. Bob le Flambeur is offered a raffle ticket. With probability p, the raffle ticket wins, and pays5 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)=³ over change in wealth z, whatis the certainty equivalent for Bob of buying one ticket (as a function of p)? What is therisk premium?Solution: If Bob buys a raffle ticket, then with probability p he gains 4 dollars (5dollars minus the price of the ticket), and with probability 1-p he loses 1 dollar. Hisexpected utility is therefore 64p-(1-p) = 65p-1. The certainty equivalent is thereforeCE(p) = 365p-1. The expected value of the lottery is 4p- (1 − p) = 5p - 1, giving arisk premium of R(p)=5p-1-65p - I.(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 tellhim 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 ticketavailable for him to purchase.Solution: Bob has three options: accept the offer, reject the offer and buy a ticket,or reject the offer and not buy a ticket. Since Bob is risk-neutral, he cares only aboutmaximizing the expected value of the lottery he chooses (i.e. we can suppose that u(x) =x). If he rejects the offer, the expected value associated with buying a ticket is 51 -1 =0.25 > 0, so he prefers to buy a ticket. If he accepts the offer, then he loses 50 cents forsure, but gains 4 with probability, giving expected value 1-0.5=0.5 > 0.25. Therefore,Bob will accept the offer.

The entire benefit or satisfaction a customer derives from purchasing a particular commodity or…

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(z) = 2³ over change in wealth z, what is the certainty equivalent for Bob of buying one ticket (as a function of p)? What is the risk premium?

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(z) = 2³ over change in wealth z, what is the certainty equivalent for Bob of buying one ticket (as a function of p)? What is the risk premium?

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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