3) A common argument against the transitivity property of preferences is that peoplecannot discern between small differences, but, then assuming transitivity impliesthat they should be indifferent between two totally different alternatives. (Onecommon example goes as follows: no one can discern the difference between a cupof coffee with 10 miligram (mg.) of sugar and another cup with 11 mg. of sugar.Therefore, anyone is indifferent between a cup with 10 mg and another with 11 mgof sugar, should also be indifferent between a cup with 10 mg and 12 mg of sugar(as she would be indifferent between the two cups with 11 mg and 12 mg of sugar,and the transitivity implies that 10 mg must be just as good as 12 mg. But, with thesame token, one can extend the chain, and say that one should be indifferentbetween a cup with 10 mg of sugar and a cup with 100 gr (not mg!) of sugar. And,no one is.) Show that with money prizes this argument is not as easily applicable,furthermore argue that, if you were indifferent between lottery L that pays $x withprobability p and nothing with probability (1-p) and lottery L' that pays $x withprobability p+d and nothing with probability (1-p-d) where dis arbitrarily small, aconman could soon get all your money (or, valuable lottery tickets). The argumentyou develop to show this result is closely related to what is known as the DutchBook argument. 1) Expected Utility formulation was initially proposed as a solution to the St.Petersburg paradox (or, its predecessor). However, does it really solve all suchparadoxes? More specific, consider an individual whose "little Bernoulli" utilityfunctions is, a la Cremer, given by u(x) = x^. Construct a lottery similar to St.Petersburg lottery in that your lottlery, too, gives a finite prize with probability one,but not only the expected value, but also the expected utility of your lottery(calculated using the u(.) above) is not finite. Discuss how that violates EU as asolution for the St. Petersburg paradox.

Expected Utility formulation was initially proposed as a solution to the St. Petersburg paradox (or, its predecessor). However, does it really solve all such paradoxes? More specific, consider an individual whose "little Bernoulli" utility functions is, a la Cremer, given by u(x) = x**. Construct a lottery similar to St. Petersburg lottery in that your lottlery, too, gives a finite prize with probability one, but not only the expected value, but also the expected utility of your lottery (calculated using the u(.) above) is not finite. Discuss how that violates EU as a solution for the St. Petersburg paradox.

Expected Utility formulation was initially proposed as a solution to the St. Petersburg paradox (or, its predecessor). However, does it really solve all such paradoxes? More specific, consider an individual whose "little Bernoulli" utility functions is, a la Cremer, given by u(x) = x**. Construct a lottery similar to St. Petersburg lottery in that your lottlery, too, gives a finite prize with probability one, but not only the expected value, but also the expected utility of your lottery (calculated using the u(.) above) is not finite. Discuss how that violates EU as a solution for the St. Petersburg paradox.

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

Let p denote a lottery over a finite set of possible prizes denoted by the vector Y; and let 8x denote another lottery that gives prize X for certain. (i) Using the utility function u(x) = 1 – e-ax, show that for CARA utility functions, adding a constant amount to each lottery prize does not change risk attitudes i.e. if 8x 2 p, then ôx+z > p' where p' denotes the lottery which simply adds an amount Z to each prize in p. х1-р —1 (ii) Using the utility function u(x) ,p 2 0, p + 1, show that CRRA 1-р utility functions have the property that proportional changes in prizes do not affect risk attitudes i.e. if 8x 2 p, then dax z p' where p' denotes the lottery which multiplies each prize in p by a > 0.
a) Consider a set of monetary outcomes X = {x1, ... , xK} where the outcomes are arranged in increasing order x, E qcx,) j=i j=i with at least one of the inequalities being strict. Explain the intuition of first-order stochas- tic dominance. Show that, for expected utility preferences with vNM utility u that is strictly increasing in money, if p first-order stochastically dominates q then p > q.
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 Yakov places a value of $35,000 on the art piece and that he values this art piece more than any other collector. Suppose that if no one else shows up, Yakov simply bids $35,0002=$17,500 $35,000 2 = $17,500 and wins the piece of art. The expected price paid by Yakov, with no other bidders present, is. Suppose the owner of the artwork manages to recruit another bidder, Bob, to the auction. Bob is known to value the art piece at $28,000. The expected price paid by Yakov, given the presence of the second bidder Bob, is.
1. Now, imagine that Port Chester decides to crack down on motorists who park illegally by increasing the number of officers issuing parking tickets (thus, raising the probability of a ticket). If the cost of a ticket is $100, and the opportunity cost for the average driver of searching for parking is $12, which of the following probabilities would make the average person stop parking illegally? Assume that people will not park illegally if the expected value of doing so is negative. Check all that apply. A. 9% B. 18% C. 17% D. 10% 2. Alternatively, the city could hold the number of officers constant and discourage parking violations by raising the fine for illegal parking. Suppose the average probability of getting caught for parking illegally is currently 10% citywide, and the average opportunity cost of parking is, again, $12. The fine that would make the average person indifferent between searching for parking and parking illegally is ____ , assuming that people will not…
a) Consider a set of monetary outcomes X = {x1,... , Xk} where the outcomes are arranged in increasing order x, g(x;) for all i = 1,... K, j=i j=i with at least one of the inequalities being strict. Explain the intuition of first-order stochas- tic dominance. Show that, for expected utility preferences with vNM utility u that is strictly increasing in money, if p first-order stochastically dominates q then p > q.
In 'the dictator' game, one player (the dictator) chooses how to divide a pot of $10 between herself and another player (the recipient). The recipient does not have an opportunity to reject the proposed distribution. As such, if the dictator only cares about how much money she makes, she should keep all $10 for herself and give the recipient nothing. However, when economists conduct experiments with the dictator game, they find that dictators often offer strictly positive amounts to the recipients. Are dictators behaving irrationally in these experiments? Whether you think they are or not, your response should try to provide an explanation for the behavior.
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)?
Consider the following model about the auctions. We have two buyers each obtain a private signal about the value of good being auctioned. The signal can be either high (H) or low (L) with equal probability. If both obtain signal H, the good is worth 1; otherwise, it is worth 0.a. What is the expected value of the good1 to a buyer who sees signal L and to a buyer who sees signal H?b. Suppose buyers bid their expected value computed in part (a). Show that they earn negative profit conditional on observing signal H.
Draw a utility function over income u(I) that describes a man who is a risk lover when his income is low but risk averse when his income is high. 1.) Using the 3-point curved line drawing tool, draw the low income portion of his utility function. Label it U₁. 2.) Using the 3-point curved line drawing tool, draw the high income portion of his utility function. Label it UH. Carefully follow the instructions above, and only draw the required objects. C 500- 450- 400- 350- 300- 250- 200- 150- 100- 50- 0 Utility 20,000 40,000 60,000 80,000 100,000 Income
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.
An individual is oered a choice of either $50 or a lottery which may result in $0and $100, each with equal probability 1/2 . If the individual has a utility function u(w) = 5 + 2w, which one would they choose? If the individual has a utility function u(w) =w1/2 + 1?
Suppose that • The employee has an outside offer to work for $27 per hour, for 1500 hours per year The employee currently works for $20 per hour, for 2000 hours per year The switching cost can be either high ($1'000) or low ($50) • The high switching cost has probability 40%; the low switching cost 60% Suppose that the cost of losing the employee is $800. What is the employer expected payoff from choosing not to match the outside offer?