A former politician,who is now the owner of an Ottawa consulting firm,is trying to decide whether to hire one,two,or three consultants.He estimates that profits next year (in thousands of dollars)will vary with demand for his consulting services as follows: If he feels the chances of low,medium,and high demand are 50%,20%,and 30%,respectively,what is his expected value of perfect information?

Question

A former politician,who is now the owner of an Ottawa consulting firm,is trying to decide whether to hire one,two,or three consultants.He estimates that profits next year (in thousands of dollars)will vary with demand for his consulting services as follows:  If he feels the chances of low,medium,and high demand are 50%,20%,and 30%,respectively,what is his expected value of perfect information?

Quizplus · Accepted Answer

To determine the best choice, we need to calculate the expected profit for each possible number of consultants:

- One consultant:

Expected profit = (0.5 x 100) + (0.2 x 90) + (0.3 x 80) 
Expected profit = 50 + 18 + 24 
Expected profit = $92,000

- Two consultants:

Expected profit = (0.5 x 120) + (0.2 x 100) + (0.3 x 80) 
Expected profit = 60 + 20 + 24 
Expected profit = $104,000

- Three consultants:

Expected profit = (0.5 x 140) + (0.2 x 110) + (0.3 x 90) 
Expected profit = 70 + 22 + 27 
Expected profit = $119,000

Based on these calculations, the best choice would be to hire three consultants since it has the highest expected profit.

To calculate the expected value of perfect information, we need to find the difference between the expected profit with perfect information and the expected profit with current information:

- Expected profit with perfect information:

Low demand: 140 
Medium demand: 125 
High demand: 110

Expected profit = (0.5 x 140) + (0.2 x 125) + (0.3 x 110) 
Expected profit = 70 + 25 + 33 
Expected profit = $128,000

- Expected profit with current information:

Expected profit = $119,000

- Difference:

EVPI = Expected profit with perfect information - Expected profit with current information 
EVPI = $128,000 - $119,000 
EVPI = $9,000

Therefore, the expected value of perfect information is $9,000.

However, since the cost of obtaining perfect information is not given, we cannot determine whether it would be worth it to invest in obtaining perfect information.

A Former Politician,who Is Now the Owner of an Ottawa