3. (10) Suppose an individual with a vn-M utility function u(x) = x is thinking of buying insurance. She has currently a wealth of $100. There is a 0.2 probability of an accident in which case she loses $40 of her wealth. (with probability 0.8, she suffers no loss) a) What is her expected utility if she buys no insurance? Define an insurance contract as a pair (a1, a2), where a = the premium paid by the individual to the insurance company and a 2 is the (net) payout made by the insurance company in the event of an accident. Assume all insurance companies are risk neutral. b) What is the expected utility of the individual if she buys insurance (a1, a2)? What are the expected profits of the insurance companies for such a contract? c) Suppose that all the contracts offered by the insurance companies are zero profit contracts (i.e. the expected profits are zero). Write down the individual's utility maximization problem. d) What contract (a1, a2) should she choose? Show your work,