There are a continuum of types of people in society, whose health status can be represented by x, which lies between 0 and 1. x follows a 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. 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 300 - 200 = 100. If x = 0.5, the probability of getting sick and receiving medical treatment is 0.05 - 0.03 * 0.5 = 0.035 and the expenditure equals 300 - 200 * 0.5 = 200. All people have an initial wealth of 500.
1. Now we consider one single person with x = 0.4. (15')
(a) What is the maximum amount she is willing to pay for a health insurance policy that covers the medical treatment in full, if she is risk-neutral? (5')
(b) How will your answer to question 1 change if she is risk-averse with utility function u(w) = √w? (5')
(c) How will your answer to question (a) change if she is risk-averse and the policy requires a coinsurance of 20% with a deductible of 50 (i.e., the buyer should pay 50 deductible plus 20% of the total medical expenditure in excess of the deductible)? (5')