There is a single (risk neutral) car insurance company and two types of consumers: low risk drivers who crash with probability 14 and high risk drivers who crash with probability 12. Half the population is high risk.

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

Customers has utility from consumption (in dollars) ofU=C^(1/2)

a. What is the expected utility for each type of driver without insurance?

b. What is the most an insurance company could charge each type of driver and still get them to buy insurance?

c.Suppose insurance companies cannot tell the drivers apart so they charge the lower of the two fees above to maximize their customer base. What is the expected cost per driver insured? Why is this a problem?

d.If the company raised the price for insurance a little bit would that fix the problem in (c)? Explain briefly