A firm is considering two business projects. Project A will return a profit of zero if conditions are poor, a profit of $4 if conditions are good, and a profit of $8 if conditions are excellent. Project B will return a profit of $2 if conditions are poor, a profit of $3 if conditions are good, and a profit of $4 if conditions are excellent. The probability distribution of conditions follows:
$$\begin{array}{l}
\begin{array} {lll }
\text {Conditions:}&\text { Poor}&\text { Good }&\text {Excellent}\
\text {Probabilities:}&\text { 40 percent }&\text {50 percent }&\text {10 percent}\
\end{array}
\end{array}$$ (i)Calculate the expected value of each project and identify the preferred project according to this criterion.
(ii)Assume that the firm has determined that its utility function for profit is as follows:
$$U ( X ) = X - 0.05 X ^ { 2 }$$ Calculate the expected utility of each project and identify the preferred project according to this criterion.
(iii)Is the firm risk averse, risk neutral, or risk seeking? How can you tell?

Question

A firm is considering two business projects. Project A will return a profit of zero if conditions are poor, a profit of $4 if conditions are good, and a profit of $8 if conditions are excellent. Project B will return a profit of $2 if conditions are poor, a profit of $3 if conditions are good, and a profit of $4 if conditions are excellent. The probability distribution of conditions follows:
 $$\begin{array}{l}
\begin{array} {lll } 
\text {Conditions:}&\text { Poor}&\text { Good }&\text {Excellent}\
\text {Probabilities:}&\text { 40 percent }&\text {50 percent }&\text {10 percent}\
\end{array}
\end{array}$$ (i)Calculate the expected value of each project and identify the preferred project according to this criterion.
(ii)Assume that the firm has determined that its utility function for profit is as follows:
 $$U ( X ) = X - 0.05 X ^ { 2 }$$ Calculate the expected utility of each project and identify the preferred project according to this criterion.
(iii)Is the firm risk averse, risk neutral, or risk seeking? How can you tell?

Quizplus · Accepted Answer

The Answer of A firm is considering two business projects. Project A will return a profit of zero if conditions are poor, a profit of $4 if conditions are good, and a profit of $8 if conditions are excellent. Project B will return a profit of $2 if conditions are poor, a profit of $3 if conditions are good, and a profit of $4 if conditions are excellent. The probability distribution of conditions follows:
 $$\begin{array}{l}
\begin{array} {lll } 
\text {Conditions:}&\text { Poor}&\text { Good }&\text {Excellent}\
\text {Probabilities:}&\text { 40 percent }&\text {50 percent }&\text {10 percent}\
\end{array}
\end{array}$$ (i)Calculate the expected value of each project and identify the preferred project according to this criterion.
(ii)Assume that the firm has determined that its utility function for profit is as follows:
 $$U ( X ) = X - 0.05 X ^ { 2 }$$ Calculate the expected utility of each project and identify the preferred project according to this criterion.
(iii)Is the firm risk averse, risk neutral, or risk seeking? How can you tell?

A Firm Is Considering Two Business Projects (I)Calculate the Expected Value of Each Project and Identify the Return