Question

3-37

The physicians in Problem 3-36 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

Construct an expanded decision tree from this problem using their provided numbers, do the calculations/decisions, and highlight the final decision. NOTE (also in the reading, when doing market study, there is a cost which gets DEDUCTED from your payoff amount (as it is an expense paid).

(This is problem 3-36 if needed

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.)

The question I need answered is 3-37 the first question posted.

Answer 1

The decision tree for the problem would be as below

Now we need to calculate the Expected monetary values at different nodes.

EMV for construction of clinic = 100000*0.5-40000*0.5 = 30000

Since 30000>0, it is advised to construct the clinic

Now, EMV through study = 0.55(max((0.82*95000-0.18*45000),-5000)+0.45(max((-5000), (0.11*95000-45000*0.89))) = 0.55*69800-0.45*5000 = 36140

Since EMV through study is greater than non-study, it is better to conduct the study