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