A decision-maker is faced with a choice between a lottery with a 30% chance of a payoff of $30 and a 70% chance of a payoff of $80, and a guaranteed payoff of $65. If the decision maker's utility function is $U = \sqrt { I }$ what is the risk premium associated with this choice?
A)$1.59
B)$2.52
C)$0
D)$3.95

Question

Quizplus · Accepted Answer

Calculating the expected utility of the lottery:

EU(lottery) = (0.3 * sqrt(30)) + (0.7 * sqrt(80)) 
EU(lottery) = 1.732

Utility of the guaranteed payoff: 
U(guaranteed) = sqrt(65) 
U(guaranteed) = 8.06

The risk premium is the difference between the guaranteed payoff and the expected utility of the lottery:

RP = U(guaranteed) - EU(lottery) 
RP = 6.33 - 1.732 
RP = 4.60

Since the risk premium is positive, it means the decision maker is risk-averse and would prefer the guaranteed payoff over the lottery. Therefore, the best choice would be the guaranteed payoff of $65.

A Decision-Maker Is Faced with a Choice Between a Lottery U=IU = \sqrt { I }U=I​

A Decision-Maker Is Faced with a Choice Between a Lottery $U = \sqrt { I }$