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 suggested 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 can purchase a market research study. The probability of a good demand given a favorable study is 0.8. The probability of a good demand given an unfavorable study is 0.1. There is a 60 percent chance that the study will be favorable. Should Mark use the study? Why? What is the maximum amount Mark should be willing to pay for this study? What is the maximum amount he should pay for any study?

Explanation / Answer

1a) 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 0.1. Therefore, Expected value of opening at: Small site: 0.1*50000 + 0.9*(-10000) = -$4,000 Large site: 0.1*80000 + 0.9*(-30000) = -$19,000 Therefore, in this case, Mark should do nothing. If he does nothing, the expected value of the "nothing" project is $0, which is greater than $-4,000 and $-19,000. 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 - 5000 = $34,800 - $5,000 = $29,800 Notice that I substracted the $5,000 which is the cost of the study. Obviuosly this cost must be paid whatever the result of the study is. 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 $29,800. 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. 1c) We've seen above that in this case, Mark should build the large site for an EV of $58,000. So the project's EV "from now on" is $58,000 if we substract the $5,000 he paid for the study, then the value is $53,000.

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