Consider two cities Where there are three types of people who want to buy disability insurance. The low-risk type (L) have a 8% chance of being disabled, the medium risk type (M) have a 15% chance of being incapacitated and the high risk type (H) have a 45% chance of being disabled. In city A, 50% of the population is of type L, 40% are of type M and 10% are of type H. In city B, 10% of the population is of type L, 60% are of type M and 30% are of type H. Longterm care insurance provides income if they are incapacitated for the rest of their life (there are no additional costs). Individuals have the following utility function over consumption (or income): 11(0) = ln(c) Individuals earn 500/- if healthy, but only 5/- if incapacitated. They make the decision to purchase insurance before the event occurs. a. The insurance company decides to sell full insurance to all types in both the cities at a premium of 85/. Which types buy in city A. What about city B? b. What is the prot earned by the company in city A? What is the prot earned in city B