Smith just bought a house for $250,000. Earthquake insurance, which would pay $250,000 in the event of a major earthquake, is available for $25,000. Smith estimates that the probability of a major earthquake in the coming year is 10 percent, and that in the event of such a quake, the property would be worth nothing. The utility (U) that Smith gets from income (I) is given as follows:
U(I) = I^0.5.
Should Smith buy the insurance?

Question

Quizplus · Accepted Answer

Smith should buy the insurance because the expected utility with insurance is higher than without it. Without insurance, the expected utility is 0.9 * (250,000^0.5) + 0.1 * (0^0.5), while with insurance, it is (250,000 - 25,000)^0.5. Calculating these, the utility with insurance is higher, indicating Smith should buy it.

Smith Just Bought a House for $250,000