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: $$\begin{array} { c c }
\text { Probability } & \text { Profit outcome (\$) } \
\hline 0.05 & \$ 5,000 \
0.10 & \$ 10,000 \
0.35 & \$ 15,000 \
0.50 & \$ 20,000
\end{array}$$ What is the expected utility of profit?
A)97
B)245
C)462
D)974
E)1,033

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: $$\begin{array} { c c } 
\text { Probability } & \text { Profit outcome (\$) } \
\hline 0.05 & \$ 5,000 \
0.10 & \$ 10,000 \
0.35 & \$ 15,000 \
0.50 & \$ 20,000
\end{array}$$ What is the expected utility of profit?
A)97
B)245
C)462
D)974
E)1,033

Quizplus · Accepted Answer

The expected utility of profit is the sum of the products of the probability of each profit outcome and the utility of that profit outcome. The utility of each profit outcome is 10 ln(profit outcome). Therefore, the expected utility of profit is:0.05 * 10 ln(5,000) + 0.10 * 10 ln(10,000) + 0.35 * 10 ln(15,000) + 0.50 * 10 ln(20,000) = 97

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