Suppose that within a given city, women ages 65 and older 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 premiums to all people within a given gender, age and geographical 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 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 profits

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 are therefore 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 providing 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 that they prefer to pay some amountfor certaineach month than to face paying the full cost 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 WTP for Insurance

Total Expected Monthly Cost

Type of Person

Number of People

($)

($)

($)

Very Healthy

500

100

110

Healthy

300

450

518

Unhealthy

200

700

980

Very Unhealthy

50

5,000

7,500

Total

1.If the insurance company must offer one plan to all women ages 65 and older, what will be the monthly premium (rounded to the nearest dollar) per person?

2.What is the Consumer surplus for this cohort of women?

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.

Amount Insurance Company Collects (# of People X Premium)

Type of Person

Chooses to buy health insurance? (Yes or No)

($)

Very Healthy

Healthy

Unhealthy

Very Unhealthy

Once consumers are given a choice of whether to buy into the premium:

3.How much will the insurance company collect in total monthly premiums?

4.How much will the insurance company pay out in expected total costs to cover the expenses of all who buy the policy?

5.Based on the groups that still want to buy insurance at the original premium, how much would the insurance company need to collect per person to cover the expected total cost per person?

6.If the insurance company raises the premium to the price in (#5), which of the following groups would still be willing to buy health insurance?

7.Explain what happens without a government mandate to purchase health insurance.

8.What is the phenomenon in #7 known as in health insurance?

Discussion questions

9.How could the model you just examined be extended to more than four types of health insurance consumers?

10.What if the insurance company does incur administrative costs? How would this affect the expected costs of running the insurance policy, the premiums charged, and the consumer surplus of those who buy insurance? (Provide realistic estimates of administrative costs and your reasons).

11.How would the results of this model change if the insurance companies were not required to provide full insurance to everyone and could offer multiple policies ( including one with either a co-pay or deductible?