Three Different Designs Are Being Considered for a New Refrigerator

question 50

Essay

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. $\begin{array}{ll}&\text { Alternative }\\\text { State of Nature }&\quad a_1\quad\quad a_2\quad\quad a_3\\\text { (Market condition) }\\\begin{array}{ll}s_1\\s_2\\s_3\end{array}&\begin{array}{|lll|}\hline\$30\quad&\$20\quad&\$10\quad \\\$19&\$21&\$15\\\$11&\$23&\$35\\\hline\end{array}\end{array}$
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?

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Definitions:

Conditioned Strength

The extent to which a conditioned stimulus can elicit a strong and reliable conditioned response after associative learning has occurred.

Unconditioned Stimulus

In classical conditioning, a stimulus that naturally and automatically triggers a response without any need for learning.

CS Preexposure Effect

The phenomenon where prior exposure to a conditioned stimulus without the unconditioned stimulus can inhibit the formation of a conditioned response when both are later paired.

Aversion

A strong dislike or disinclination toward something often because of anticipated negative consequences or outcomes.