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 $U = I + 500$ , what is the risk premium associated with this choice?
A) $0
B) $1
C) $2
D) $3

Question

Quizplus · Accepted Answer

To find the risk premium, we need to compare the expected utility of the gamble and the expected utility of the certain payoff.

Expected utility of the gamble: 
0.3(500+30) + 0.7(500+80) = 387

Expected utility of the certain payoff:
500+65 = 565

Since the expected utility of the certain payoff is higher than the expected utility of the gamble, there is no risk premium. Therefore, the decision-maker should choose the certain payoff of $65.

A Decision-Maker Is Faced with a Choice Between a Lottery U=I+500U = I + 500U=I+500

A Decision-Maker Is Faced with a Choice Between a Lottery $U = I + 500$