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

To determine whether Smith should buy earthquake insurance, we need to calculate the expected utility with and without insurance. 
Without insurance, the expected utility can be calculated as:
U(I) = (250,000)(1)(0.9) + 0(0.1) = $225,000

With insurance, the expected utility can be calculated as:
U(I) = (I - 25,000)(1)(0.9) + (250,000 - I + 25,000)(0)(0.1)
Solving for the value of I that maximizes expected utility, we find that:
I = $245,000

Therefore, the expected utility with insurance is:
U(I) = (245,000 - 25,000)(1)(0.9) + (250,000 - 245,000 + 25,000)(0)(0.1) = $207,000

Since the expected utility is greater with insurance than without insurance, Smith should buy earthquake insurance.

Smith Just Bought a House for $250,000