5. Certainty Equivalent (10 points) Suppose Charles has a utility function defin

Question

5. Certainty Equivalent (10 points) Suppose Charles has a utility function defined as: U(Y) = VY, where Y is income. Suppose that Eric offers Charles a risky investment opportunity. This opportunity has a 50/50 chance of either paying ou unit of income or 100 units of income. Find a Y such that Charles is indifferent between getting Y with certainty and the risky opportunity above. Some important equations: where EO means the expected (or average) value and p, is the probability of outcome i. In this problem N = 2.

Explanation / Answer

The certainty equivalent income is the certain amount of income that gives the same expected utility to the insurer as his uncertain income. Certainty equivalent is given as a function of expected utility. Find E(U) first

EU = 50% x (1^0.5) + 50% x (100^0.5) = 5.5

Certainty equivalent is the certain income Ye such that

5.5 = (Ye)1/2

Hence Ye = 30.25

This is the required value of Ye.

I = $5184

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