Question

Joe's utility(U) depends upon his income (Y) according to the table below. Use this information to answer the following questions 2. eY 12 15 18 21 24 27 30 4 10 Suppose Joe is offered a prize which depends on the outcome of the coin toss. With 0.5 probability, he will win є4 and with 0.5 probability he will win €10. (a) What is the expected value of the prize? What is the expected utility associated with this prize? (b) Suppose Joe is offered an alternative certain prize of 6. Would he prefer this alternative certain prize to the prize involving the coin toss? Explain why/why not (c) Is Joe risk averse/risk neutral/risk loving? Explain how you got your answer.

Answer 1

(a) Expected value of prize E (Y) = (0.5) + (E 4) + (0.5) (E 10) E (Y) = E 2 + E 5 E (Y) = E 7 Expected value of utility E (U) = (0.5) (12) + (0.5) (30) E (U) = 21 (b) Joe has a offer of an alternative certain prize of E 6. The utility associated with a certain prize of E 6 is 18 People wants to maximize the expected utility Therefore Joe would not prefer the alternative certain prize to the prize involving the coin Joe�s marginal utility of money is constant as income increases, which implies Joe is risk neutral