is then 201.]; P51 + l1 Pisa PISI ti [1 Pllsz ii The patient has the option of visiting a doctor in period 1 to get diagnosed. The visit is free. If she visits the doctor, she will lmow the true 3 with certainty. If she does not visit the doctor: she does not learn any information about .51 and will keep believing that the probability of state 5'] is onehalf. If she visits the doctor, she oan choose t after the visit. {a} Write the patient's expected utility as a function of t if she does not visit the doctor. What it does she choose? What is her expected utility given the optimal t? [b] Write the patient's expected utility as a function oft if she visits the doctor and learns that her state of health is s] = 25. What t does she choose'iI What is her utility given the optimal t? {c} Repeat the exercise in part {b} for the case when the patient visits the doctor and learns that her state of health is 33 = 35. [d] Write the patient's total expected utility From visiting the cloctor. This is the weighted sum of the utilities in parts Eb} and {c}, with the weights equal to the probabilities of the two possibilities. Does the patient visit the doctor? [e] Now suppose that .s] = D, so that the patients possible problem is more serious. The other possibility is still 33 = 361 with the two health states still being equally likely. Using the same steps as in parts {a} through {d}, solve for whether the patient goes to the doctor. [f] Conventional economic wisdom says that when information is more important for making decisionssuch as above, when a patients problem is potentially more seriousa person is more likely to seek out that information. How does the oonsideration of anticipatory utility qualify this insight? 4 3. [3Dpts]A. patient lives for two periods1 l and 2. Her wellbeing in period 2 depends on her state of health as well as some actiorn t I: D taken in period 1. Suppose the patient's state of health can be represented by a real number s 2 [1 For example, higher numbers could represent better health and higher potential lifetime utility. The patient's initial belief is that s = s] = 25 with probability one-half and s = 52 = 36 with probability onehalf. The patient derives utility frorm two sources. First1 she woruld like to take the approrpri ate actiorn. Formally, if her state of health is s and she takes action t, her \"instrumental utility" is Is t|. This means that in terms of instrumental utility, it is optimal to align the action perfectly 1with the stateto set t = s. As an example, lower values of t could represent taking health problems more seriously1 for instance by having a bet- ter diet or exercising; then, the above instrumental utility means that a more seriorus health condition calls for a morre seriorus response. Second1 the person derives anticipatory utility from her beliefs. Her anticipatory utility depends on the average state given her belie. Specically, if she thinks the probability of the state 31 is p, then her anticipatory utility is 21] 33.51 + [1 33:13:. The patient's overall utility, which combines expected instrumental utility and anticipatory utility