Solution for A and B: Part A) Construct a decision tree to help analyze this pro

Question

Solution for A and B:

Part A) Construct a decision tree to help analyze this problem. What should the medical professionals do?

For favorable market - profit of $100,000.

For unfavorable market - loss of $40,000.

Expected Monetary Value of Node B :

[0.5 * $100,000] + [0.5 * (-$40,000)] = $30,000

At node A, there are 2 alternatives.

Construct clinic:- $30,000

Do not construct clinic:- $0

So, the medical professional should choose "Construct Clinic", EMV of node A becomes $30,000.

Part B)

(a) Develop a new decision tree for the medical professionals to reflect the options now open with the market study.

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

Solving the decision tree,

EMV of Node E = [0.82 * $95,000] + [0.18 * (-$45,000)] = $69,800

EMV of Node G = [0.11 * 95,000] + [0.89 * (-$45,000)] = -$29,600

At Node D, there are 2 alternatives.

Construct Clinic: $69,800

Do not construct: -$5,000

Thus, I will recommend to choose "Construct Clinic".

So, EMV of Node D becomes $69,800.

At Node F, there are 2 alternatives.

Construct Clinic: -$29,600

Do not construct: -$5,000

Thus, I will recommend to choose "Do not construct".

So, EMV of Node F becomes -$5,000.

2-26 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? CHAPTER 2 • DECISION ANALYSIS (d) What is the efficiency of the market study's information?

Explanation / Answer

Answer C

Let's calcuate payoff of the node C. It will be

.55* 69800 + (.45)*(-5000)=38390 +(-2250)= 36140.

By taking the market study,they are achieving a payoff of 36140( expected value). So, the maximum amount they would be willing to pay is additional fee which wouldmake the pyoff of nodes B and C are equivalent.

Let's assume that amount to be x. So,payoff of node D would change to 69800-x, whereas payoff of node would remain -5000, as other option is worse( already calculated).

So, equating the payoffs of node B and C would lead to this equation

30000=.55( 69800-x) + .45*(-5000) = 38390-.55x-2250

=>.55x=38390-2250-30000=6140

=> x=11163.636

So, the maximum amount physician would be willing to pay would be 11163.36 + 5000=16163.36, at this amount payoff of two nodes B and C would be equivalent.It's all about additional benefit

Answer D

The effeciency of market study information is additional payoff/cost of study =6140/500=1.228=122.8%

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