Asymmetric Information and Insurance Markets

There is a single (risk neutral) car insurance company and two types of consumers: low risk drivers who crash with probability and high-risk drivers who crash with probability . Half the population is high risk.

Everyone earns $9. A car crash requires payment of $8.

Customers has utility from consumption in dollars of .

• Without insurance, what is the expected income net of crash costs of a safe driver?

• Without insurance, what is the expected income net of crash costs of a risky driver?

• Without insurance, what is the expected utility of a safe driver?

• Without insurance, what is the expected utility of a risky driver?

Suppose the insurance company can perfectly tell the two types apart.

• What amount should it charge for full insurance to the safe driver to make the most profit subject to the driver choosing to purchase insurance?

• What amount should it charge for full insurance to the risky driver to make the most profit subject to the driver choosing to purchase insurance?

Suppose the insurance company cannot tell drivers apart.

• What is the expected cost of car crashes per driver if everyone buys insurance?

• If the company charges the highest possible price that will get every driver to purchase insurance, what is the expected revenue net of car crash costs it will get per driver?

• Is it possible to provide full insurance to everyone in this market, if drivers' types are not observable?