Consider the St. Petersburg paradox. Decision- maker has an exponential utility function with A=4 and B=2 and the risk tolerance level is R=7,000. What is the highest price that the decision-maker is willing to pay for the lottery?

Consider the St. Petersburg paradox. Decision- maker has an exponential utility function with A=4 and B=2 and the risk tolerance level is R=7,000. What is the highest price that the decision-maker is willing to pay for the lottery?

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

See similar textbooks

Similar questions

Fred wants to hire Barney to manage his retail store. Barney can apply a high level of effort (at a cost to him of $30), a medium level of effort (at a cost to him of $10), or a low level of effort (at a cost to him of $0). Fred's profits depend not only of the level of Barney's effort but also on the state of consumer demand. Fred believes that demand will be high with probability 50 percent (and therefore demand will be low with probability 50 percent). Fred has determined the following possible profit levels (before paying Barney) will occur depending on Barney's effort and the state of consumer demand: Demand low high effort low 20 40 medium 40 80 high 80 100 Of the choices below, what is the largest percentage range of profit provided to Barney that would ensure Barney would supply high effort? a. any percent greater than 75.00 percent (3/4). b. any percent greater than 66.66 percent (2/3). c. any percent greater than 50.00 percent (1/2).d. any…
Nicolaus I Bernoulli offers his friend Pierre Rémond de Montmort a game where they need to repeatedly toss a fair ducat until they get a head for the first time. The game stops then, and they count the number n of coin tosses it took to get the desired outcome, and Montmort gets 2^n ducats. Assume that Montmort's utility function is u(w)=w^0.14. How much should Montmort pay to play this game?
When a famous painting becomes available for sale, it is often known which museum or collector will be the likely winner. Yet, the auctioneer actively woos representatives of other museums that have no chance of winning to attend anyway. Suppose a piece of art has recently become available for sale and will be auctioned off to the highest bidder, with the winner paying an amount equal to the second highest bid. Assume that most collectors know that Valerie places a value of $15,000 on the art piece and that she values this art piece more than any other collector. Suppose that if no one else shows up, Valerie simply bids $15,000/2=$7,500 and wins the piece of art. The expected price paid by Valerie, with no other bidders present, is $________.. Suppose the owner of the artwork manages to recruit another bidder, Antonio, to the auction. Antonio is known to value the art piece at $12,000. The expected price paid by Valerie, given the presence of the second bidder Antonio, is $_______. .
Assume, in producing one unit of a good X, an agent can exert either the good effort (G) or the bad effort (L), which cause production defects with probability 0.25 or 0.75 respectively. His utility function in effort e and wage w is U(w, e) = 100 (10/w) c(e) where c(G) = 2 for the good effort and c(L) = () for the bad effort. Production defects are contractible and so can be included in the agent's contract, but effort is not contractible. Good X sells for $20 if there are no defects and $0 otherwise. The principal is risk-neutral and likes profit. Assume the agent has a reservation utility/outside option of U=0. If effort is not contractible then:: Select one: O a. There is insufficient information to know the principal's choice of contract because we do not know the agent's level of absolute risk aversion. O b. the principal will be indifferent between writing a contract to achieve the good effort level and writing a contract to achieve the bad effort level O c. the principal will…
Consider the lottery that assigns a probability T of obtaining a level of consumption CH and a probability 1-T an individual facing such a lottery with utility function u(c) that has the properties that more is better (that is, a strictly positive marginal utility of consumption at all levels of c) and diminishing marginal utility of consumption, u"(c) CL. Consider du(c) for the first derivative of the utility function with respect to dc du(c) du' (c) consumption and u"(c) (which is also the derivative of the first derivative of the utility function). to be the second derivative of the utility function dc dc2 1. Provide a definition for the certainty equivalent level of consumption for the simple lottery described above.
Why do sellers generally prefer a Vickrey auction to a regular sealed bid if sellers don’t receive the highest bid in the Vickrey auction? Sellers only have to sell their item if the bid is the highest-price bid. The second-highest bid in a Vickrey auction is generally higher than the highest bid in a regular sealed-bid auction. The second-highest bid is about the same in both auctions. Sellers prefer the final price is not revealed to all bidders. Sellers would never prefer Vickrey auctions.
An individual is offered a choice of either $50 or a lottery which may result in $0 or $100, each with equal probability 1/2. If the individual has a utility function u(w) = w, which one would they choose? If the individual has a utility function u(w) =sqr(w)?
Shane just bought a house worth $360,000 in an area that is known for floods. A flood occurs with a 5% chance and if it occurs, his home is ✓ for reduced in value to $202,500. Shane has utility function given by U(X)=√√X. He would be willing to pay a maximum of flood insurance. The fair insurance premium for flood insurance is Shane's risk premium is Suppose, instead, that Shane's utility function is given by U(X) = X². Then, the maximum he would be willing to pay for flood insurance is
Consider the following game, with a risk-neutral principal with preferences π = q - w hiring an agent with preferences U = √w-e.. The agent's reservation utility is given by Ū = 2, and the agent can choose between an effort level of 0 or an effort level of 10. Output is either 0 or 400 and follows the following probability distribution, a function of effort level and some uncertain factor: e=0 e=10 Probability (q=0) Probability (q=400) 0.6 0.4 0.9 0.1 What would the contract look like if the principal tried to push the wages when q=0 to zero? Would the principal want to do this? Explain.
Prospect Y = ($6, 0.25 ; $15, 0.75) If Will's utility of wealth function is given by u(x)=x0.25, what is the value of CE(Y) for Will? (In other words, what is Will's certainty equivalent for prospect Y?) (The certainty equivalent represents the maximum amount a person would be willing to pay to acquire a risky prospect, and equivalently, the lowest price for which they would be willing to sell a risky prospect if they already owned it) (Note: The answer may not be a whole number; please round to the nearest hundredth) (Note: The numbers may change between questions, so read carefully)
Consider the following claim: “If a decision maker prefers one given lottery that yields $x with probability 1 over another given lottery whose expected return is $x, then we can fully characterize the agent's risk attitude. That is, this information comparing two given lotteries is enough to determine if the decision maker is risk averse, risk loving or risk neutral.” If this claim is TRUE, then provide a proof. If it is FALSE, then prove your argument by providing an explanation.
Priyanka has an income of £90,000 and is a von Neumann-Morgenstern expected utility maximiser with von Neumann-Morgenstern utility index . There is a 1 % probability that there is flooding damage at her house. The repair of the damage would cost £80,000 which would reduce the income to £10,000. a) Would Priyanka be willing to spend £500 to purchase an insurance policy that would fully insure her against this loss? Explain. b) What would be the highest price (premium) that she would be willing to pay for an insurance policy that fully insures her against the flooding damage?