Now assume that an individual’s income is £200,000 in a good year and £40,000 in a bad year and she can pay a premium of £20,000 to get a payout of £160,000 if she has a bad year. Does this mean that for some a, if she would not insure at the lower income she will now, or that for some a if she did insure at the lower income she will not now, or that for all a, she will make the same insurance decision as she did at the lower income? What does your answer tell you about the risk attitudes of somebody with a utility function ? [You can attempt to answer this question with general analysis or by arithmetic examples. If you do the latter you may wish to use a spreadsheet.]

U=Y power alpha
Background:

There are many people with a job with uncertain income. Each person has a 90% chance of earning £100,000 but with bad luck (probability 10%) will only get £20,000. People can insure against this possibility. For a premium of £10,000 the insurer will pay a sum of £80,000 if the bad luck occurs. At the moment assume that the income from the job is the person’s only income.