Question

Suppose that an economist has a utility function U = (Income)^0.25. Her income is $65K a year, but there is a 10 percent chance of becoming ill and making only $57K.


(a) What is her expected utility if she does not have insurance?

(b) What is the actuarially fair insurance premium?

(c) How much is she willing to pay for insurance?

Answer 1

a. The calculation of expected utility (U) is as follows:

0.9 × (Income)^0.25 + 0.1 × (Income)^0.25

0.9 × ($65,000)^0.25 + 0.1 × ($57,000)^0.25 = 15.91.

b. The actuary fair insurance premium = 0.1 × ($65,000 - $57,000) = 0.1 × $8,000 = $800.

c. The amount that she is willing to pay for insurance is calculated as follows:

Expected Utility (U) = (Income)^0.25

or, 15.91 = (Income)^0.25

or, Income = $64,074.

Therefore, the amount that she is willing to pay for insurance = Income - Expected Utility Income under no insurance = $65,000 - $64,074 = $926.