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A patient lives for two periods, 1 and 2. Her well-being in period 2 depends on her state of health as well as some action
A patient lives for two periods, 1 and 2. Her well-being in period 2 depends on her state of health as well as some action t 0 taken in period 1. Suppose the patient's state of health can be represented by a real number s 0. For example, higher numbers could represent better health and higher potential lifetime utility. The patient's initial belief is that s = s1 = 25 with probability one-half and s = s2 = 36 with probability one-half. The patient derives utility from two sources. First, she would like to take the appropriate action. Formally, if her state of health is s and she takes action t, her "instrumental utility" is |s t|. This means that in terms of instrumental utility, it is optimal to align the action perfectly with the stateto set t = s. Because lower values of s represent worse health, corresponding low values of t could represent taking health problems more seriously, for instance by having a better diet or exercising; in other words, a more serious health condition calls for a more serious response. Second, the person derives anticipatory utility from her beliefs. Her anticipatory utility depends on
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