Question

# Suppose that an economist has a utility function U = (Income)0.25. Her income is \$65K a...

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?

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.