10899305d01 - Econ 149 Health Economics Problem Set...

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Econ 149: Health Economics Problem Set IV (Extra credit) Answer Key 1. Your utility function is given by U = ln(4 C ) , where C is consumption. You make $30,000 per year and enjoy jumping out of perfectly good airplanes. There’s a 5% chance that, in the next year, you’ll break both legs and will incur medical costs of $15,000 and will lose an additional $5,000 from missing work because of the loss of a working pair of legs for some time. (a) What is your expected income without insurance? What is your expected utility with- out insurance? (See Chapter 8 for a review.) E ( C ) = 0 . 95(30 , 000) + 0 . 05(30 , 000 - 15 , 000 - 5 , 000) = 29 , 000 E ( U ) = 0 . 95 ln[4(30 , 000)] + 0 . 05 ln[4(30 , 000 - 15 , 000 - 5 , 000)] = 11 . 640316 (b) Suppose you can buy insurance that will cover the medical expenses but not the fore- gone part of your salary. How much is an actuarially fair policy, and what is your expected utility if you buy it? (Hint: you’ll need to calculate the utility of income in each state.) First, we need to calculate the actuarially fair premium which is defined as the expected loss for the insurance company. This insurance only covers the medical loss, so the expected loss is E ( loss ) = 0 . 95(0) + 0 . 05(15 , 000) = 750 . Now, we can use this premium to calculate expected income and utility if you buy this type of insurance. E ( C ) = 0 . 95(30 , 000 - 750) + 0 . 05(30 , 000 - 5 , 000 - 750) = 29 , 000 E ( U ) = 0 . 95 ln[4(30 , 000 - 750)] + 0 . 05 ln[4(30 , 000 - 5 , 000 - 750)] = 11 . 660556 (c) Suppose you can buy insurance that will cover your medical expenses and foregone salary. How much would such a policy be if its actuarially fair, and what is your ex- pected utility if you buy it? This insurance covers both the medical loss and the loss of income, so the expected loss is E ( loss ) = 0 . 95(0) + 0 . 05(15 , 000 + 5 , 000) = 1 , 000 . Now, we can use this premium to calculate expected income and utility if you buy this type of insurance. E ( C ) = 0 . 95(30 , 000 - 1 , 000) + 0 . 05(30 , 000 - 1 , 000) = 29 , 000 E ( U ) = 0 . 95 ln[4(30 , 000 - 1 , 000)] + 0 . 05 ln[4(30 , 000 - 1 , 000)] = 11 . 661345 2. How do fee-for-service and capitation payment systems affect the alignment of physician and patient desire? Under which system would we expect to see more supplier-induced demand? What impacts do the different payment systems have on the amount of care the patient receives? Fee-for-service is a method of payment under which the provider is paid for each procedure or service that is provided to a patient. Capitation is a method of reimbursement in managed care plans in which a provider is paid a fixed amount per person over a given period regard- less of the amount of services rendered. Under fee-for-service the physician has an incentive to over provide service, because she is paid per procedure, but the physician’s incentives are fairly in line with the patients (if the patient requests a procedure the physician is likely to give it). Under capitation the doctor’s actions are not in line with the patients desires. The doctor has an incentive to deny care to minimize costs.
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