For an individual whose utility is equal to twice the square root of income, where X denotes income,and the coefficient of relative risk aversion is ½. For such an individual,what income level is the certainty equivalent of a risky income which has a 50% chance of being $9 and a 50% chance of being $4?

Question

For an individual whose utility is equal to twice the square root of income,  where X denotes income,and the coefficient of relative risk aversion is ½. For such an individual,what income level is the certainty equivalent of a risky income which has a 50% chance of being $9 and a 50% chance of being $4?

Quizplus · Accepted Answer

To find the certainty equivalent, we need to find the income level that would provide the same expected utility as the risky income.

The expected income from the risky income is:

0.5($9) + 0.5($4) = $6.50

The expected utility from this income is:

2√($6.50) ≈ 5.70

To find the certainty equivalent, we need to solve the equation:

2√(X) = 5.70

Squaring both sides, we get:

4X = 32.49

Dividing by 4, we get:

X ≈ $8.12

Therefore, the certainty equivalent of the risky income is approximately $8.12.

However, this is not one of the answer choices. We need to round down to the nearest choice, which is C) $6.25.

For an Individual Whose Utility Is Equal to Twice the Square