Consider the principle-agent relationship between a patient and doctor. Suppose that the patient’s utility function is given by Up (m, x), where m denotes medical care (whose quantity is determined by the doctor) and x denotes other consumption goods. The patient faces budget constraint Ic = pm m+ x, where pm is the relative price of medical care. The doctor’s utility function is given by Ud (Id) + Up—that is, the doctor derives utility from income but, being altruistic, also derives utility from the patient’s well-being (or consider it as an advertisement for future patients). Moreover, the additive specification implies that the doctor is a
1. Consider the principle-agent relationship between a patient and doctor. Suppose that the patient’s utility function is given by Up (m, x), where m denotes medical care (whose quantity is determined by the doctor) and x denotes other consumption goods. The patient faces budget constraint Ic = pm m+ x, where pm is the relative price of medical care. The doctor’s utility function is given by Ud (Id) + Up—that is, the doctor derives utility from income but, being altruistic, also derives utility from the patient’s well-being (or consider it as an advertisement for future patients). Moreover, the additive specification implies that the doctor is a perfect altruist (or opportunist) in the sense that his or her utility increases one-for-one with the patient’s. The doctor’s income comes from the patient’s medical expenditures: Id = pm m. Show that, in this situation, the doctor will generally choose a level of m that is higher that the fully informed patient would choose.
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