Question

4. Sally is an expected utility maximizer with utility function U(I) = I. Sally has initial income

I = 100 and faces a 50% probability of needing a surgical procedure which costs $36. What

is the maximum Sally is willing to pay for full insurance against the cost of the surgery?

(a) $0.

(b) $18.

(c) $19.

(d) $20.

Answer 1

Maximum amount she is willing to pay for full insurance is the difference between initial income and certainty equivalent.

Expected income = 50%*(100 - 36) + 50%*(100) = $82

For certainty equivalent, we first find expected utility

EU = 50%*100 + 50%*(100 - 36) = 82

Certainty equivalent income is the certain amount of income that gives the same expected utility to the insurer as his uncertain income. Here expected utility is 82 so utility function is U = I which implies I = 82. Thus, Certainty equivalent is $82.

Therefore, the maximum amount for full insurance is 100 - 82 = $18

Select option B