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Question 3 [25 Points). Adverse Selection {see topic 10}: Suppose person 1' has \"health risks\" given by 9,. People can insure against the costs associated with health risks. An equilibrium consists of a market price for health insurance 33* = E[I9| E 6*] and a set of people 6* = {9 : r09) g 33*} who choose to buy insurance at that price. Note that r09) is the reserva- tion price, that is, the maximum price someone is willing to pa},r for health insurance. The maximum price individual i is willing to pa}r is assumed to be r[d,-) = 2* 3,, Le, healthier people (those with lower health risks) have a lower reser- vation price and are thus less likely to buy insurance. Suppose there are three health risk levels: HH = 4, 3M = E, and 9;; = 20. In the population we consider, the share of individuals for each health risk level is one third. That is, the share of people for each health risk level is SH = 1f3, SM = 1/3, and SL = 1/3. (a) Find the market price p" and state which health risk types will buy insurance and which will not. This is the outcome we can expect to occur in an unregulated market.l (h) What would happen if we were to regulate the market and require that all individuals must buy health insurance? How high would the new equilibrium price he