Bob le Flambeur is offered a raffle ticket. With probability p, the raffle ticket wins, and pays 5 dollars. With probability 1-p, the ticket loses and pays nothing. One ticket costs 1 dollar. (a) If Bob has von Neumann-Morgenstern utility u(x) = x³ over change in wealth , what is the certainty equivalent for Bob of buying one ticket (as a function of p)? What is the risk premium? (b) Now suppose that, instead of the utility function above, Bob is risk-neutral. An un- scrupulous raffle saleswoman makes Bob the following offer. For 50 cents, she will tell him whether the ticket for sale will win or lose before Bob decides whether to buy it. If p = 1, will Bob accept the saleswoman's offer? Assume that there is only one ticket available for him to purchase.
Bob le Flambeur is offered a raffle ticket. With probability p, the raffle ticket wins, and pays 5 dollars. With probability 1-p, the ticket loses and pays nothing. One ticket costs 1 dollar. (a) If Bob has von Neumann-Morgenstern utility u(x) = x³ over change in wealth , what is the certainty equivalent for Bob of buying one ticket (as a function of p)? What is the risk premium? (b) Now suppose that, instead of the utility function above, Bob is risk-neutral. An un- scrupulous raffle saleswoman makes Bob the following offer. For 50 cents, she will tell him whether the ticket for sale will win or lose before Bob decides whether to buy it. If p = 1, will Bob accept the saleswoman's offer? Assume that there is only one ticket available for him to purchase.
Chapter1: Making Economics Decisions
Section: Chapter Questions
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Transcribed Image Text:Bob le Flambeur is offered a raffle ticket. With probability p, the raffle ticket wins, and pays
5 dollars. With probability 1-p, the ticket loses and pays nothing. One ticket costs 1 dollar.
(a) If Bob has von Neumann-Morgenstern utility u(x) = x³ over change in wealth x, what
is the certainty equivalent for Bob of buying one ticket (as a function of p)? What is the
risk premium?
(b) Now suppose that, instead of the utility function above, Bob is risk-neutral. An un-
scrupulous raffle saleswoman makes Bob the following offer. For 50 cents, she will tell
him whether the ticket for sale will win or lose before Bob decides whether to buy it.
If p = 1, will Bob accept the saleswoman's offer? Assume that there is only one ticket
available for him to purchase.
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