Exercise 14.5 Valuing improvements in longevity and the implied value of life. (25 points, each part is worth 5 points.) Suppose that there is a individual who lives up to two periods. That is, the individual lives for certain during period 1. In that period his sub utility function is given by: u (c1) = log c1. The individual is alive in period 2 with probability p. If he is alive, his state sub-utility function is given by: u (c) = log C2 and if he dies, he receives the fixed utility level B. Suppose that the individual has access to a perfect capital market and suppose that he discounts the future at a rate of B. Suppose that his endowment is given by (w1, w2). a. Set up the individual's utility maximization problem. Make sure that you explain how the probability of death affects the problem. What are reasonable values for B? b. How much does the individual save or borrow? c. How do his savings or loans depend on the probability of death? d. Suppose, now, that a technological improvement reduces the probability of death. What is this improvement worth to the individual? Suggest a meaningful way to compute the social value of technological improvement and compute it. Who values the social improvement most? (Note: there are many ways to do this. Make sure that you are very clear about the way in which you are doing this and make your life easy!) e. How much current income is the individual willing to forego to reduce his probability of death