Question

She says that she will conduct her research and issue the economic forecast, either positive or negative, as she finds appropriate. Given her proposal, the company is now forced to do a bit of research itself. It finds that independent of her tall claims, the past experience indicates that there is only a 96% chance that the economy will be actually positive (either bright or stable with equal probabilities) if she predicts it to be positive, but there is a 4% chance that it will actually end up being negative (i.e. depressed) even though the forecast is positive. Conversely, there is an 89% chance that the economy will be actually 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. Using information from the past, the research also reveals that there is a 70% chance that the professor will issue a positive report and a 30% chance the report will be negative.

· Create a new pay-off table with appropriate alternatives, states of nature, probabilities, and pay off values, and evaluate the outcome from the best course of action (5 points).

· What is the maximum you will be willing to pay the professor for her services? (5 points)

Hints: Think about the baseline return/s that you will compare to 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.

Answer 1

P( Economy is actually positive when professor predicts it to be positive ) = 70% * 96% = 0.672

P( Economy is actually negative when professor predicts it to be positive ) = 70% *4% = 0.028

P( Economy is actually positive if professor predicts it to be negative ) = 30% * 11% = 0.033

P( Economy is actually positive if professor predicts it to be negative ) = 30% * 89% = 0.267

New Payoff Table

			Predicted Forecast
			Positive	Negative
Actual Forecast	Positive	0.672	0.033
		Negative	0.028	0.267

NO amount of the professor is given in the question , so exact amount couldn't be told but the answer would just be amount * probabilities

Maximum amount to be paid for his services would be calculated taking the probabilities that he predicts positive and actual forecast is positive and the probability that he predicts negative and the actual forecast is also negative

= 0.672 + 0.267 = 0.939 of the total amount asked by the professor