Question

Calculate the Expected Utilities for Choice A and B.

Choice	Possible Outcome	Utility	Probability
A	A1	10	0.5
	A2	5	0.3
	A3	2	0.2
B	B1	100	0.1
	B2	0	0.9

What choice should a rational actor make? Why?

Answer 1

Expected utility is the sum of all the utilities which the consumer gets from all the possible outcomes.

To find the expected utility, we will use the below formula:

Expected Utility = P1.U1 + P2.U2 + ......+ Pn. Un

Here, P stands for probability, U stands for utility, n = number of outcomes

Expected Utility of A :

EU(A) = EU(A1) + EU(A2) +EU(A3)

EU(A) = 10 * 0.5 + 5 * 0.3 + 2 * 0.2 = 5 + 1.5 + 0.4 = 6.9

EU(A) = 6.9

Expected Utility of B :

EU(B) = EU(B1) + EU(B2)

EU(B) = 100 * 0.1 + 0 * 0.9 = 10 + 0 = 10

EU(B) = 10

A rational actor would always choose the option which will give him maximum utility. So, given two choices he will prefer the option in which he gets more utlity irrespective of its riskiness.

In option A, he is getting expected utility of 6.9 whereas in option B he is getting expected utility of 10. So, a rational actor would choose Option B because of higher expected utility i.e.10 > 6.9