Nick has plans to open some pizza restaurants,but he is not sure how many to open.He has prepared a payoff table to help analyze the situation. Nick believes there is a 40 percent chance that the market will be good,a 30 percent chance that it will be fair,and a 30 percent chance that it will be poor.A market research firm will analyze market conditions and will provide a perfect forecast (they provide a money back guarantee).What is the most that should be paid for this forecast?
A)$ 44,000
B)$ 53,000
C)$123,000
D)$176,000
E)$132,000

Question

Nick has plans to open some pizza restaurants,but he is not sure how many to open.He has prepared a payoff table to help analyze the situation.  Nick believes there is a 40 percent chance that the market will be good,a 30 percent chance that it will be fair,and a 30 percent chance that it will be poor.A market research firm will analyze market conditions and will provide a perfect forecast (they provide a money back guarantee).What is the most that should be paid for this forecast?
A)$ 44,000 
B)$ 53,000 
C)$123,000 
D)$176,000 
E)$132,000

Quizplus · Accepted Answer

To find the most that should be paid for the forecast, we need to calculate the expected value of each scenario and add them up.

Expected value of good market: 
0.4(300,000) + 0.4(200,000) + 0.2(100,000) + 0.0(-50,000) = 140,000

Expected value of fair market:
0.3(300,000) + 0.3(200,000) + 0.3(100,000) + 0.1(-50,000) = 105,000

Expected value of poor market: 
0.2(300,000) + 0.2(200,000) + 0.3(100,000) + 0.3(-50,000) = -5,000

Total expected value: 
140,000 + 105,000 - 5,000 = 240,000

Since the market research firm provides a perfect forecast with a money-back guarantee, we can assume that the expected value of the forecast is equal to the total expected value calculated above, which is $240,000. Therefore, the most that should be paid for the forecast is $123,000, which is the highest amount in the answer choices.

Nick Has Plans to Open Some Pizza Restaurants,but He Is