Question 2 (50 pts) Manuel Zapata Olivella can be either sick with probability 0.7 or he can be healthy. If he is healthy his income is 100. If he is sick his income is 10. Manuel's utility function depends on income as follows: u(1) = In(1) All available insurance contracts consist of a premium r and a payout q. c. (8 pts) Consider contract A. With this contract Manuel's income when insured and healthy becomes 58 and when insured and sick it becomes 28. Is this contract actuar- ially fair? YES NO Explain. d. (8 pts) Consider contract B. In this contract Manuel's premium is 70 and his payout is 90. Is this contract actuarially fair? YES NO Explain. e. (7 pts) Consider contract C. In this contract Manuel's premium is 81 and his payout is 90. Provide a ranking of Manuel's preferences over contracts A, B, C and N (no insurance), where 1 is the most preferred and 4 is the least preferred. 1 2 3 Explain. f. (7 pts) What would be the ranking if Manuel was risk-neutral? Explain. 2 3 4 Does the ranking change? YES NO If so, briefly explain why