Mark M Upp has just been fired as the university bookstore m

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 S30.000 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 Brooklyn College. 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. Draw a decision tree to determine the following, Should Mark use the study? Why? What is the maximum amount Mark should be willing to pay for this study? The revised probabilities have already been calculated for you.

Solution

I\'ll assume here that Mark only cares abuout the expected value of

his project and doesn\'t mind risk considerations. In order to answer

this question, we must then compute the expected value of all possible

alternatives. Let\'sa go through them one by one.

- Mark doesn\'t use the study

In this case, the probability of high demand is 0.5. Therefore,

Expected value of opening at:

   Small site: 0.5*50000 + 0.5*(-10000) = $20,000

   Large site: 0.5*80000 + 0.5*(-30000) = $25,000

So clearly, if Mark doesn\'t use the study, then he must choose to open

the large site, because of the greater expected value of it.

- Mark uses the study, and he gets a \"favorable\" one.

In this case, the probability of high demand is 0.8. Therefore,

Expected value of opening at:

   Small site: 0.8*50000 + 0.2*(-10000) = $38,000

   Large site: 0.8*80000 + 0.2*(-30000) = $58,000

Again, in this case, Mark should build the large site. Finally, the

last case would be

- Mark uses the study and he gets an \"unfavorable\" one.

In this case, the probability of high demand is 0.2. Therefore,

Expected value of opening at:

   Small site: 0.2*50000 + 0.8*(-10000) = $2,000

   Large site: 0.2*80000 + 0.8*(-30000) = -$8,000

Now, we know that there is a 60% chance that the study will be

favorable. We also know that if the study is favorable, Mark will

build the large site (EV: $58,000) and if he the study is not

favorable, he will do nothing (EV: $0). Therefore, the expected value

of performing the study is:

EV of study: 0.6*58000 + 0.4*0 = $34,800

Finally, in order to determine wether to use the study or not, we must

compare the EV of using the study and the EV of not using it. We

concluded that if he didn\'t use the study, he would build the large

site, for an expected value of $25,000. We\'ve also seen that the

expected value of the study is $34,800. Therefore, since the latter is

greater, he must choose to do the study.

1b) As you can see in the previous equation, if the study were free of

charge, the expected value of using it would have been $34,800,

compared to $25,000 of not using it. This tells us that Mark should be

willing to pay up to (34800-25000)=$9,800 for the study. Let\'s see

why. If the study costs a bit more (say, $9,801), the EV of the study

becomes $24,999, which is less than $25,000, so he shouldn\'t use the

study; and obviously he shouldn\'t use it if it is even more expensive.

If the study costs a bit less (say, $9,799), then the EV of the study

becomes $25,001, which is greater than $25,000 so he should use it;

and clearly he should use it if it were cheaper than that. So the

limit is at $9,800. In general, one should be willing to pay up to the

excess expect value of using a study over the expected value of not

using it.