Suppose that your utility function is given by (I) = ??n(4??) , where ??n(??) stands for the natural logarithm of x, and I is the amount of income you make in a given year. Suppose that you typically make $30,000 per year, but there is a 5 percent chance that, in the next year, you will get sick and lose $20,000 in income due to medical costs.
a. What is your expected utility if you do not have insurance to protect against this adverse event?
b. Suppose you can buy insurance that will cover your losses if you get sick. What would be the actuarially fair premium? What is your expected utility if you buy the insurance policy?
c. What is the most that you would be willing to pay for this policy?