Willy owns a small chocolate factory, located close to a river that occasion- ally floods in the spring, with disastrous consequences. Next summer, Willy plans to sell the factory and retire. The only income he will have is the pro- ceeds of the sale of his factory. If there is no flood, the factory will be worth $500,000. If there is a flood, then what is left of the factory will be worth only $50,000. Willy can buy flood insurance at a cost of 0.10 for each $1 worth of coverage. Willy thinks that the probability that there will be a flood this spring is 0.1. Let cF denote dollars if there is a flood and cN F denote dollars if there is no flood. Willy's utility function is u =pc. Willy is trying to decide how much flood insurance (K ) to buy.

(a) What is the risk attitude of Willy? Why?

(b) Please find the expected wealth and expected utility of Willy.

(c) Find the equation that shows the relationship between cF and cN F .

(d) Find the optimal level of cF ,cN F and K .

(e) Suppose the insurance is unfair, and =0.2. What are the optimal level of cF ,cN F and K .