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. 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 0.032. The expenditure also depends on x, equal to 300 2007. 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 300 200 = 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 ~ 0.5 = 200. All people have an initial wealth of 500. Now we consider a health insurance policy that requires a coinsurance of 20% with a de- ductible of 50. The premium level is 5. (15') (a) If all the people in the society are risk neutral. Denote x the fraction of people that will purchase this policy, please show an equation that x satisfies. Is the fraction of people that will purchase this policy x larger or smaller than your answer in 2(a)? (10) (b) Does raising the premium level always improve the insurer's profit? Explain your an- swer. (5') 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. 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 0.032. The expenditure also depends on x, equal to 300 2007. 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 300 200 = 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 ~ 0.5 = 200. All people have an initial wealth of 500. Now we consider a health insurance policy that requires a coinsurance of 20% with a de- ductible of 50. The premium level is 5. (15') (a) If all the people in the society are risk neutral. Denote x the fraction of people that will purchase this policy, please show an equation that x satisfies. Is the fraction of people that will purchase this policy x larger or smaller than your answer in 2(a)? (10) (b) Does raising the premium level always improve the insurer's profit? Explain your an- swer. (5')