Health economy. Suppose that there are two types of people, sick and healthy. Sick types have 90% chance of incurring a $1,000 hospital bill. Healthy types have a 20% chance of incurring a $1,000 hospital bill. a) Suppose that the health insurance industry is a perfectly competitive industry, there are no administrative costs, and people's health type is public information. How much will an insurance company charge both types of people to cover this potential hospital bill in an ideal insurance contract? Jay is a sick type with an endowment of $10,000. Assume his utility over money is defined as U(M) = M2/3, where M denotes money. This is an example of a concave function. b) What is Jay's utility from his expected income? What about his utilities in the two states? c) What is Jay's expected utility of the lottery he faces? (Hint: the lottery is that Jay will either have $10,000 or $9,000 depending on the realized state). d) Represent Jay's situation graphically using the numbers from (b) - (c). e) Propose an insurance contract that is both full and actuarially fair in Jay's situation. Should Jay buy it? Why