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In this exercise, you are asked to analyze the health insurance. There are a continuum types of people in the society, whose health status can be represented by x, which lies in between 0 and 1. x follows uniform distribution U[0, 1]. A larger value of x indicates that the person's health condition is better. The probability of getting sick and receiving medical treatment is 0.05 0.03x. The expenditure is 200, a constant if one is sick and does not depend on x. For example, if x = 1, the probability of getting sick is 0.05 0.03 = 0.02. If x = 0.5, the probability of getting sick is 0.05 0.03 x 0.5 = 0.035. All people have an initial wealth of 500. 3. Now we consider the health insurance plan that covers the 80% of the total medical cost. The premium level is 6. (10') (a) If all the people in the society are risk neutral and correctly calculate their probability of getting sick and the medical expenditure, what is the fraction of people that will purchase this policy? Is the insurer's profit positive, negative, or zero? (5') (b) If all the people miscalculates their probability of getting sick as 0.065 0.03x, will the fraction of people that will purchase this policy be higher or lower than your answer in question 3(a)? Is the insurer's profit positive, negative, or zero under this scenario? (Hint: You don't have to solve for the exact number. Illustrate the economic logic. (5) 4. Now consider risk averse buyers. Suppose all the people have utility function u(w) = VW. = 2 (a) What is the fraction of people that will purchase the policy in question 3? Denote the answer to this question x. Please lay out the equation x needs to satisfy. (5') (b) Suppose that the insurance industry is monopolistic and the insurer has pricing power over the health insurance policy. The insurer is considering raising the premium level further to 6.5. Is it a good idea? Suppose you are a consultant to the insurer. Please state your opinions, and why or why not. (5) In this exercise, you are asked to analyze the health insurance. There are a continuum types of people in the society, whose health status can be represented by x, which lies in between 0 and 1. x follows uniform distribution U[0, 1]. A larger value of x indicates that the person's health condition is better. The probability of getting sick and receiving medical treatment is 0.05 0.03x. The expenditure is 200, a constant if one is sick and does not depend on x. For example, if x = 1, the probability of getting sick is 0.05 0.03 = 0.02. If x = 0.5, the probability of getting sick is 0.05 0.03 x 0.5 = 0.035. All people have an initial wealth of 500. 3. Now we consider the health insurance plan that covers the 80% of the total medical cost. The premium level is 6. (10') (a) If all the people in the society are risk neutral and correctly calculate their probability of getting sick and the medical expenditure, what is the fraction of people that will purchase this policy? Is the insurer's profit positive, negative, or zero? (5') (b) If all the people miscalculates their probability of getting sick as 0.065 0.03x, will the fraction of people that will purchase this policy be higher or lower than your answer in question 3(a)? Is the insurer's profit positive, negative, or zero under this scenario? (Hint: You don't have to solve for the exact number. Illustrate the economic logic. (5) 4. Now consider risk averse buyers. Suppose all the people have utility function u(w) = VW. = 2 (a) What is the fraction of people that will purchase the policy in question 3? Denote the answer to this question x. Please lay out the equation x needs to satisfy. (5') (b) Suppose that the insurance industry is monopolistic and the insurer has pricing power over the health insurance policy. The insurer is considering raising the premium level further to 6.5. Is it a good idea? Suppose you are a consultant to the insurer. Please state your opinions, and why or why not

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