Anyone have a clue as to the answer?

No. I am not joking. Anyone have any ideas? This question is motivated by the observation that a scary proportion of patients do not visit their doctor when they notice a serious symptom of cancer on themselves. Let s " {0, 1} denote whether a person actually has cancer, where s = 0 means that the person does not have cancer, and s = 1 means that she has cancer. The person's initial belief is that the probability of cancer is 1/10. Let a " {0, 1} denote two possible actions: to aggressively treat the cancer (a = 1), or not to do anything (a = 0). The decision maker derives utility from two sources. First, she would like to take the appropriate action. If she has cancer, it is best to aggressively treat it, and otherwise that is not necessary. Formally, the person's "instrumental utility" is v > 0 if a = s, and 0 if a not = s. Second, the person also derives utility from her beliefs: she "wants to" believe that she does not have cancer. Formally, if she believes that the probability of s =1 is p, then her "anxiety" is w(1 - p) where w > 0. Her total utility is the sum of instrumental utility and anxiety: v(1-1 a - sl) + w(q-p) The decision maker has the option of visiting a doctor to get diagnosed. The doctor will tell her for certain whether she has cancer ( i.e. the doctor reveals s to the patient). (a) Derive the patient's expected utility if she goes to the doctor and her expected if she does not. Would she go? (b) Now suppose that before deciding whether to visit the doctor, the decision-maker acquires a symptom of cancer that objectively means that her probability of having cancer is now 1/2. Suppose that she rationally interprets both the symptom and the doctor's diagnosis. Derive her expected utility if she goes to the doctor and if she does not. Would she go? (c) Now suppose the patient is irrational in the following way. Although the symptom is objectively serious--it means a probability of cancer of 1/2--she can "convince herself" that it is not serious, believing that the probability of having cancer is still the original one. But she cannot convince herself that the doctor's diagnosis is not serious, so if she goes to the doctor she will find out the true objective s. Derive the patient's expected utility from going to the doctor, and her expected utility from not going. When does going to the doctor yield higher expected utility? And to think. I took this course for "fun." The category is "crime" because that is what asking such questions should be.