Before people turn 65, they can purchase long-term care insurance to ensure that they are taken care of in their old age, but it is very expensive. No insurance provider will sell the insurance to anyone over 65. There are two types of people: high-risk people, who have a 50% chance of having a serious health event before they die, and low-risk people, who have only a 10% chance of a serious health event. There are 1,000 people in the population; 1/3 of the population is high - risk, and the rest are low-risk. If a serious health event occurs, the insurance will pay out 2,000,000; if not, they will only have to pay 200,000 on average. All people are risk averse, so they are willing to pay for insurance according to the following formula:

WTP = (p + 0.1) EP_event + (1 - p) EP_{no event}

where: p = probability that a serious health event occurs

EP_event = the insurance payout if an serious health event occurs

EP_{no event} = the insurance payout if a serious health event does not occur

a. What is each type of person willing to pay for long-term care insurance? Draw an insurance market for each type, and use your answer to draw their demand curve for long-term care insurance.

b. What is the price the insurance company will charge each type of person, assuming they sell fair insurance and can tell the difference between them? Add supply curves to your graphs from (a). Do both types buy insurance if there is full information?

c. Now assume that the insurance company does not know which type of person is which. What is the average price they will set for the market? Who will buy insurance? How does this illustrate the adverse selection problem?