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, 600 people purchase insurance. What is the highest premium the insurance company could charge to get 600 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.

C. How many people buy insurance at the new Year 2 premium? Explain.

D. Year 3. Based on premium setting rules above, what is the Year 3 premium?

E. How many people buy insurance at the new Year 3 premium? Explain.

F. Year 4. What is the Year 4 premium?

G. How many people by insurance at the new Year 4 premium. Explain

H. Now consider how an insurance mandate, enforced with a tax penalty, might impact the insurance market.

The government imposes a $400 fine for being uninsured. Insurance companies assume this means everyone will get insurance, so for year 1 they set the premium equal to the average expected claim of the entire population. What is the new premium?

I. Remember that there is a $400 penalty for being uninsured; this changes the premium point at which people will not want to buy insurance. If the premium is set to $450 and there is a $400 penalty if people choose not to get insurance, how many people will choose to get insurance?

J. 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?

K. How many people buy insurance at this new premium (remember to account for impact of the penalty)? Remember that people only buy insurance if their expected spending is lower than the premium (indifference between the two means they don't get insurance)? Explain.

L. Thinking about what you know about adverse selection, what are two reasons why insurance companies or consumers might not behave as predicted in the scenarios from this assignment?