Question: The Acme Auto Insurance Company is risk neutral and seeks to offer insurance at its actuarially fair price. All drivers have the same initial income, $400, and if they are involved in an auto accident, their income falls to $0. All have the same utility index: U(Y) = Y1/2 There are two groups of drivers: half are safe drivers with a 25% chance of being in the accident, and the others are risky drivers with a 75% chance of being in an accident. Each individual knows whether she is a safe or risky driver.
a) If the Company can identify a safe driver from a risky driver, what premium will it charge a driver in each group? What amount of insurance will each type of driver buy? How much income will each type of driver have in the two states of the world? ??highlight ??
b) If the Company cannot identify a safe driver from a risky driver, it only knows that there is an overall 50% chance of an individual being in an accident, so it charges a premium of 50% to everyone. Solve for the optimal decision for each type of driver (assume there is no limit on the amount of insurance an individual can buy). What is Acme's expected profit per driver? Is it in long run equilibrium? Explain precisely what is going on here.