Please answer 1-4. thank you!

Exercise 1: Valuing Improvements in Longevity and the Implied Value of Life. Suppose that an individual may live up to two periods. That is, the individual lives for certain during period t. In that period, his sub-utility function is given by: " (c) = log Ct- The individual survives period & and lives into period t + 1 with probability p. If he is alive in period t + 1, then his state sub-utility function is given by: (C+1) = log Ct+1 and if he dies, he receives the fixed utility level B. We make the following assumptions: 1. The individual has access to a perfect capital market. 2. The individual discounts the future at a rate of B. 3. The individual's endowment is given by (wt, with). Please answer the following questions: 1. 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? 2. Solve the individual's utility maximization problem and determine the amount he saves. 3. How do savings depend on the probability of death? 4. 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 do it and remember to make your life easy!)