A company is considering whether to market a new product. Assume, for simplicity, that if this product is marketed, there are only two possible outcomes: success or failure. The company assesses that the probabilities of these two outcomes are p and 1 - p, respectively. If the product is marketed and it proves to be a failure, the company will have a net loss of $450,000. If the product is marketed and it proves to be a success, the company will have a net gain of $750,000. If the company decides not to market the product, there is no gain or loss. The company is also considering whether to survey prospective buyers of this new product. The results of the consumer survey can be classified as favorable, neutral, or unfavorable. In similar cases where proposed products were eventually market successes, the fractions of cases where the survey results were favorable, neutral, or unfavorable were 0.6, 0.3, and 0.1, respectively. In similar cases where proposed products were eventually market failures, the fractions of cases where the survey results were favorable, neutral, or unfavorable were 0.1, 0.2, and 0.7, respectively. The total cost of administering this survey is C dollars.
a. Let p = 0.4. For which values of C, if any, would this company choose to conduct the consumer survey?
b. Let p = 0.4. What is the largest amount that this company would be willing to pay for perfect information about the potential success or failure of the new product?
c. Let p = 0.5 and C = $15,000. Find the strategy that maximizes the company’s expected earnings in this situation. Does the optimal strategy involve conducting the consumer survey? Explain why or why not.