A plant manager wants to know how much he should be willing to pay for perfect market research.Currently there are two states of nature facing his decision to expand or do nothing.Under favorable market conditions the manager would make $100,000 for the large plant and $5,000 for the small plant.Under unfavorable market conditions the large plant would lose $50,000 and the small plant would make $0.If the two states of nature are equally likely,how much should he pay for perfect information?
A)$0
B)$25,000
C)$50,000
D)$100,000
E)$145,000

Question

Quizplus · Accepted Answer

To determine how much the plant manager should be willing to pay for perfect information, we need to calculate the expected values for each decision given the two states of nature:

- Expand: (0.5)($100,000) + (0.5)(-$50,000) = $25,000
- Do Nothing: (0.5)($5,000) + (0.5)($0) = $2,500

The expected value of expanding is higher than the expected value of doing nothing, but without perfect information, the manager cannot be sure which state of nature will occur. If the manager had perfect information and knew with certainty which state of nature would occur, they would always choose the option with the highest expected value.

Therefore, the maximum amount the plant manager should be willing to pay for perfect information is the difference between the expected value of expanding and the expected value of doing nothing, which is $25,000 - $2,500 = $22,500. However, it is unlikely that the plant manager would pay the full amount, so the closest answer choice is B) $25,000.

A Plant Manager Wants to Know How Much He Should