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Consider the Akerlof's Market for Lemons developed in class with many identical buyers and identical sellers in the market for health insurance. The payoff of a buyeri is U3 = dX, P and that of a seller] is Us = P c)? 2 0. Each buyer knows their own type, Xi, while sellers only know that the distribution of health types in the population is uniformly distributed, X E [a, b], with an average, 1?. In addition, each buyer values restoring their own health more than it costs sellers, i.e., d > c. Assume the following parametric values: a = 0,!) = 10,c = 1, and d = 2. Suppose that the government is to provide health insurance to the individuals in relatively poor health, i.e., X E [9, 10], with the intent to prevent an adverse selection death spiral. g is a parameter, whose domain is 0 S g S 10. a) (2 pts.) Briefly explain why the buyers in relatively poor health have a higher value of X. b) (6 pts.) Calculate the share of buyers that must be served by the government such that all buyers in the private market are willing to purchase health insurance. Show all steps. Since all buyers, including those served by the government, are willing to purchase health insurance, a policy maker decides that the government insurance, X E [g, 10], is redundant. He argues that if the relatively healthy individuals find it in their self-interest to buy health insurance in the private market, why would n't those in relatively poor health who use their heath insurance more not purchase it on the private market? Briefly describe the implications of scrapping this government policy on: i. (2 pts.) the prevailing price, ii. (2 pts.) the share of buyers who purchase health insurance in the private market, iii. (2 pts.) efficient allocation of health insurance