Suppose a decision maker has a utility function $U = \sqrt { I }$ and is faced with a lottery where there is a 30% chance of earning $30 and a 70% chance of earning $80. What is the expected utility of this lottery?
A) 7.6
B) 7.9
C) 8.2
D) 8.5

Question

Quizplus · Accepted Answer

To find the expected utility, we need to calculate the weighted average of the utility of each outcome, where the weights are the probabilities of those outcomes. Thus,
Expected Utility = 0.3 * sqrt(30) + 0.7 * sqrt(80)
Expected Utility = 3.11 + 3.69
Expected Utility = 6.8
Therefore, the expected utility of this lottery is 6.8, which is closest to answer choice B (7.9).

To determine the best choice, we need to compare the expected utility of the lottery to the utility of each alternative. Let's assume there are two options:

Option 1: a guaranteed payment of $50 
Utility of Option 1 = sqrt(50) = 7.07

Option 2: the lottery described above 
Expected Utility of Option 2 = 6.8

Since the utility of Option 1 is greater than the expected utility of Option 2, the decision maker should choose Option 1 (taking the guaranteed payment of $50).

Suppose a Decision Maker Has a Utility Function U=IU = \sqrt { I }U=I​

Suppose a Decision Maker Has a Utility Function $U = \sqrt { I }$