The concept behind EVPI is that you purchase perfect information (the envelope), then open the envelope to see which outcome occurs, and then make an easy decision. You do not, however, get to choose what information the envelope contains. In contrast, sometimes a company can pay, not to obtain information, but to influence the outcome. Consider the following version of the Acme problem. There is no possibility of a test market, so that Acme must decide right away whether to market nationally. However, suppose Acme can pay to change the probabilities of the national market outcomes from their current values, 0.45, 0.35, and 0.20, to the new values p, (7/11)(1 - p), and (4/11)(1 - p), for some p. (In this way, the probabilities of fair and awful stay in the same ratio as before, 7 to 4, but by making p large, the probability of a great outcome increases.)
a. How much should Acme be willing to pay for the change if p = 0.6? If p = 0.8? If p = 0.95?
b. Are these types of changes realistic? Answer by speculating on the types of actions Acme might be able to take to make the probability of a great national market higher. Do you think such actions would cost more or less than what Acme should be willing to pay for them (from part a)?
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