Joe's Wealth Is $100 and He Is an Expected Utility

Multiple Choice

Joe's wealth is $100 and he is an expected utility maximizer with a von Neumann-Morgenstern utility function U(W) =W^1/2.Joe is afraid of oversleeping his economics exam.He figures there is only a 1 in 10 chance that he will, but if he does, it will cost him $100 in fees to the university for taking an exam late.Joe's neighbor, Mary, never oversleeps.She offers to wake him one hour before the test, but he must pay her for this service.What is the most that Joe would be willing to pay for this wake-up service?

A) $10
B) $15
C) $19
D) $100
E) $50