Mark M. Upp has just been fired as the university bookstore manager for setting

Question

Mark M. Upp has just been fired as the university bookstore manager for setting prices too low (only 20 percent above suggest retail). He is considering opening a competing bookstore near the campus, and he has begun an analysis of the situation. There are two possible sites under consideration. One is relatively small, while the other is large. If he opens at Site 1 and demand is good, he will generate a profit of $50,000. If demand is low, he will lose $10,000. If he opens at Site 2 and demand is high, he will generate a profit of $80,000, but he will lose $30,000 if demand is low. He also has the option of not opening either. He believes that there is a 50 percent chance that demand will be high. Mark got lucky and received a free survey from a University. The probability of a good demand given a favorable study is 0.8. The probability of a good demand given an unfavorable study is 0.2. There is a 60 percent chance that the study will be favorable.

A)Draw a decision tree

B) Should Mark use the study? Why?

Explanation / Answer

The problem is about decision tree, having two stages to make decisions. First stage is about making choice between---1. No action    2. Opens at Site 1(small)       3. Opens at Site2(large)         4.Go for survey

Second stage is about choices 1, 2, 3 based on survey

Pay-off for action 1.No action is Zero

Expected Pay-off for action 2. Opens at small Site 1 is $20,000 (50000*.5 -10000*.5)=(25000-5000)

Expected Pay-off for action 3. Opens at large Site 2 is $25,000 (80000*.5 -30000*.5) =(40000-15000)

Above calculations are based on values of profits and loses and 50% chance that demand is high

For action 4 evaluation we are required to rework the probability of high and low demands based on outcome of survey. Favorable survey study has probability of .6 (60% chance), application of Baye's theorem about posterior probabilities is as follows

Expected pay-off for Site 1 is when we have Favorable survey is $38,000(50000*.8 -10000*.2)=(40000-2000)

Expected pay-off for site 1 when we have Unfavorable survey is $2,000(50000*.2 - 10000*.8)=(10000-8000)

Expected pay-off for Site 2 is when we have Favorable survey is $58,000(80000*.8 -30000*.2)=(64000-6000)

Expected pay-off for site 2 when we have Unfavorable survey is $-8,000(80000*.2 - 30000*.8)=(16000-24000)

From above it is clear that we should choose Site 1(pay-off 2000) when survey is unfavorable and select Site 2 (pay-off 58000) when survey is favorable.

Therefore net expected pay-off for choice 4. to study survey is $35,600(58000*.6 + 2000*.4)=(34800+800)

B) From above we find that the maximum expected pay-off of $35,600 is with respect to study, therefore it is recommended to have free study and based on the outcome of survey make the final decision to go for large Site 2 in case of favorable and in the case of unfavorable go for small Site 1.

Cond. Probabilities given Probabilities joint Cal. Probabilities High demand Low demand High demand Low demand High demand Low demand Favorable survey 0.6 0.8 0.2 0.48 0.12 0.857142857 0.272727273 Unfavorable survey 0.4 0.2 0.8 0.08 0.32 0.142857143 0.727272727 0.56 0.44 1 1

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