Suppose that half the population is healthy and the other half is unhealthy. The cost of getting sick $1000 for healthy people and $10000 for unhealthy people. In a given year, any one person {regardless of health) either becomes sick or does not become sick. The probability that anyone person gets sick is 0.4. Each person's utility of wealth function is U{Y)=W-5, where Y is the person's wealth. Each person's initial wealth is $30,000. Although each person knows whether he or she is healthy, the insurance company does not have this information. The insurance company offers complete, fair insurance. Because the insurance company cannot determine whether a person is healthy or not, it must offer each person the same coverage at the same price. The only costs to the company are the medical expenses ofthe coverage. Under these conditions, the insurance company covers all the medical expenses of its policyholders, and its expected profit is zero. (Please show all the calculations you need for your answers.)

a) If everyone purchases the insurance, what is the price ofthe insurance?

b) At the price you determined in part a, do healthy people purchase insurance?

c) If only unhealthy people purchase insurance, what is the price?

d) At the price you determined in part c, do unhealthy people purchase the insurance?

e) Is there an adverse selection problem here?

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