Homework. Mathematics & Economics Math Problem. Assignment

HW #1 – Ch. 3: 19, 21-23, 26, 30, 36
(pp. 99-103)
I. According to the decision tree, it may be worthwhile for the firm to hire a market research company to conduct the market survey, since the expected monetary value (EMV) is $147,376 while it is only $103,050 if the survey is not conducted.
How much should the firm pay for the market survey?
It can depend on the efficiency of the sample information.
Recall that the expected value of perfect information, EVPI, is defined as the difference between the expected value with perfect information (EVwPI) and the expected value without perfect information (EVwoPI) which is just the maximum of the expected monetary values with respect to the prior state-of-nature probabilities. In this problem,
EVPI = [$550,000(.25) + 129,000(.45) + 0(.30)] – 103,050 = $92,500.
Moreover, the expected value of sample information, EVSI, is defined to be the difference between the expected value with sample information (EVwSI) and the expected value without sample information (EVwoSI) which, again, is just the maximum of the expected monetary values with respect to the prior state-of-nature probabilities. We get that
EVSI = $147,376 – 103,050 = $44,326.
This is the maximum amount the firm would be willing to pay for sample information obtained from the survey conducted by external market research – namely, whether the survey results turn out to be positive or negative.
By definition, the efficiency, E, of sample information is the quotient of EVSI by EVPI:
E = 44,326/92,500= 47.92%.
Although the sample information is only about 48% “as efficient as perfect information,” the firm may still decide to pay for the market survey.
What would you do as the chief operating officer of the firm?
II. The Decision Rule is the following: If the external market research firm is not hired to conduct a market survey, then build a medium-sized facility with an expected payoff of $103,050. If the firm is hired to conduct a survey and the survey obtains positive results, then advise to build a large facility with an expected payoff of $370,600. If the survey results are negative, then advise to build a small facility with an expected payoff of $56,200