There are three types of residents in Bruintown. The health gurus (H), regular people (R) and people prone to sickness (P). Assume each group represents one third of the population. The utility of each resident of Bruintown is given by u(w) = 2w 0.05w?; where w represents the wealth of a particular resident. Initially, each resident has a wealth of 12. Residents face a health shock, that is, there is some positive probability that a resident will get sick. If residents get sick, they have to visit the doctor which costs 8 dollars and fully heals the resident. Each group has a different propensity to being sick: health gurus have a probability of 0.1; regular people have a probability of 0.4 and people prone to sickness have a probability of 0.8. 10. Ashe Center is promoting a health insurance plan. Let's assume that every resident of Bru- intown will take up this plan, because it will be fully paid for by the government. What is the actuarial fair premium (that is, the premium that yields zero profits to the insurance company)? (a) 2 ECON 101 Winter 2023 - UCLA