The manager's utility function for profit is U( $\pi$)= 10 ln( $\pi$),where $\pi$ is the dollar amount of profit.The manager is considering a risky decision with the four possible profit outcomes shown below.The manager makes the following subjective assessments about the probability of each profit outcome: $$\begin{array} { c c }
\text { Probability } & \text { Profit outcome (\$) } \
\hline 0.05 & \$ 5,000 \
0.10 & \$ 10,000 \
0.35 & \$ 15,000 \
0.50 & \$ 20,000
\end{array}$$ Given this utility function for profit,the utility of profit is
A)equal to 198 for $20,000.
B)increasing as profit gets larger,so the manager is risk-loving.
C)decreasing as profit gets larger,so the manager is risk-averse.
D)both a and b
E)both a and c

Question

The manager's utility function for profit is U( $\pi$)= 10 ln( $\pi$),where  $\pi$ is the dollar amount of profit.The manager is considering a risky decision with the four possible profit outcomes shown below.The manager makes the following subjective assessments about the probability of each profit outcome: $$\begin{array} { c c } 
\text { Probability } & \text { Profit outcome (\$) } \
\hline 0.05 & \$ 5,000 \
0.10 & \$ 10,000 \
0.35 & \$ 15,000 \
0.50 & \$ 20,000
\end{array}$$ Given this utility function for profit,the utility of profit is
A)equal to 198 for $20,000.
B)increasing as profit gets larger,so the manager is risk-loving.
C)decreasing as profit gets larger,so the manager is risk-averse.
D)both a and b
E)both a and c

Quizplus · Accepted Answer

The utility function $U(\pi) = 10 \ln(\pi)$ is a logarithmic function, which means as profit ($\pi$) increases, the utility derived from the profit increases as well, but at a decreasing rate. This characteristic indicates risk-aversion, not risk-loving behavior. However, the correct interpretation of the utility function's behavior in relation to risk preferences is that it shows risk aversion, not risk-loving behavior. Therefore, the explanation mistakenly identifies the behavior as risk-loving when it should be risk-averse. The calculation for a specific profit amount (e.g., $20,000) would indeed show an increase in utility with higher profits, but the interpretation of the utility function's shape in relation to risk preferences was incorrect in the explanation provided.

The Manager's Utility Function for Profit Is U π\piπ )= 10 Ln

The Manager's Utility Function for Profit Is U $\pi$ )= 10 Ln