1. The Demand for Health Insurance
James is self-employed and without health insurance. He derives utility from his income (????), derived entirely from teaching health economics. James’s utility function can be summarized by the following equation: ???? = 5????? Currently James makes $40,000 per year. Since his job of teaching health economics is so stressful, James realizes that there is a 25 percent probability he will suffer a heart-attack in the next year. The treatment cost of a heart attack will be $30,000 if a heart attack occurs.
a. What is James’s expected wealth and expected utility without any health insurance coverage? (10 pts)
b. What is James’s certainty equivalent, i.e. the amount of wealth he would take for sure that would make him equally as happy as without insurance? (5 pts)
c. Suppose James could get an insurance policy offering full insurance for a $7,600 premium. What is James’s expected wealth and expected utility with insurance? Would he buy it? Why or why not? (10 pts)
2. Moral Hazard
Caroline has the following (inverse) demand curve for medical care: ????(????) = 90? (1/10)q
????. Open enrollment has just started and she is considering health insurance coverage for the next year. She estimates there is a 1/3 probability she will get sick and want medical care. The current price of medical care is $60.
a. Draw Caroline’s demand curve for medical care. (2 pts)
b. What quantity of medical care would Caroline demand without insurance (indicate this price and quantity on the graph)? Calculate Caroline’s benefit (consumer surplus) from buying medical care on the diagram. How much would she spend on medical care if she gets sick? At the beginning of the year, how much would she expect to spend on medical care? (8 pts)
c. Now suppose Caroline purchases an insurance policy for $6,000 which will pay for all of Caroline’s medical expenses. What quantity of medical care would Caroline demand (indicate this quantity on the graph)? How much would the insurance company spend on medical care if Caroline gets sick? At the beginning of the year, how much would the insurance company expect to spend on medical care? (8 pts)
d. Now suppose the insurance contract includes a deductible of $18,000 with unlimited coverage after Caroline pays the deductible. Shade the area corresponding to the deductible and the gain to Caroline’s consumer surplus. Can you tell whether Caroline would still purchase health insurance? (7 pts)