(Table: Insurance Claims) Five People Vary in Health Status

Essay

(Table: Insurance Claims) Five people vary in health status. Each person knows his or her own health status and expected medical bills, which are given in the table. These people are considering buying health insurance. Assume that each person is equally likely to file a claim.
a. Suppose that the insurance company does not know the health status of any one person but does know the expected claims of the group. If the insurance company sets the premium based on the average expected claims of these five people, what is the premium?
b. At the premium determined in part a, who buys health insurance? What will happen to the premium over time?