e The value of a perfect forecast is given by the EVPI First calculate the

E the value of a perfect forecast is given by the

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e. The value of a perfect forecast is given by the EVPI. First calculate the following; EV with PI = (85)0.2 + (100)0.3 + (120)0.5 = 107 EVPI = (EV with PI) – (Best EMV without PI) = 108 – 107 = 1 Thus, a perfect forecast is worth 1 (thousand). f. The location that minimizes the EOL is Sweetwater. g. The expected value of perfect information (EVPI) is 1. This is found in part e , and it is also the minimum EOL.
6 Problem 6 A group of medical professionals is considering the construction of a private clinic. If the medical demand is high (i.e., there is a favorable market for the clinic), the physicians could realize a net profit of \$100,000. If the market is not favorable, 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 the clinic will be successful. Construct a decision tree to help analyze this problem. What should the medical professionals do?   EMV for node 1 = 0.5(100,000) + 0.5(–40,000) = \$30,000. Choose the highest EMV, therefore construct the clinic. Problem 7 The physicians in Problem 6 have been approached by a market research firm that offers to perform a study of the market at a fee of \$5,000. The market researchers claim their experience enables them to use Bayes' theorem to make the following statements of probability: probability of a favorable market given a favorable study = 0.82 probability of an unfavorable market given a favorable study == 0.18 probability of a favorable market given an unfavorable study = 0.11 probability of an unfavorable market given an unfavorable study = 0.89 probability of a favorable research study = 0.55 probability of an unfavorable research study = 0.45 (a) Develop a new decision tree for the medical professionals to reflect the options now open with the market study. (b) Use the EMV approach to recommend a strategy. (c) What is the expected value of sample information? How much might the physicians be willing to pay for a market - study? (d) Calculate the efficiency of this sample information. a.
7 b. EMV(node 2) = (0.82)(\$95,000) + (0.18)(–\$45,000) = 77,900 – 8,100 = \$69,800 EMV(node 3) = (0.11)(\$95,000) + (0.89)(–\$45,000) = 10,450 – \$40,050 = –\$29,600 EMV(node 4) = \$30,000 EMV(node 1) = (0.55)(\$69,800) + (0.45)(–\$5,000) = 38,390 – 2,250 = \$36,140 The EMV for using the survey = \$36,140. EMV(no survey) = (0.5)(\$100,000) + (0.5)(–\$40,000) = \$30,000 The survey should be used. c. EVSI = (\$36,140 + \$5,000) – \$30,000 = \$11,140. Thus, the physicians would pay up to \$11,140 for the survey. Problem 8. Bayesian Analysis
8 Peter Martin is 'going to help his brother who wants to open a food store. Peter initially believes that there is a 50-50 chance that his brother's food store would be a success. Peter is considering doing a market research study. Based on historical data, there is a 0.8 probability that the marketing research will be favorable given a successful food store. Moreover, there is a 0.7 probability that the marketing research will be unfavorable given an unsuccessful food store. (a) If the marketing research is favorable, what is Peter's revised probability of a successful food store for his brother?