HAP-425-DL1 & 001 — Fall 2022
Prof. Phillip C. Zane
Week 5 Assignment: Adverse Selection
Homework problems:
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Please show your work and/or explain how you arrived at your answer (numerical answers with
no explanation will not receive full credit). If you played the Adverse Selection Game earlier this
week, you should be able to get through this homework set fairly quickly. You may find it useful
to use an Excel spreadsheet (or similar software) to speed up your work. If you use a
spreadsheet, submitting your spreadsheet along with written answers suffices to show your work.
Assume 100 people join an insurance pool (a group of people insured through community
rating). Based on past experience insuring people in this area and based on the age distribution,
the insurance company expects a range of anticipated health insurance claims as shown in Table
1 below.
Table 1:
Number of insured
10
10
10
10
10
10
10
10
10
10
Anticipated Health Claims/year/person
$200
400
500
700
1000
1300
1600
2000
3000
4500
1. Year 1:
D
Customers will buy insurance if their anticipated health claims are greater than the insurance
premium. Assume the insurance policy is “full” insurance: the insurance will cover all health
care expenditures incurred by the insured person. Suppose in the first year, all 100 people
purchase the insurance policy. What is the highest premium the insurance company could have
charged for all 100 people to have purchased insurance? What is the lowest premium that the
insurance company would have to charge to cover all anticipated claims?
HAP-425-DL1 & 001 — Fall 2022 — Prof. Phillip C. Zane & George Mason University
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2. Year 2:
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Year 1 turned out exactly as anticipated, with claims made and paid according to Table 1 above.
For year 2, assume that the insurance company charges the lowest premium necessary for it to
have enough money to pay all health claims last year (this is the same as the premium in year 1).
This is the calculated premium for year 2. But this year, some people compare their expected
health care expenditures with the premium being charged and some decide that the insurance
policy is too expensive. Of the 100 people in the population described above in Table 1, how
many will purchase insurance at the calculated premium?
3. Year 3:
In year 3, the insurance company once again calculates its premium by looking at the prior year
expenses (how much the insurer paid out to cover the insured customers’ claims) and dividing it
by the number of customers it is insuring. What is the premium in the third year? At this new
premium, how many customers will purchase insurance in the third year?
4. Now suppose a new situation. The population to be insured is the same one we started with in
question 1 (years 2 and 3 never happened). The premium is the same one you calculated in
questions 1 and 2, the lowest premium necessary to cover all claims. The difference for question
4 is that Congress has passed a statute that requires everyone to have insurance; anyone who
does not have insurance must pay a fee of $750. Assume that nothing else changes. Now the
population must decide whether to continue purchasing insurance based not only on the
anticipated health claims, but also on the fee for not purchasing insurance. Complete the table
below and write one or two sentences about how and why the thresholds and outcomes are
different from the outcomes in questions 2 and 3.
Premium
Yr. 1
Yr. 2
Yr. 3
Total number who
have dropped insurance
Total Number
Remaining
D
Yr. 4
Threshold for
buying insurance
5. What could we include to make our model more realistic? Provide two possible reasons (with
a two-sentence explanation for each reason) that insurance customers in the real world may not
behave in the ways predicted by questions 2 and 3.
HAP-425-DL1 & 001 — Fall 2022 — Prof. Phillip C. Zane & George Mason University
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