Suppose Ana's Current Wealth (W) Is $8000 and Ana Obeys

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The Answer is To find the expected monetary payoff of the gamble, we calculate the weighted average of the possible outcomes. The expected monetary payoff (EM) is given by:

EM = (0.5 * $5000) + (0.5 * (-$5000)) = $2500 - $2500 = $0

The expected utility of the gamble is found by calculating the utility of each possible outcome and taking the weighted average. The expected utility (EU) is given by:

EU = (0.5 * (8000 + 5000)^0.5) + (0.5 * (8000 - 5000)^0.5)
= (0.5 * 13000^0.5) + (0.5 * 3000^0.5)
= (0.5 * 113.86) + (0.5 * 54.77)
= 57.43 + 27.39
= 84.82

To find Ana's certainty equivalent, we solve for the value of the certain amount of wealth that would give her the same level of utility as the gamble. Let CE be the certainty equivalent. We solve for CE in the equation:

U(CE) = EU
CE^0.5 = 84.82
CE = 84.82^2
CE = 7189.47

The risk premium is the difference between the expected value of the gamble and the certainty equivalent. The risk premium (RP) is given by:

RP = EU - W
RP = 84.82 - 8000
RP = -7915.18

Since the risk premium is negative, Ana would prefer to hang on to her $8000 endowment rather than accept the gamble. This is because the expected utility of the gamble is lower than the utility of her current wealth, indicating that she would be better off sticking with her current wealth rather than taking the gamble.

Suppose Ana's Current Wealth (W) Is $8000 and Ana Obeys

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Suppose Ana's Current Wealth (W) Is $8000 and Ana Obeys

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Correct Answer:Answered by ExamLex AIShow Answer

Correct Answer:
Answered by ExamLex AI