16.7 Doctor–patient relationship Consider the principal–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 = pmm + 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-be ing. Moreover, the additive specification implies that the doctor is a perfect altruist in the sense that his or her util ity increases one-for-one with the patient’s. The doctor’s income comes from the patient’s medical expenditures:

Id = pmm. Show that, in this situation, the doctor will generally choose a level of m that is higher than a fully informed patient would choose.