Question

Suppose there are two types of people: Healthy and Unhealthy. It costs more to
insure unhealthy people because they are likely to incur more medical bills.
Suppose the marginal cost (MC) of providing an insurance policy is $1,000 for a
healthy person and $4,000 for an unhealthy person. Assume healthy people are
willing to pay $1,500 for health insurance, and unhealthy people are willing to pay
$5,000. Suppose the insurance company charges P = MC so as to earn zero profit.

a) With complete information, will all people be insured? If no, explain why. If yes,
what would be the price of insurance for each type of people?

b) Now suppose there is asymmetric information. People know whether they are
healthy or unhealthy, but the insurance company can’t tell. However, it knows that
20% of the population is unhealthy. If people can choose whether to buy insurance
or not, who will buy insurance? And what will be the price of insurance in
equilibrium? Is this outcome efficient? Explain why or why not.

 

Answer 1

Question 1.

A. When there is complete information, the insurance company will charge different prices/insurance premium for healthy people and unhealthy people.

According to the rule, P=MC,

For healthy people, insurance company will charge price, Ph=MCh= $1,000

Since healthy people are willing to pay as much as $1,500 for insurance, all healthy people will buy insurance.

For unhealthy people, insurance company will charge, Pu=MCu=$4,000

Since unhealthy people are willing to pay as much as $5,000 for insurance, all unhealthy people also buy insurance.

Thus, with complete information, everyone will be insured with healthy people paying $1,000 and unhealthy people paying $4,000.

B. When the insurance company does does have complete information, it will charge price according to the expected marginal cost of insurance.

Percentage of unhealthy people= 20%= 0.2

Therefore, percentage of unhealthy people= 80%= 1-0.2=0.8

Expected marginal cost= percentage of healthy people*Marginal cost for healthy people+ percentage of unhealthy people*marginal cost for unhealthy people

Expected marginal cost= 0.8*1,000+ 0.2*4,000

Expected marginal cost= 800+800= $1,600

Thus, the insurance company will charge a single price to everyone (because it cannot distinguish between people) equal to $1,600.

Since $1,600 is greater than what healthy people are willing to pay ($1,500), healthy people will not buy insurance and exit the market.

Unhealthy people will buy the insurance because $1,600 is less than what they are willing to pay ($5,000). Thus, unhealthy people will buy insurance.

This market outcome is not efficient because the asymetric information drives out healthy people out of market/insurance market. Only unhealthy people will buy insurance and insurance company will make loss and in the long run, it may exit. Asymmetric information creates market failure situation.