Consider the principal-agent relationship between a patient and doctor. Suppose that the patient’sutility function is given by UP(m, x), where m denotes medical care (whose quantity is determinedby the doctor) and x denotes other consumption goods. The patient faces budget constraintIc=pmm+x, where pm is the relative price of medical care. The doctor’s utility function is given byUd(Id) +Up—that is, the doctor derives utility from income but, being altruistic, also derives utilityfrom the patient’s well-being. Moreover, the additive specification implies that the doctor is a perfectaltruist in the sense that his or her utility increases one-for-one with the patient’s. The doctor’s incomecomes from the patient’s medical expenditures: Id=pmm. Show that, in this situation, the doctor willgenerally choose a level of m that is higher than a fully informed patient would choose.
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