Background information for questions 9-11: 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. ~ TTT I 1 s 1 ie1ey ~ 1 " =1 i 11. Now assume that individuals choose whether to have insurance or not, and pay for the insur- ance premium themselves. If Ashe Center charges the premium you computed in the previous question, which types of residents will sign up? In this case, what is the per-person expected profit for Ashe Center? (Assume that negative per-person profit is sustainable) (a) All types will purchase the insurance. The per-person expected profit is zero. (b) Types R and P will purchase the insurance. The per-person expected profit is -1.33 (c) Types R and P will purchase the insurance. The per-person expected profit is 1.5 (d) Only type P will purchase the insurance. The per-person expected profit is -4.53 (e) Only type P will purchase the insurance. The per-person expected profit is -8