Suppose your current wealth (W) is $8000 and you obey the principles of expected utility theory. Suppose you are offered a gamble where you can win $5000 with one-half chance but you can lose $5000 with one half-chance. Suppose your utility function is defined as U(W) = W^0.5. (The square root of your wealth). For you the risk premium of this is (approx.):
A) 878.
B) 7119.98
C) 8,000.
D) 89.44.

Question

Quizplus · Accepted Answer

The risk premium is the difference between the expected value of the gamble and the certainty equivalent. The expected value of the gamble is (0.5 * 5000) + (0.5 * -5000) = 0. The certainty equivalent is the amount of money that would make you indifferent between taking the gamble and receiving the certainty equivalent for sure. To find the certainty equivalent, we solve the following equation:U(CE) = 0.5 * U(5000) + 0.5 * U(-5000)(CE)^0.5 = 0.5 * (5000)^0.5 + 0.5 * (-5000)^0.5CE = 878.08Therefore, the risk premium is 878.08 - 0 = 878.08.

Suppose Your Current Wealth (W) Is $8000 and You Obey