There are a continuum types of people in the society, whose health status can be represented...

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There are a continuum types of people in the society, whose health status can be represented by, 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 also depends on x, equal to 300-200x. - - 200 = For example, if x = 1, the probability of getting sick and receiving medical treatment is 0.05 0.03 = 0.02 and the expenditure equals to 300 100. If x = 0.5, the probability of getting sick and receiving medical treatment is 0.05 -0.03 x 0.5 = 0.035 and the expenditure equals to 300 - 200 x 0.5 = 200. All people have an initial wealth of 500. 2. Now we consider a health insurance policy that covers the total expenditure in full. The premium level is 7. (20') (a) If all the people in the society are risk neutral. What is the fraction of people that will purchase this policy? Is the insurer's profit positive, negative, or zero? [Hint: if X follows U[0, 1], the probability of X < xo when 0 < xo <1 is xo. ](10') (b) If all the people in the society are risk-averse, is the fraction of people that will purchase this policy larger or smaller than your answer to question 2(a)? How will the insurers' profit change compared with your answer in question 2(a). (10') There are a continuum types of people in the society, whose health status can be represented by, 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 also depends on x, equal to 300-200x. - - 200 = For example, if x = 1, the probability of getting sick and receiving medical treatment is 0.05 0.03 = 0.02 and the expenditure equals to 300 100. If x = 0.5, the probability of getting sick and receiving medical treatment is 0.05 -0.03 x 0.5 = 0.035 and the expenditure equals to 300 - 200 x 0.5 = 200. All people have an initial wealth of 500. 2. Now we consider a health insurance policy that covers the total expenditure in full. The premium level is 7. (20') (a) If all the people in the society are risk neutral. What is the fraction of people that will purchase this policy? Is the insurer's profit positive, negative, or zero? [Hint: if X follows U[0, 1], the probability of X < xo when 0 < xo <1 is xo. ](10') (b) If all the people in the society are risk-averse, is the fraction of people that will purchase this policy larger or smaller than your answer to question 2(a)? How will the insurers' profit change compared with your answer in question 2(a). (10')