10–2. Suppose that a health insurance company is considering offering insurance to a population consisting of healthy and unhealthy people. Healthy people are expected to have

$1,000 per year in medical bills, while unhealthy people are expected to have bills of

$5,000 per year. The company knows that the population consists of 25,000 healthy people and 25,000 unhealthy people. However, it cannot tell whether any given individual is healthy or unhealthy. Individuals know their own type and only purchase insurance if the premium is no more than $100 above their expected medical bills. The insurance must be priced at least $100 above expected per-person costs for the insurance company to cover its costs and to be profitable. In equilibrium, what price will the insurance charge in this market? Who will buy the insurance? Assume for this problem that there are no binding regulations that limit insurance prices or force people to purchase insurance.