Jim Holtzhauer is playing the tables at Vegas. He currently has $10,000, which I will denote as 10K in order to keep things simple. He is looking at a bet where with ½ chance he can win 6K while with ½ chance he will lose 2K. Jim's utility of wealth function is given by U(W) = (W)^2. (U(W) is equal to the W Squared). Based on this information, you would conclude that:
A) Jim will not accept this gamble since the expected utility of the gamble is less than the utility he gets from holding on to the 10K he has now.
B) Jim will accept this gamble since the expected utility of the gamble is more than the utility he gets from holding on to the 10K he has now.
C) Jim's Certainty Equivalent is 24K^2.
D) Jim's Certainty Equivalent is [(1/2)(8K)^2+(1/2)(16K)^2].

Question

Quizplus · Accepted Answer

The expected utility of the gamble is calculated as follows: $$E[U(W)] = \frac{1}{2}U(10K+6K) + \frac{1}{2}U(10K-2K) = \frac{1}{2}(16K)^2 + \frac{1}{2}(8K)^2 = \frac{1}{2}(256K^2) + \frac{1}{2}(64K^2) = 128K^2 + 32K^2 = 160K^2.$$ The utility of not gambling is $$U(10K) = (10K)^2 = 100K^2.$$ Since $160K^2 > 100K^2$, Jim will accept the gamble.

Jim Holtzhauer Is Playing the Tables at Vegas