Three different designs are being considered for a new refrigerator, and profits will depend on the combination of the refrigerator design and market condition. The following payoff table summarises the decision situation, with amounts in millions of dollars. $\begin{array} { ccc }
&\text { Alternative }\
\text { State of Nature }& a_{1} & a_{2} & a_{3}\\text { (Market condition) }\
s_{1} & \$ 30 & \$ 20 & \$ 10 \
s_{2} & \$ 19 & \$ 21 & \$ 15 \
s_{3} & \$ 11 & \$ 23 & \$ 35
\end{array}$
Assume that the following probabilities are assigned to the three market conditions:
P( $S _ { 1 }$ ) = 0.2, P( $S _ { 2 }$ ) = 0.4, P( $S _ { 3 }$ ) = 0.4.
a. Calculate the expected monetary value for each design with present information. Which design should be selected in order to maximise the firm's expected profit?
b. Convert the payoff table to an opportunity loss table.
c. Calculate the expected opportunity loss for each design with present information. Which design should be selected in order to minimise the firm's expected loss?
d. Determine the expected payoff that would be realised if perfect information were available.
e. What is the most the firm would be willing to pay for a research study designed to reduce its uncertainty about market conditions?

Question

Three different designs are being considered for a new refrigerator, and profits will depend on the combination of the refrigerator design and market condition. The following payoff table summarises the decision situation, with amounts in millions of dollars. $\begin{array} { ccc  }
&\text { Alternative }\
\text { State of Nature }& a_{1} & a_{2} & a_{3}\\text { (Market condition) }\
s_{1} & \$ 30 & \$ 20 & \$ 10 \
s_{2} & \$ 19 & \$ 21 & \$ 15 \
s_{3} & \$ 11 & \$ 23 & \$ 35
\end{array}$
 Assume that the following probabilities are assigned to the three market conditions:
P( $S _ { 1 }$ ) = 0.2, P( $S _ { 2 }$ ) = 0.4, P( $S _ { 3 }$ ) = 0.4.
a. Calculate the expected monetary value for each design with present information. Which design should be selected in order to maximise the firm's expected profit?
b. Convert the payoff table to an opportunity loss table.
c. Calculate the expected opportunity loss for each design with present information. Which design should be selected in order to minimise the firm's expected loss?
d. Determine the expected payoff that would be realised if perfect information were available.
e. What is the most the firm would be willing to pay for a research study designed to reduce its uncertainty about market conditions?

Quizplus · Accepted Answer

The Answer of Three different designs are being considered for a new refrigerator, and profits will depend on the combination of the refrigerator design and market condition. The following payoff table summarises the decision situation, with amounts in millions of dollars. $\begin{array} { ccc  }
&\text { Alternative }\
\text { State of Nature }& a_{1} & a_{2} & a_{3}\\text { (Market condition) }\
s_{1} & \$ 30 & \$ 20 & \$ 10 \
s_{2} & \$ 19 & \$ 21 & \$ 15 \
s_{3} & \$ 11 & \$ 23 & \$ 35
\end{array}$
 Assume that the following probabilities are assigned to the three market conditions:
P( $S _ { 1 }$ ) = 0.2, P( $S _ { 2 }$ ) = 0.4, P( $S _ { 3 }$ ) = 0.4.
a. Calculate the expected monetary value for each design with present information. Which design should be selected in order to maximise the firm's expected profit?
b. Convert the payoff table to an opportunity loss table.
c. Calculate the expected opportunity loss for each design with present information. Which design should be selected in order to minimise the firm's expected loss?
d. Determine the expected payoff that would be realised if perfect information were available.
e. What is the most the firm would be willing to pay for a research study designed to reduce its uncertainty about market conditions?

Three Different Designs Are Being Considered for a New Refrigerator