Question 3 (36 points) Suppose there are two types of people, high risk (H) and low risk (L) with utility function U(c) = 20.5. Each has income (=consumption) of $100. The high risk people are 10% of the population and have a 75% chance of getting cancer in which case their income would be zero. The low risk people are the remainder of the population and have a 25% chance of getting cancer and hence zero income. The private insurance industry is perfectly competitive. (a) Suppose private insurers are able to distinguish the two types. What market price would emerge for each risk type? How much insurance would each type purchase? (b) Suppose private insurers cannot distinguish between types and attempt to price according to average risk. What is the premium per dollar of insurance for average risk? What problem do you foresee? (c) Insurers are afraid the government will take over the industry and decide to price in a different way. Mindful of the social consequences they will price so that the high risk is fully insured. What condition must be placed on the low-risk for this to be an equilibrium