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 would take the bet since his expected utility from taking the bet is 20K² utils while the expected utility of staying with 4K is 16K² utils. B) Jim would not take the bet since his expected utility from taking the bet is 16K² utils while the expected utility of staying with 4K is 20K² utils. C) Jim would not take this bet since he is risk averse and his expected utility from taking the bet is negative. D) Jim would take this bet because the expected value of the gamble: ½ chance of winning 2K and ½ chance of losing 2K is positive.

Question

Quizplus · Accepted Answer

The expected utility from taking the bet is calculated using Jim's utility function U(W) = W^2. If he wins, his wealth will be 6K (4000 + 2000), and the utility is (6K)^2 = 36K. If he loses, his wealth will be 2K (4000 - 2000), and the utility is (2K)^2 = 4K. The expected utility is the average of these two outcomes: (36K + 4K) / 2 = 20K. The utility of not betting and staying with 4K is (4K)^2 = 16K. Since 20K > 16K, Jim would take the bet.

Jim Holtzhauer Is Playing the Tables at Vegas