A home owner has a utility function of U (m) = √m, where m is income....

A home owner has a utility function of U (m) = √m, where m is income. The home owner is considering buying flood insurance because they live near a river that has flooded in the past. If it is a dry year, she will have an income of $60,000 to spend on other things. If it is a rainy year and there is a flood, then she has to pay for repairs to her house. Then her income will only be $20,000 to spend on non-flood costs. The probability of a flood based on historical data is 4%.

(a) (a) If the home owner can buy insurance for a premium of $0.04 per dollar of coverage, how large of an insurance policy should the homeowner buy? Set up the expected utility maximization problem and solve for K, the optimal insurance policy size.

(b) Now suppose we do not know the cost of the insurance policy. But you now know that in the event of a flood, that the insurance policy will pay you 75% of damages. What is the maximum amount the homeowner would be willing to pay for such an insurance policy?

(c) Explain in words how to generally calculate expected utility. What information do you need? What terms do you multiply versus add? Be clear in your explanation.

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Expert Solution

Rahul Sunny answered 1 year ago

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