an amount y from your neighbor To motivate what is next, notice that the "full insurance", equal-sharing contract we studied in class assumed that x=$60, 000 and y=$60, 000.

(c) If we allow for all kinds of contracts (not necessarily equal-sharing), what is the worst contract (from your point of view) that your neighbor can offer you that you would still acceptwhich would make you indifferent between accepting the contract or staying with your risky income?

(d) What is the best contract (from your point of view) that your neighbor can offer you?