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 the table below.

Number of insuredAnticipated Health Claims/year/person

10$600

10750

10900

101050

101200

101350

101500

101650

102250

104500

1.Year 1:

Customers will buy insurance if their anticipated health claims are greater than the premium. Let's say in the first year, all 100 people purchase the insurance plan. What is the highest premium the insurance company could have charged for all 100 people to have joined?

Given,

Customers will buy insurance if the anticipated health claims are greater than the premium.

Here,

Demand curve of the insurance pool

No of people willing to buy

Premium

100

$600

90

750

80

900

70

1050

60

1200

50

1350

40

1500

30

1650

20

2250

10

4500

Since, all the people have joined in this the premium needs to be less than or equal to the lowest claims.

Thus,

Premium should not be > $600 so that the lowest 10 customers can join too.

Thus, the maximum premium charged = $600

2.Year 2:

The claims experience of the customers is found to be generally consistent with expectations of the insurance company. What would be the premium in the second year? If those customers who had claims in the first year that were less than or equal to the premium now decide not to continue to buy insurance, how many will continue to be insured in the second year?

Total premium that can be collected for different prices:

No of people willing to buy

Premium

Total Premium Collected

100

$600

60000

90

750

67500

80

900

72000

70

1050

73500

60

1200

72000

50

1350

67500

40

1500

60000

30

1650

49500

20

2250

45000

10

4500

45000

The customers in the first year decided not to continue insurance.

So,

The highest premium can be collected for $1050 which will generate maximum revenue for the insurance company.

The customers who anticipated health claims greater than or equal to $1050 will continue.

Thus, the total number of people who will be insured in the second year is 70 i.e. $73,500.

3.Year 3:

What would be the premium in the third year? If those customers who had claims in the second year less than or equal to the premium now decide not to continue to buy insurance, how many will continue to be insured in the third year?

Here,

The customers in the second year decided not to continue insurance.

So,

The highest premium can be collected for $1200 which will generate maximum revenue for the insurance company i.e. $72,000.

The customers who anticipated health claims greater than or equal to $1200 will continue.

Thus, the total number of people who will be insured in the second year is 60

4.Year 4:

What would be the premium in the fourth year? If those customers who had claims in the third year less than or equal to the premium now decide not to continue to buy insurance, how many will to continue to be insured in the fourth year?

Here,

The customers in the third year decided not to continue insurance.

So,

The highest premium can be collected for $1350 which will generate maximum revenue for the insurance company i.e. $67,500.

The customers who anticipated health claims greater than or equal to $1200 will continue.

Thus, the total number of people who will be insured in the second year is 50.

5.Determine what happens in the first four years if there is a $750 penalty for not carrying insurance.Fill in the table below and write one or two sentences about how and why the outcome is different than the outcome in parts A through D.Assume that nothing else changes, except that now the population decides whether to continue purchasing insurance based not only on their anticipated health claims, but also the penalty they will pay if they do not purchase insurance.

PremiumThreshold forTotal number who Total Number

buying insurancehave dropped insuranceRemaining

Yr. 1

Yr. 2

Yr. 3

Yr. 4

6.Provide two possible reasons (with a two sentence explanation for each reason) why insurance customers in the real world may not behave in the ways predicted by parts

A through E.