Jim Sellers is thinking about producing a new type of electric razor for men. If the market is good, he would get a return of $140,000, but if the market for this new type of razor is poor, he would lose $84,000. Because Ron Bush is a close friend of Jim Sellers, Jim is considering the possibility of using Bush Marketing Research to gather additional information about the market for the razor. Ron has suggested two options to Jim. The first alternative is a sophisticated questionnaire that would be administered to a test market. It will cost $5,000. The second alternative is to run a pilot study. This would involve producing a limited number of the new razors and trying to sell them in two cities that are typical of American cities. The pilot study is more accurate but is also more expensive. It will cost $20,000. Ron has suggested that it would be a good idea for Jim to conduct either the questionnaire or the pilot before making the decision concerning whether to produce the new razor. But Jim is not sure if the value of either option is worth the cost.
For the sake of solving this problem, assume that Jim has the following probability estimates available: the probability of a successful market without performing the questionnaire or pilot study is 0.5, the probability of a successful market given a positive questionnaire result is 0.78, the probability of a successful market given a negative questionnaire result is 0.27, the probability of a successful market given a positive pilot study result is 0.89, and the probability of a successful market given a negative pilot study result is 0.18. Further, the probability of a positive questionnaire result is 0.45 and the probability of a positive pilot study result is also 0.45.
(a) Draw the decision tree for this problem and identify the best decision for Jim.
(b) What is the value of the questionnaire’s information? What is its efficiency?
(c) What is the value of the pilot study’s information? What is its efficiency?