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# Decision Trees

Please give name of program used to solve problem and details on how you solved each problem.

3-21 During the next year, Allen must decide whether to invest \$10,000 in the stock market or in a CD at an interest rate of 9%. If the market is is good, Allen believes that he could get a 14% return on his money. With a fair market, he expects to get an 8% return. If the market is bad, he will most likely get a 0% return. Allen estimates that the probability of a good market is 0.4, the probability of a fair market is 0.4, and the probability of a bad market is 0.2, and he wishes to maximize his long-run average return.

a. Develop a decision table for this problem
b. What is the best decision?

3-28. A group of medical professionals is considering the contruction of a private clinic. If the medical demand is high (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. If they don't proceed at all there is \$0 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 professional do?

3-29. The physicians from problem 3-28 above have been approached by a market research firm that offers to perform a study of the market at a fee of \$5,000. They say the Byes' theorem allows them 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 a 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?

#### Solution Preview

See the attached files for the decision trees. I didn't use a program to solve these problems, just the calculations you'll see below.

Ch.3pg.104

3-21 During the next year, Allen must decide whether to invest \$10,000 in the stock market or in a CD at an interest rate of 9%. If the market is is good, Allen believes that he could get a 14% return on his money. With a fair market, he expects to get an 8% return. If the market is bad, he will most likely get a 0% return. Allen estimates that the probability of a good market is 0.4, the probability of a fair market is 0.4, and the probability of a bad market is 0.2, and he wishes to maximize his long-run average return.

a. Develop a decision table for this problem

b. What is the best decision?

Invest in Stock Market Invest in CD

Good market Fair Market Bad Market
(0.4) (0.4) (0.2)

14% return 8% return 0% return 9% return

Allen can either decide to invest in the stock market or invest in a CD. Because the CD has a fixed rate, it doesn't matter what the market is like ... he'll always get a 9% return. The stock market can give him ...

\$2.19