Question

There is an insurance pool of 1000 people. All are covered via community rating. The distribution of expected health care costs per person is shown in the table below.

Number of people	Expected health care claims
100	$0
100	$100
100	$200
100	$300
100	$400
100	$500
100	$600
100	$700
100	$800
100	$900

A. Year 1. Customers only buy insurance if their expected health care claims are higher than the premium. In the first year, 500 people purchase insurance. What is the highest premium the insurance company could charge to get 500 people to buy insurance? Explain.

B. Year 2. Expected health care claims are accurate. The insurer wants to cover costs, so they set their year 2 premium equal to the average claim for people who were covered in the prior year. What is the new premium? Explain.

Answer 1

A:

The maximum premium that can be charged is 499$.So that 500 people purchase the insurance who are willing to pay from 500 to 1000$, range with 100 people in each amount

B

The Total cost of premium due to claims for insurer

(500x100)+(600x100)+(700x100)+(800x100)+(900x100)=350,000 $

Total no of claims =500

The average premium to be charged for 2nd year = 350,000 /500 = 700 $