please only do: if you can teach explain steps of how to solve each part b 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(r) = ³ over change in wealth , 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 - 1.(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) =r). If he rejects the offer, the expected value associated with buying a ticket is 5-1=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.

Introduction The utility function illustrates the functional connection between quantities consumed…

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) = 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? Solution: If Bob buys a raffle ticket, then with probability p he gains 4 dollars (5 dollars minus the price of the ticket), and with probability 1-p he loses 1 dollar. His

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) = 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? Solution: If Bob buys a raffle ticket, then with probability p he gains 4 dollars (5 dollars minus the price of the ticket), and with probability 1-p he loses 1 dollar. His

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter7: Uncertainty

Section: Chapter Questions

Problem 7.3P

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