Insurance contracts are a useful laboratory for examining risk tolerance and the subjective estimation of probabilities. (a) Jared is considering buying boat insurance. His annual income is I = 100, and the cost to replace his boat in the event that he crashes it is L = 36. Jared's utility function over his own wealth is u(w) = w. Jared's subjective estimate of the probability that he crashes his boat this year is ] = 0.05. What is the maximum amount that Jared would be willing to pay for boat insurance for the year? Assume the insurance company covers the entire cost of replacing the boat. (Hint: consider Jared's wealth and his expected utility of that wealth in the case with and without insurance, and find the point where he's indifferent.) (b) A contract requires consent from two parties, so in this case, we also need to consider the insurance company's perspective. Assume that the answer you found in part (a) also happens to be the minimum insurance premium that Geico would accept in order to insureJared's boat for the year. Further assume that Geico is risk-neutral with respect to its insurance policies, and intends to operate with zero underwriting loss. What must beGeico's subjective estimate of the probability that Jared crashes his boat this year?