Using the following:
The manager's utility function for profit is U $\pi$ = 50 $\pi$, 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:
$$\begin{array} { c c }
\text { Probability } & \text { Profit outcome (\$) } \
\hline 0.20 & - \$ 15,000 \
0.30 & - \$ 5,000 \
0.30 & \$ 5,000 \
0.20 & \$ 25,000
\end{array}$$
-What is the expected utility of profit?
A) -2,500
B) 5,000
C) 15,000
D) 30,000
E) 100,000

Question

Using the following:
The manager's utility function for profit is U $\pi$ = 50 $\pi$, 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:
 $$\begin{array} { c c } 
\text { Probability } & \text { Profit outcome (\$) } \
\hline 0.20 & - \$ 15,000 \
0.30 & - \$ 5,000 \
0.30 & \$ 5,000 \
0.20 & \$ 25,000
\end{array}$$
-What is the expected utility of profit?
A) -2,500
B) 5,000
C) 15,000
D) 30,000
E) 100,000

Quizplus · Accepted Answer

The expected utility of profit is calculated as the sum of the products of the probability of each profit outcome and the utility of that outcome. In this case, the utility of each outcome is given by the manager's utility function, U(\pi) = 50π. Therefore, the expected utility of profit is:E(U) = 0.20 * U(-15,000) + 0.30 * U(-5,000) + 0.30 * U(5,000) + 0.20 * U(25,000)= 0.20 * (-750,000) + 0.30 * (-250,000) + 0.30 * (250,000) + 0.20 * (1,250,000)= -2,500

Using the Following: the Manager's Utility Function for Profit Is π\piπ

Using the Following:
the Manager's Utility Function for Profit Is $\pi$