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66 CHAPTER 3 DECISION ANALYSIS (d) What is the efficiency of the market study's information? 3-27 In Problem 3-26, you helped a group of medical profes- sionals analyze a decision, using EMV as the decision criterion. This group has also assessed its utility for money: U(-$45,000) = 0,U(-$40,000) = 0.1, U(-$5,000) = 0.7, U( $0) = 0.9, U($95,000) = 0.99, and U($100,000) = 1. (a) Are the medical professionals risk seekers or risk avoiders? Justify your answer. (b) Use expected utility as the decision criterion and determine the best decision for the medical pro- fessionals (including the option to use the mar- ket research firm). 3-28 Jerry Young is thinking about opening a bicycle shop in his hometown. Jerry loves to take his own bike on 50-mile trips with his friends, but he believes that any small business should be started only if there is a good chance of making a profit. Jerry can open a small shop, a large shop, or no shop at all. Because 3-26 A group of medical professionals is considering con structing a private clinic. If patient demand for the clinic is high, the physicians could realize a net profit of $100,000. If the demand is low, they could lose $40,000. Of course, they don't have to proceed at all, in which case there is no cost. In the absence of any market data, the best the physicians can guess is that there is a 50-50 chance that demand will be good. (a) Construct a decision tree to help analyze this problem. What should the medical professionals do? (b) The physicians have been approached by a mar- ket research firm that offers to perform a study of the market at a fee of $5,000. The market researchers claim that their experience enables them to use Bayes' theorem to make the follow- ing statements of probability: probability of high demand given a positive study result = 0.82 probability of low demand given a positive study result = 0.18 probability of high demand given a negative study result = 0.11 probability of low demand given a negative study result = 0.89 probability of a positive study result = 0.55 probability of a negative study result = 0.45 Expand the decision tree in part (a) to reflect the op- tions now open with the market study. What should the medical professionals do now? (c) What is the maximum amount the physicians would be willing to pay for the market study