Suppose that within a given city, women between the ages of 30 and 41 fall into one of four health categories: very healthy, healthy, unhealthy, and very unhealthy. As a part of the new PPACA, the government has mandated 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 do 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." The following table presents the number of people in each group and the expected monthly cost of oviding care for each category of person. The table also presents the maximum that an individual is willing to pay within each group. As you can see, this is higher than the expected cost. This reflects the fact that people are generally risk averse. In the context of health insurance, this means they 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 ($) Maximum Willingness to Pay for Insurance ($) Total Expected Monthly Cost ($) Type of Person Number of People 500 50 55 1 300 500 575 2 Very Healthy Healthy Unhealthy Very Unhealthy Total 150 980 700 6,000 3 4 50 9,000 5 6 If the insurance company must offer one plan to all women between the ages of 30 and 41, the monthly premium (rounded to the nearest dollar) must be per person in order for the total amount the insurance company collects to be equal to the total amount it expects to pay out. Suppose the government repeals the mandate, and now it allows each person to decide whether she wants to buy into the policy. Complete the following table, assuming that the premium is the one you calculated above. If a type of person will not purchase insurance at this premium, enter "0" into the appropriate cell, since the insurance company collects no money from them. Type of Person Very Healthy Healthy Unhealthy Very Unhealthy Chooses to buy health insurance? 8 Yes/No 9 Yes/No 10 - Yes/No 11 - Yes/No Amount Insurance Company Collects (Number of People x Premium) ($) 12 13 14 15 Once consumers are given a choice of whether to buy into the premium, the insurance company will collect a total of 16 in monthly premiums, and it will pay out an expected total of 17 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 18 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. 19 O Very Healthy O Healthy Unhealthy Very Unhealthy Without a government mandate to purchase insurance, as premiums rise the 20 healthy people are likely to stop purchasing insurance. This causes the insurance company to face 21 expected costs per person, thus forcing it to 22 premiums in order to break even. The cycle continues until only the 23 healthy remain to purchase insurance. This phenomenon is known as a death spiral
