Question: Jerry Young is thinking about opening a bicycle shop in his hometown. Jerry loves to take his own bike on 50-mile trips with his friends, but he believes that any small business should be started only if there is a good chance of making a profit. Jerry can open a small shop, a large shop, or no shop at all. Because there will be a five-year lease on the building that Jerry is thinking about using, he wants to make sure that he makes the correct decision. Jerry has done some analysis about the profitability of the bicycle shop. If Jerry builds the large bicycle shop, he will earn $60,000 if the market is good, but he will lose $40,000 if the market is bad. The small shop will return a $30,000 profit in a good market and a $10,000 loss in a bad market. At the present time, he believes that there is a 59% chance that the market will be good.
Jerry also has the option of hiring his old marketing professor for $5,000 to conduct a marketing research study. If the study is conducted, the results could be either favorable or unfavorable. It is estimated that there is a 0.6 probability that the survey will be favorable. Furthermore, there is a 0.9 probability that the market will be good, given a favorable outcome from the study. However, the marketing professor has warned Jerry that there is only a probability of 0.12 of a good market if the marketing research results are not favorable.
(a) Develop a decision tree for Jerry and help him decide what he should do.
(b) How much is the marketing professor's information worth? What is the efficiency of this information?