A risk-averse decision maker is trying to decide which alternative to choose. The payoff table for the alternatives, given two possible states of nature, is shown below. Assuming that the decision makers risk tolerance (R) is 5, which decision should she choose based on the utility of each outcome? Assume the exponential utility function is applicable.
$$\begin{array} { | l | r | r | }
\hline { \text { Alternative } } & \text { High } & { \text { Low } } \
\hline \text { A } & 20 & 5 \
\hline \mathrm { B } & 25 & 11 \
\hline \mathrm { C } & 30 & 15 \
\hline \mathrm { D } & 10 & 12 \
\hline \mathrm { E } & 50 & - 28 \
\hline \text { Prior Probability } & 0.3 & 0.7 \
\hline
\end{array}$$
A) Alternative A
B) Alternative B
C) Alternative C
D) Alternative D
E) Alternative E

Question

A risk-averse decision maker is trying to decide which alternative to choose. The payoff table for the alternatives, given two possible states of nature, is shown below. Assuming that the decision makers risk tolerance (R) is 5, which decision should she choose based on the utility of each outcome? Assume the exponential utility function is applicable.
$$\begin{array} { | l | r | r | } 
\hline { \text { Alternative } } & \text { High } & { \text { Low } } \
\hline \text { A } & 20 & 5 \
\hline \mathrm { B } & 25 & 11 \
\hline \mathrm { C } & 30 & 15 \
\hline \mathrm { D } & 10 & 12 \
\hline \mathrm { E } & 50 & - 28 \
\hline \text { Prior Probability } & 0.3 & 0.7 \
\hline
\end{array}$$
A) Alternative A
B) Alternative B
C) Alternative C
D) Alternative D
E) Alternative E

Quizplus · Accepted Answer

The exponential utility function is given by $U(x) = 1 - e^{-\frac{x}{R}}$, where $x$ is the outcome and $R$ is the risk tolerance. For each alternative, we calculate the expected utility by applying the utility function to each outcome, weighted by the probability of that outcome. The alternative with the highest expected utility is the preferred choice for a risk-averse decision maker. For Alternative C, the expected utility calculation would show the highest value when compared to the other alternatives, given the provided probabilities and the risk tolerance of 5. This is because Alternative C offers a balanced payoff with a relatively high outcome in both states of nature, which, when adjusted for risk preference using the exponential utility function, results in the highest expected utility.

A Risk-Averse Decision Maker Is Trying to Decide Which Alternative