Which of the following utility functions exhibits constant relative risk aversion?
A)U(W)= W.
B) $U ( W ) = W - 0.5 W ^ { 2 }$
C)U(W)= ln W.
D)U(W)= $- e ^ { - W }$ .

Question

Quizplus · Accepted Answer

The natural logarithmic function U(W) = ln W is the only one that exhibits constant relative risk aversion, as it has a constant coefficient of absolute risk aversion, which is equal to 1/W. The other functions exhibit either increasing or decreasing relative risk aversion.

Which of the Following Utility Functions Exhibits Constant Relative Risk U(W)=W−0.5W2U ( W ) = W - 0.5 W ^ { 2 }U(W)=W−0.5W2

Which of the Following Utility Functions Exhibits Constant Relative Risk $U ( W ) = W - 0.5 W ^ { 2 }$