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 2 p, respectively. If the product is marketed and it proves to be a failure, the company will have a net loss of $650,000. If the product is marketed and it proves to be a success, the company will have a net gain of $1,150,000. If the company decides not to market the product, there is no gain or loss. The company can first survey prospective buyers of this new product. The results of the consumer survey can be classified as favorable, neutral, or unfavorable. Based on similar surveys for previous products, the company assesses the probabilities of favorable, neutral, and unfavorable survey results to be 0.5, 0.3, and 0.2 for a product that will eventually be a success, and it assesses these probabilities to be 0.2, 0.3, and 0.5 for a product that will eventually be a failure. The total cost of administering this survey is C dollars.

1. Draw (by hand or with technology) a decision tree representing the New Product decision problem.
2. Determine the strategy that maximizes the profit.
3. Compute and interpret the EVPI.
4. Compute and interpret the EVI. What is the relationship between the EVI and the EVPI? Why?

A B C D E F 1 New Product Decision (W&A 9.42) 2 3 Net Gain or Loss from New Product 4 Product Successful $1,150,000 5 Product Failure -$650,000 6 7 Cost of Survey $50,000 8 9 Product Outcome Prior Probability 10 Success 0.4 11 Failure 0.6 12 13 Accuracy Probabilities Probability the Survey Indicates 14 Given the Outcome Favorable Neutral Unfavorable 15 Success 0.5 0.3 0.2 16 Failure 0.2 0.3 0.5 17