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Table 14.10
Business Fire
Income
Probability
Yes
$160,000
0.10
No
490,000
0.90
-(Table 14.10) Suppose the person's utility function is given by U = I^0.5, where I is income. What guaranteed income level would offer the same expected utility level as that from the uncertain income (i.e., find the certainty equivalent) ?

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To find the certainty equivalent, we need to find the guaranteed income that would offer the same expected utility as the uncertain income. The expected utility of the uncertain income is: 
E(U) = (0.10)((160,000)1(0.5)(1)0.5) + (0.90)((490,000)1(0.5)(1)0.5) = 525.13

We need to find I such that U = (I)1(0.5)(1)(0.5) = 525.13, which gives us I = 448,900. Therefore, the certainty equivalent is $448,900.

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