In the academic world there is no dearth of all-knowingprofessors. An even more all-knowing professor now joins the fray.She claims that her research is so thorough that she can alwayspredict the future economic outlooks without fail. Hence, insteadof offering probabilities about states of nature, as the previousprofessor did, she proposes that she will create a white-paper onthe future of the economy. If the paper predicts a negative outlookthe economy is certain to be ‘depressed’. On the other hand, if shepredicts a positive outlook the economy is certain to be either‘bright’ or ‘stable’ with equal probabilities.
She says that she will conduct her research and issue theeconomic forecast, either positive or negative, as she findsappropriate. Given her proposal, the company is now forced to do abit of research itself. It finds that independent of her tallclaims, the past experience indicates that there is only a 96%chance that the economy will be actually positive (either bright orstable with equal probabilities) if she predicts it to be positive,but there is a 4% chance that it will actually end up beingnegative (i.e. depressed) even though the forecast is positive.Conversely, there is an 89% chance that the economy will beactually negative (i.e. depressed) if she issues a negative report,however an 11% chance that it will actually end up being positive(either bright or stable) even though the report is negative. Usinginformation from the past, the research also reveals that there isa 70% chance that the professor will issue a positive report and a30% chance the report will be negative.
· Create a new pay-off table with appropriate alternatives,states of nature, probabilities, and pay off values, and evaluatethe outcome from the best course of action (5 points).
· What is the maximum you will be willing to pay the professorfor her services? (5 points)
Hints: Think about the baseline return/s that you will compareto the returns with her prediction?
You will need to think back to the ‘AND’ or the‘Multiplication’ rules and/or the ‘OR’ or the ‘Addition’ rules(Chapter 2) to calculate the probabilities in this case.
