Explain clearly

Exercise 8.9 A person lives for 1 or 2 periods. If he lives for both periods he has a utility function given by U(n , 12) = u(r) + ou(r2) (8.7) where the parameter & is the pure rate of time preference. The probability of survival to period 2 is y, and the person's utility in period 2 if he does not survive is 0. 1. Show that if the person's preferences in the face of uncertainty are repre- sented by the expected-utility functional form ITwu(xw) (8.8) MED then the person's utility can be written as u(x) + o'u(12). (8.9) What is the value of the parameter &'? 2. What is the appropriate form of the utility function if the person could live for an indefinite number of periods, the rate of time preference is the same for any adjacent pair of periods, and the probability of survival to the next period given survival to the current period remains constant?Exercise 8.10 A person has an objective function Zu(y) where u is an increase ing, strictly concave, twice-differentiable function, and y is the monetary value of his final wealth after tar. He has an initial stock of assets K which he may keep either in the form of bonds, where they earn a return at a stochastic rate r, or in the form of cash where they earn a return of zero. Assume that Er > ( and that Prfr 0. 1. If he invests an amount B in bonds (0 0 then the individual will definitely under- report income. 3. If the optimal income report a* satisfies 0 RL. It is possible to take out partial cover on a pro-rata basis, so that an amount th of the loss can be covered at cost to where 0