Suppose your current wealth (W) is $10,000. Suppose you are offered a gamble where you can win $4000 with one-half chance but you can lose $4000 with one half-chance. Suppose your utility function is defined as U(W) = W^0.5. (The square root of your wealth). To you, the expected utility of accepting this gamble is:
A) 97.89.
B) 100.00.
C) 89.44.
D) 86.39.

Question

Quizplus · Accepted Answer

The expected utility of accepting the gamble can be calculated using the given utility function U(W) = W^0.5 and the probabilities of winning or losing. If you win, your wealth becomes $14,000, and if you lose, it becomes $6,000. The expected utility is the average of the utility of winning and losing, given the probabilities:Expected Utility = 0.5 * U(Winning) + 0.5 * U(Losing) = 0.5 * sqrt(14,000) + 0.5 * sqrt(6,000) = 0.5 * 118.32 + 0.5 * 77.46 = 59.16 + 38.73 = 97.89.

Suppose Your Current Wealth (W) Is $10,000