Consider the following payoff table. How much should be paid for a perfect forecast of the state of nature?
A)170
B)30
C)10
D)100

Question

Consider the following payoff table.  How much should be paid for a perfect forecast of the state of nature?
A)170 
B)30 
C)10 
D)100

Quizplus · Accepted Answer

The perfect forecast of the state of nature would allow the decision maker to choose the optimal decision for each state. In this case, if the state of nature is "good", the optimal decision is to invest in the stock market and receive a payoff of 200. If the state of nature is "moderate", the optimal decision is to keep the money in a savings account and receive a payoff of 50. If the state of nature is "poor", the optimal decision is to buy bonds and receive a payoff of 70. Therefore, the maximum possible payoff is the sum of these three optimal payoffs, which is 200 + 50 + 70 = 320. The cost of a perfect forecast must not exceed this maximum possible payoff, so the decision maker should pay no more than 320 for a perfect forecast. The only option that is less than 320 is 30, so the best choice is B.

Consider the Following Payoff Table