Mr. Gesundheit is worried he might contract coronavirus and is considering buying health insurance from Feeling Blue.Feeling Blue believes there is a 40% chance that Gesundheit will get coronavirus and be costly to insure.He will offer Gesundheit two insurance plans: (1) a comprehensive plan with price/premium and actuarial value and (2) a skimpy plan with price/premium and actuarial value .Mr. Gesundheit has utility function , where is the actuarial value of the plan (e.g., if the actuarial value is 10%, ), is its price/premium, and i is Mr. Gesundheit's type such that and .If Gesundheit does not buy insurance, he can file for bankruptcy as ``implicit insurance.''It is costless to Gesundheit to file for bankruptcy.Bankruptcy will cover 10% of Mr. Gesundheit's expected costs.The expected cost of an insurance plan with value is .

(a)What are the constraints we need in this problem?Which of these constraints are binding? [15 points]

(b)Find the optimal bundles and that maximize Feeling Blue's expected profit. [10 points]

(c)How much would you be willing to pay Dr. Fauci to find out if Mr. Gesundheit will get coronavirus and be costly to insure? [10 points]

(d)Suppose Dr. Fauci actually charges 450.What is the probability of Gesundheit contracting coronavirus that would make Feeling Blue indifferent between hiring and not hiring Dr. Fauci?[15 points]