please see the attached file.

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 different returns based on whether the market is good or bad. To determine the average rate of return, multiply the probabilities by the returns and add them:

(0.4)(14) + (0.4)(8) + (0.2)(0) = 8.8

If he invests in the stock market, he can expect an average return of 8.8% (of course, it can be higher or lower). Since 8.8% is less than 9%, he should invest in the CD.

Ch.3pg.104-105

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?

Construct the Clinic Do Nothing

Demand is high Demand is low
(0.5) (0.5)

gain $100,000 lose $40,000 gain and lose nothing

Like in the problem above, you can calculate the average return by multiplying the values by the probabilities and adding them together:

(0.5)(100,000) + (0.5)(-40,000) = 50,000 - 20,000 = 30,000

If they build the clinic they will have an expected gain of $30,000 given that it is equally likely that the clinic will have high and low demand. This is greater than $0, so they should build the clinic.

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?

Favorable study Unfavorable study
(0.55) (0.45)

Favorable market Unfavorable Market Favorable market Unfavorable Market
(0.82) (0.18) (0.11) (0.89)

Clinic Nothing Clinic Nothing Clinic Nothing Clinic Nothing
+100,000 0 -40,000 0 +100,000 0 -40,000 0

The EVM approach is what we've been doing in all of these problems: multiplying the expected payoffs by the probabilities. Let's assume that if they get a favorable study, they will build the clinic, and if they get an unfavorable study, they won't.

(0.55)(0.82)(100,000) + (0.55)(0.18)(-40,000) + (0.45)(0.11)(0) + (0.45)(0.89)(0)
= 45,100 - 3960
= 41,140

Their expected return is $41,140.

If you look at the results of the last question, without the study, the physicians had an expected return of $30,000. That means that this information is worth 41,140 - 30,000 = $11,140. They probably would be willing to pay up to $11,140 for the survey.