12. a. Peter is contemplating to sell a risky asset that gives 625 with probability 0.60 and 100 with probability 0.40. Peter's utility from income/wealth is given by = where y refers to his income/wealth.

(i) If Peter currently does not have insurance for the risky asset, how much will he be willing to accept to sell this asset? Also, illustrate your answer graphically.

(20 marks)

(ii) If Peter currently has an insurance with full cover from a perfectly competitive insurance market, how much will he be willing to accept to sell the asset? Explain your answer. (25 marks)

b. (i) For Jimmy both current and future consumption are normal goods. He has strictly convex and strictly monotonic preferences. The initial real interest rate is positive. He is initially a lender. If the real interest rate rises, using the substitution and income effects, argue what will happen to his period 1 consumption level? Clearly illustrate your argument on a graph. (25 marks)

(ii) Mr. Kandle will live for only two periods. In the first period he will earn 101,000. In the second period he will earn 44,000. Mr. Kandle has a utility function (1, 2) = 122, where c1 and c2 are his period 1 and 2 consumption levels, respectively. The real interest rate is r = 0.1. What are his optimal consumption levels c1 and c2. Does he borrow or lend? How much? (30 marks