A farmer has a utility function of U(m) = ln(m), where m is income. The farmer is considering buying crop insurance. If the farmer has a good year, she will have an income of $300,000.
If there is a worm infestation the crop will have low yields and income will only be $15,000. The probability of an infestation is is 3%.
If the farmer can buy insurance for a premium of $0.05 per dollar of coverage, how large of an insurance policy should the farmer buy?