# Statistics/Probability

Revised the R = $1000 to R=$1,000,000.

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The management of Orange Computers was considering launching a new product called the whopper101. The problem was that if a certain competitor had developed a new technology as had been rumored, they would quickly blow the whopper101 out of the water resulting in a loss of $500K. The board of directors assessed the chance that the competitor had this technology at 70%. If the competitor did not have this technology the board anticipated profits of $2,000,000.

The chair, Steve Tasks, the company founder, was not happy making a launch/no launch decision with such a high degree of uncertainty and asked how can we get information about whether they have this technology or not? There are a few ways we can go about itâ? said his slimeball assistant Will Cheet. As you know, we have used one of their ex-employees, Barbara Bayes, to assist us in making assessments before. I think she'll have an 85% chance of getting it right if we ask her. Let's incorporate that possibility in our decision tree. She'll probably want about $5000 for supplying her expert opinion. I wonder if it's worth it because even after we get her view there will still be some uncertainty. You know, I'm sure that for $50,000 we could hire someone inside their company to tell us for sure.

Draw the tree for Orange's Decision problem and determine the optimum decision based on expected values. Include the possibility of launching or not 1) without information, 2) with Barbaraâ??s input and 3) using the industrial spy.

Repeat using an exponential utility function with R=$1,000,000.

#### Solution Preview

We first compute the expected payoffs of each of the options, and then compute the expected utility.

I) if nothing is done, then there is a 30% chance that the company will suffer a 500,000 loss, and a 70% chance that the company will gain 2,000,000. The expected gain is 0.3 X (-500,000) + 0.7 X 2,000,000 = 1 250 000.

III) If they hire a spy, then there is a 30% chance that the competitor has the technology (in which case they will not lauch whopper101, so the only loss they incur is -50,000 for the spy) and there is a 70% chance that they don't have the technology (in which case the profit is 2,000,000 - 50,000 = ...

#### Solution Summary

Statistics/Probability