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 the gamble since he is risk averse.
B) Jim will not accept the gamble since his expected utility from accepting the gamble is 100K^2 while the expected utility from keeping the 10K is 160K^2.
C) Jim will not accept the gamble since his expected utility from accepting the gamble is 160K^2 while the expected utility from keeping the 10K is 100K^2.
D) Jim's Certainty Equivalent is approximately 12.65K.

Question

Quizplus · Accepted Answer

The expected utility from the gamble can be calculated as 0.5*(10K+6K)^2 + 0.5*(10K-2K)^2 = 0.5*256K^2 + 0.5*64K^2 = 160K^2. Since the utility of keeping 10K is (10K)^2 = 100K^2, the gamble offers a higher expected utility, indicating Jim is not risk averse in this scenario. The Certainty Equivalent (CE) is the amount of money that gives the same utility as the expected utility of the gamble, solving U(CE) = 160K^2 gives CE = sqrt(160K^2) = 12.65K, indicating Jim would be indifferent between the gamble and a sure amount of approximately 12.65K.

Jim Holtzhauer Is Playing the Tables at Vegas