2. The insurance death spiral Suppose that within a given city, men ages 65 and older fall into one of four health categories: very healthy, healthy, unhealthy, and very unhealthy. As a part of the Patient Protection and Affordable Care Act (PPACA), the government mandates that insurance companies must charge the same premium to all people within a given gender, age, and geographic region. The insurance company must determine the premium it should charge to all people in this category so that it can cover the total cost of care. In order to complete your analysis, make the following assumptions: 1. The insurance company does not incur any costs to run or administer the policies, and it does not make any profit. 2. The population is large enough so that expected values hold at the aggregate level. 3. Anyone who pays the monthly premium receives complete coverage of all medical expenses (in other words, everyone is offered full insurance). 4. All citizens are risk averse and therefore are willing to pay a premium above the expected value of their costs, up to the amount indicated in the column \"Maximum Willingness to Pay for Insurance" in the following table. The following table presents the number of very healthy, healthy, unhealthy, and very unhealthy people, as well as the expected monthly cost of providing care for each category. The table also presents the maximum that an individual is willing to pay within each group, which is higher than the expected cost. This reflects the fact that people are generally risk averse. In the context of health insurance, this means that people prefer to pay some amount for certain each month than to face paying the full costs of somewhat unpredictable care. Complete the following table by computing the total expected monthly cost of care for each type of citizen, the total number of people in this market, and the total expected monthly cost of insuring all citizens. Expected Monthly Cost Maximum Willingness to Pay for Total Expected Monthly Cost Type of Number of of Care Insurance of Care Person People (Dollars per person) (Dollars per person) (Dollars) Very Healthy 600 100 110 [: Healthy 250 450 518 : Unhealthy 250 700 980 : Very 50 5,500 8,250 I: Unhealthy If the insurance company must offer one plan to all men ages 65 and older, the monthly premium (rounded to the nearest dollar) must be :] per person in order for the total amount the insurance company collects to be equal to the total amount it expects to pay out. Suppose the government repeals the mandate, and now it allows people to decide whether they want to buy into the policy. Complete the following table, assuming that the premium is the one you calculated in the prior question. If a type of person will not purchase insurance at this premium, enter \"0\" into the appropriate cell, since the insurance company collects no money from these people. Amount Insurance Company Collects Type of Person Chooses to Buy Health Insurance? (Number of People x Premium) Very Healthy V Healthy Yes Unhealthy Very Unhealthy n Once consumers are given a choice of whether to buy into the premium, the insurance company will collect a total of in monthly premiums, and it will pay out an expected total of: to cover the expenses of all those who buy the policy. Based on the groups that still want to buy insurance at the original premium, the insurance company would need to collect per person to cover the expected total cost per person. If the insurance company raises the premium to this price, which of the following groups would still be willing to buy health insurance? Check all that apply. D Very Unhealthy D Very Healthy C] Healthy [3 Unhealthy Without a government mandate to purchase insurance, as premiums rise, the V healthy people are likely to stop purchasing insurance. This causes the insurance company to face V expected costs per person, thus forcing it to V premiums in order to break even. The cycle continues until only the V healthy remain to purchase insurance. This phenomenon is known as a death spiral