Sally is a UT student and an athlete on the Longhorn gymnastics team. She has $22,500 in annual income and her utility function is U = I½. In any given year she faces a 25% chance of a serious sports injury. If the injury happens, medical expenditures for Sally will be $12,500. A health insurance company offers a policy that will cover all medical expenditures due to sports injuries at the premium of $4,000 per year.
(a) What is Sally's expected utility without health insurance?
(b) What is the actuarially fair premium? What is the loading fee in this case?
(c) What is Sally's maximum willingness to pay for health coverage?
(d) What is Sally's risk premium? Will she buy insurance?