Jim Holtzhauer is playing the tables at Vegas. He currently has $4000, which I will denote as 4K in order to keep things simple. He is looking at a bet where with ½ chance he can win 2K 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 has no Certainty Equivalent since he always prefers to gamble rather than settle for a certain amount. B) Jim's certainty equivalent is 4K.^. C) Jim's certainty equivalent is 4.47K. D) Jim is risk-averse.

Question

Quizplus · Accepted Answer

Jim's utility function is U(W) = W^2. The expected utility of the gamble is 0.5*(6K)^2 + 0.5*(2K)^2 = 0.5*36 + 0.5*4 = 20. The certainty equivalent is the amount of wealth that gives him the same utility as the gamble. Solving U(CE) = 20 gives CE = sqrt(20) = 4.47K.

Jim Holtzhauer Is Playing the Tables at Vegas