Every person has $1,000 to spend. There are two groups of people: 100 sick people and 300 healthy people. A sick person visits the hospital with probability p= 0.25. A healthy person visits the hospital with probability p= 0.05. Any hospital visit costs $400. All individuals have the following expected utility function: EU= (1−p)√Cg+p√Cb
a) What is the actuarially fair price for a sick person? For a healthy person?b)Suppose the insurance company can distinguish between sick and healthy individuals. What price(s) will they charge each group for full insurance?
c)Suppose the insurance company cannot distinguish between sick and healthy individuals. If they charge one price to everyone for full insurance, what price x do they need to charge to make zero expected profits when everyone buys? (Hint: It is somewhere in between the actuarially fair prices, but not halfway since groups are of different sizes.)