$\begin{array}{|l|l|l|l|l|}
\hline \text { Investment } & \text { A } && \text { B } \
\hline \text { State description } & \text { Bad state } & \text { Good state } & \text { Bad state } & \text { Good state } \
\hline \text { Probability } & 0.25 & 0.75 & 0.25 & 0.75 \
\hline \text { Payoff } & 180 & 240 & ? ? & 190 \
\hline
\end{array}$
-Assume the information in the table regarding the probability and payoffs of assets A and B relates to an investor who has a log utility function.What does the payoff for asset B need to be in the good state to make the investor indifferent between the two assets?

Question

Quizplus · Accepted Answer

For investment A,the utility from the bad state is ln(180)= 5.193,and in the good state is ln(240)= 5.481.Given the probability of each state occurring,the expected utility from the investment is therefore (0.25)(5.193)+ (0.75)(5.481)= 5.410.The investment for asset B must also be 5.410 if the investor is to be indifferent between the assets,and we know the utility of the good state for asset B is ln(190)= 5.247.If we denote the unknown utility from the bad state to be U,then 5.410 = (0.25)(U)+ (0.75)(5.247),which solving for U gives 5.900.To obtain a utility of this amount the payoff must be e^5.90⁰ = $365.04.

-Assume the Information in the Table Regarding the Probability and