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 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.
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 since he is risk averse.
D) Jim's Certainty Equivalent is [(1/2)*4K2+(1/2)36K2].

Question

Quizplus · Accepted Answer

The expected utility from accepting the gamble is calculated as follows: With a ½ chance, his wealth increases to 16K (10K + 6K), and with a ½ chance, his wealth decreases to 8K (10K - 2K). Thus, the expected utility is (1/2)*(16K)^2 + (1/2)*(8K)^2 = (1/2)*256K^2 + (1/2)*64K^2 = 128K^2 + 32K^2 = 160K^2. The utility of keeping the 10K is (10K)^2 = 100K^2. Therefore, Jim will accept the gamble since 160K^2 > 100K^2.

Jim Holtzhauer Is Playing the Tables at Vegas