Consider the following decision scenario: $$\begin{array} { c}
{ \text { State of Nature } } \
\begin{array} { | l | l | l | l | }
\hline { } & \text { High } & \text { Med. } & \text { Low } \
\hline \text { A } & \$ 20 ^ { * } & 20 & 5 \
\hline \text { B } & 25 & 30 & 11 \
\hline \text { C } & 30 & 12 & 13 \
\hline \text { D } & 10 & 12 & 12 \
\hline \text { E } & 50 & 40 & - 28 \
\hline
\end{array}\end{array}$$ *PV for profits ($000) With equally likely states of nature, the alternative that has the largest expected monetary value is:
A) A.
B) B.
C) C.
D) D.
E) E.

Question

Consider the following decision scenario: $$\begin{array} { c} 
{ \text { State of Nature } } \
\begin{array} { | l | l | l | l | } 
\hline  { } & \text { High } & \text { Med. } & \text { Low } \
\hline \text { A } & \$ 20 ^ { * } & 20 & 5 \
\hline \text { B } & 25 & 30 & 11 \
\hline \text { C } & 30 & 12 & 13 \
\hline \text { D } & 10 & 12 & 12 \
\hline \text { E } & 50 & 40 & - 28 \
\hline
\end{array}\end{array}$$ *PV for profits ($000) With equally likely states of nature, the alternative that has the largest expected monetary value is:
A) A.
B) B.
C) C.
D) D.
E) E.

Quizplus · Accepted Answer

To find the expected monetary value (EMV) for each alternative, we sum the products of the probability of each state of nature and the payoff for that state of nature. With equally likely states of nature, the probability of each state is 1/5.
- EMV of alternative A = (1/5 x 20) + (1/5 x 20) + (1/5 x 5) = 13
- EMV of alternative B = (1/5 x 25) + (1/5 x 30) + (1/5 x 11) = 21.2
- EMV of alternative C = (1/5 x 30) + (1/5 x 12) + (1/5 x 13) = 11
- EMV of alternative D = (1/5 x 10) + (1/5 x 12) + (1/5 x 12) = 8.4
- EMV of alternative E = (1/5 x 50) + (1/5 x 40) + (1/5 x -28) = 22.4

Therefore, alternative B has the largest EMV of 21.2 and is the best choice.

Consider the Following Decision Scenario *PV for Profits ($000) with Equally Likely States of Nature