Some people are good drivers, and others are bad drivers. The former have a 10% chance of crashing their cars, and the latter have a 30% chance. All have a total wealth of 400, but this will fall to 100 if they crash their cars. In other words, each will lose 300 of wealth if they crash. You are an insurance company manager who wishes to offer a pair of policies to all drivers. Each policy is designed to break even (zero profit) given the people who choose to buy that policy. The first policy has a premium of 90 and covers all losses (it will pay 300 in the event of a crash). The second policy has a premium of 5 and will pay 50 in the event of a crash. Who will buy which policy? Will the insurance company make a profit, break even, or lose money?
Each person has a utility function as follows:
Utility = (Wealth)0.5