u(x) = 1000(1+ A firm wants to insure a plant against a disaster. With probability p=0.05, the firm incurs a loss of 1000. With probability 1-p, there is no loss. An insurer, whose preferences are captured by utility function 1/3 1000 proposes to insure the firm. If the price of the insurance product is the insurer would receive c with probability 1-p, and c-1000 with probability p. (Hint: compute the probabilities with at least four digits). Answer the questions from (a) to (e). (a) Write the expected utlity of the insurer as a function of c. Show that the insurer does not accept to insure when c= 80. Interpret your result (b) Show that the insurer accepts with c= 80 if the probability of loss is lower, at p=0.01. What is the highest probability the insurer can accept when c = 807 (c) Suppose that the loss in case of a disaster is 250 instead of 1000. Show that the insurer accepts the deal when - 20. Explain your result in the light of the risk-spreading result. (d) What is the highest probability the insurer can accept when the loss is 250 and c = 207 How does the answer illustrate the risk-spreading result? (e) Suppose the firm cannot pay more than Pin total to cover the loss of 1000. There are n identical insurers that can equally share the risk and equally share P between them. Write the expected utility of a single insurer as a function of n and P. Show that it is not possible to find enough insurers to insure the risk if p