There are two types of drivers, high-risk drivers with an accident probability of 2=3 and low risk drivers with an accident probability of 1=3. In case of an accident the driver suffers a loss of 1. The initial wealth of both types of drivers is 2. Both types are expected utility maximizers with utility index u(z) = ln z.
(i) what is the maximum insurance premium that each type would be willing to pay to fully insure their accident risk?
(ii) there is an equal number of drivers of both types so that the overall accident prob- ability is 1=2. Assume that the government offers an insurance contract that has a premium of 1=2 and covers the full cost of the accident. Would the low risk types accept this contract?
(iii) Now assume that the government offers a full coverage contract that has a premium of 2=3 and a partial coverage contract with coverage C and premium C=3. Write down the inequality that must be satis?ed to ensure that high-risk types prefer the full coverage contract over the partial coverage contract.