Consider the following payoff table in which D1 through D4 represent decisions, S1 through S4 represent states of nature, and the values in the cells represent profits. $\begin{array}{c}
\begin{array}{c}
\
\text { D1 } &\
\text {D2 } &\
\text {D3} &\
\text {D4} &\
\end{array}
\begin{array}{|c|c|c|c|}
\hline S 1 & S 2 & S 3 & S 4 \
\hline 30 & 20 & -50 & 100 \
\hline 60 & 120 & 40 & -80 \
\hline 20 & 0 & 60 & 80 \
\hline 40 & -60 & 80 & 80\
\hline
\end{array}\end{array}$ Suppose that each state of nature is equally likely to occur.The expected value of perfect information is:
A)0
B)40
C)50
D)90

Question

Consider the following payoff table in which D1 through D4 represent decisions, S1 through S4 represent states of nature, and the values in the cells represent profits. $\begin{array}{c}
\begin{array}{c}
\
 \text { D1 } &\
 \text {D2  } &\
 \text {D3} &\
 \text {D4} &\
\end{array}
\begin{array}{|c|c|c|c|}
\hline S 1 & S 2 & S 3 & S 4 \
\hline 30 & 20 & -50 & 100 \
\hline 60 & 120 & 40 & -80 \
\hline 20 & 0 & 60 & 80 \
\hline 40 & -60 & 80 & 80\
\hline
\end{array}\end{array}$ Suppose that each state of nature is equally likely to occur.The expected value of perfect information is:
A)0
B)40
C)50
D)90

Quizplus · Accepted Answer

The expected value of perfect information (EVPI) is calculated by comparing the expected value with perfect information to the expected value without perfect information. First, calculate the expected value (EV) for each decision without perfect information, assuming each state of nature (S1, S2, S3, S4) is equally likely (probability = 0.25 for each).For D1: EV = (30 + 20 - 50 + 100) / 4 = 25For D2: EV = (60 + 120 + 40 - 80) / 4 = 35For D3: EV = (20 + 0 + 60 + 80) / 4 = 40For D4: EV = (40 - 60 + 80 + 80) / 4 = 35Without perfect information, the best decision is D3 with an EV of 40.With perfect information, you would always choose the decision that maximizes profit for each state of nature:- For S1: Choose D2 (60)- For S2: Choose D2 (120)- For S3: Choose D4 (80)- For S4: Choose D1, D3, or D4 (100)The expected value with perfect information is: (60 + 120 + 80 + 100) / 4 = 90EVPI = EV with perfect information - Best EV without perfect information = 90 - 40 = 50

Consider the Following Payoff Table in Which D1 Through D4