Your utility function is given by U = M1/2. You have a choice: take $100 in cash or flip a coin. If you flip a coin, the outcomes are as follows: heads, you win $225; tails, you win $49. You will
A)take the $100 in cash.
B)take the gamble.
C)be indifferent between the cash and the gamble.
D)it is impossible to say with the information given.

Question

Quizplus · Accepted Answer

To determine the preferred option, we calculate the expected utility of the gamble and compare it to the utility of taking $100 in cash. The utility of taking $100 in cash is U($100) = ($100)^{1/2} = 10. For the gamble, the expected utility is the average of the utility of winning $225 and the utility of winning $49, which is (U($225)^{1/2} + U($49)^{1/2}) / 2 = (($225)^{1/2} + ($49)^{1/2}) / 2 ≈ (15 + 7) / 2 = 11. Therefore, since the expected utility of the gamble (11) is higher than the utility of taking $100 in cash (10), the choice would be to take the gamble.

Your Utility Function Is Given by U = M1/2