1. Why Buy Insurance Assume you have the following Utility function: U = Income. This utility function corresponds to risk aversion.

Assume that you earn $100,000

. You have a 75% chance of staying healthy and a 25% chance of getting sick

If you get sick, it will cost you $25,000 in medical bills

. You are offered health insurance at the actuarially fair price. If you are offered health insurance at the actuarially fair price then you will fully insure.

a) What does actuarially fair mean?

b) What is your expected income if you do not buy health insurance?

c) If you decide to purchase insurance, what would be the actuarially fair premium?

d) What is your expected income if you buy health insurance (assume that you fully insure)?

e) What is your expected utility if you do not buy health insurance? f) What is your expected utility if you do buy health insurance?

g) Based upon your answers, should you buy health insurance or not?

h) You have a friend who is considering whether or not to buy health insurance with income and risks as listed above. Assume this friend has NOT taking ECON 480/680 and therefore does not know terminology like risk aversion or expected utility. Explain clearly to this friend in everyday language why they are better off by purchasing health insurance.

i) Draw in excel the utility function. Indicate the income if sick; income if healthy; expected utility, and utility of expected value. Label and describe below in words (like the handout).