Problem

You are considering buying one of two types of health insurance. You guess that in the next year there is a 1 percent chance of serious illness that will cost you $67,500 in health care; a 9 percent chance of a moderate illness that will cost you $2,500; and a 90 percent chance of regular health care needs that will cost you $500. One type of health insurance is emergency-only coverage; it will cover your expenses for serious illness but not moderate illness or regular care. The other type covers moderate illness and regular expenses, but its payout is capped, so it will not cover the cost of a serious illness.

a. What is the expected value of payouts from the emergency-only insurance?

b. What is the expected value of payouts from the capped-coverage insurance?

c. Which is the more risk-averse option?