A risk premium, RP, can be computed with the following formula, where I1 and I2 are the two payoffs to a lottery, with probabilities p and (1-p), respectively:
A) $p \left( I _ { 1 } \right) + ( 1 - p ) I _ { 2 } = R P$
B) $p U \left( I _ { 1 } \right) + ( 1 - p ) U \left( I _ { 2 } \right) = R P$
C) $p U \left( I _ { 1 } \right) + ( 1 - p ) U \left( I _ { 2 } \right) = U ( E V - R P )$
D) $U ( E V ) = R P$

Question

A risk premium, RP, can be computed with the following formula, where I1 and I2 are the two payoffs to a lottery, with probabilities p and (1-p), respectively: 
A) $p \left( I _ { 1 } \right) + ( 1 - p ) I _ { 2 } = R P$
B) $p U \left( I _ { 1 } \right) + ( 1 - p ) U \left( I _ { 2 } \right) = R P$
C) $p U \left( I _ { 1 } \right) + ( 1 - p ) U \left( I _ { 2 } \right) = U ( E V - R P )$
D) $U ( E V ) = R P$

Quizplus · Accepted Answer

The correct formula for computing a risk premium involves the expected utility of the outcomes, where $U$ represents the utility function, $I_1$ and $I_2$ are the payoffs, $p$ is the probability of $I_1$, and $EV$ is the expected value of the lottery. The risk premium, $RP$, is the difference between the expected value of the lottery and the certain amount that gives the same utility as the lottery's expected utility. Therefore, option C correctly represents the calculation involving utilities and the risk premium.

A Risk Premium, RP, Can Be Computed with the Following p(I1)+(1−p)I2=RPp \left( I _ { 1 } \right) + ( 1 - p ) I _ { 2 } = R Pp(I1​)+(1−p)I2​=RP

A Risk Premium, RP, Can Be Computed with the Following $p \left( I _ { 1 } \right) + ( 1 - p ) I _ { 2 } = R P$