Your utility of wealth is u(w) = √w. A bet pays 64 with chance 1/3 and 25 with chance 2/3. What is its risk premium, the expected payoff minus the certainty equivalent? Give a whole number.

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Your utility of wealth is $u (w) = w$ . A bet pays $64$ with chance $\frac{1}{3}$ and $25$ with chance $\frac{2}{3}$ . What is its risk premium, the expected payoff minus the certainty equivalent? Give a whole number.

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Hint

The certainty equivalent is the sure amount whose utility equals the expected utility.

Solution

The expected utility is $\frac{1}{3} \times 8 + \frac{2}{3} \times 5 = 6$ .
So the certainty equivalent is $c = 6 \times 6 = 36$ .
The expected payoff is $\frac{1}{3} \times 64 + \frac{2}{3} \times 25 = 38$ .
The premium is $38 - 36 = 2$ .

Answer: $2$

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