Ms. Sen has a von Neumann-Morgenstern utility function given by U = 1-(1/M), where M is the present value of her lifetime income. If Ms. Sen becomes a teacher, she will make M=5 with probability 1. If she becomes an actress, she will make M=400 if she becomes a star, but only M= 2 if she fails to become a star. The probability of her becoming a star is 0.01. Mr. Ghatak is an infallible judge of acting talent. After a brief interview, he can state with certainty whether Ms. Sen will become a star if she chooses to pursue a career in acting. What is the most she would be willing to pay for this information? [6+10

Suppose that Mira has a utility function given by U=2I+10√I. She is  considering two job opportunities. The first job pays a salary of $40,000 for sure. The second job pays a base salary of $20,000 but offers the possibility of a $40,000 bonus on top of your base salary. She believes that there is a probability of p=0.50 that she will earn the bonus. What is the expected salary of the second job?  Which offer gives Mira a higher expected utility?  Based on this information, is Mira risk adverse, risk neutral, or risk-loving?

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Amy likes to go fast in her new Mustang GT. Their utility function over wealth is v(w) where w is wealth. If Amy goes fast she gets an increase in utility equal to F. But when Amy drives fast, she is more likely to crash: when she drives fast the probability of a crash is 10%, but when she obeys the speed limit, the probability of a crash is only 5%. Amy's car is worth $2000 unless she crashes, in which case it is worth $0. If Amy doesn't have insurance, driving fast isn't worth the risk, so she will alway obey the speed limit. If Amy is offered an insurance contract with full insurance for a premium P with the deductible D, which of the inequalites below is her incentive compatibility constraint that makes sure that she will still obey the speed limit even when she is fully insured? 0.05U(2000 – P – D) + 0.95U(2000 – P) > 0.05U(0 – P – D + 2000) + 0.95U(2000 – P) 0.05U(2000 – P – D) + 0.95U(2000 – P) > 0.1(U(2000 – P – D) + F) + 0.90(U(2000 – P) + F) 0.05U(2000 – P – D) + 0.95U(2000)…