Suppose all individuals have a utility function of U = , where C is the amount of consumption a person has in any given period. There are two types of people: those at high risk, with a 4% chance of accident, and those at low risk, with a 2% chance of accident. Half of individuals are high risk, and half are low risk. The income of all individuals is $40,000 per year, and a catastrophic accident costs $30,000 in the year of the accident.

a. Calculate the actuarially fair insurance premium for each type of person, assuming the insurance company can identify who is high risk and who is low risk.

b. How much will a high-risk individual be willing to pay for insurance? A low-risk individual?