A price cut would increase the firm's profits by $2 million if demand is weak but would decrease profit by $3 million if demand proves to be strong. The firm's best assessment is a .3 probability that demand will be weak. The expected value of perfect information from market research is:
A) $0.
B) $.6 million.
C) $.9 million.
D) $1.4 million.
E) $2.1 million.

Question

Quizplus · Accepted Answer

To find the expected value of perfect information (EVPI), we need to compare the expected profit with perfect information to the expected profit without perfect information.

Expected profit with perfect information:
- If the firm knows whether demand will be weak or strong, it can choose the appropriate price cut (or no price cut) to maximize profit. 
- If demand is weak, the firm will choose to cut the price and increase profit by $2 million. 
- If demand is strong, the firm will choose not to cut the price and earn a profit of $0 (since it won't lose any profit by not cutting the price). 
- Therefore, the expected profit with perfect information is (.3 x $2 million) + (.7 x $0) = $600,000.

Expected profit without perfect information:
- If the firm doesn't know whether demand will be weak or strong, it must choose a price cut that maximizes expected profit. 
- If it cuts the price, it earns an expected profit of (.3 x $2 million) + (.7 x (-$3 million)) = -$1 million. 
- If it doesn't cut the price, it earns an expected profit of (.3 x $0) + (.7 x $0) = $0. 
- Therefore, the expected profit without perfect information is -$1 million.

EVPI:
- The EVPI is the difference between the expected profit with perfect information and the expected profit without perfect information. 
- EVPI = $600,000 - (-$1 million) = $1.6 million.

However, the question asks for the expected value of perfect information from market research, which means we have to consider the cost of obtaining perfect information. Without information, the firm expects a profit of -$1 million. If it pays more than $1 million for market research, it will lose money even if it can make a perfectly informed decision. Therefore, the EVPI from market research is the maximum amount the firm should pay for information, which is $1 million.

Since none of the answer choices match $1 million exactly, the closest choice is B ($.6 million), which represents the expected value of information that costs $600,000. This is less than the maximum the firm should pay, so it is a reasonable choice.

A Price Cut Would Increase the Firm's Profits by $2