If Ann's utility function is U = W^0.5,and she invests in a business which can yield $6,400 with probability 1/5,and $3600 with probability 4/5,then her risk premium to avoid bearing this risk is A)$36. B)$41.6. C)$64. D)$100.

Question

Quizplus · Accepted Answer

The risk premium is the difference between the expected utility with and without risk. The expected utility with risk is:```EU(with risk) = (1/5) * U(6400) + (4/5) * U(3600) = (1/5) * (6400)^0.5 + (4/5) * (3600)^0.5 = 128 + 144 = 272```The expected utility without risk is:```EU(without risk) = U(4800) = (4800)^0.5 = 219.1```Therefore, the risk premium is:```Risk premium = EU(with risk) - EU(without risk) = 272 - 219.1 = 52.9```The closest answer choice is A) $36, which is the correct answer.

If Ann's Utility Function Is U = W0

If Ann's Utility Function Is U = W⁰