. Explain the interpretation of a utility function and why such a function should be increasing. is said that the utility function of a decision maker is given by Ua(x) = 2ax – x², x € R for some a > 0.For which lotteries with random outcomes X is the above function a utility function? Explain your answer and give an example of a lottery or specify a distibution of the random variable X for which the function mentioned in relation 2 is not a utility function. 3. Consider a decision maker with initial wealth 0 and this decision maker needs to play a lottery L having a random outcome X bounded above by a > 0. This means P(X < a) = 1. Is this decision maker risk averse or risk seeking for this particular lottery? Explain your answer and give the definion of riskaverse and risk seeking! 4. Let a > 0 be given and L a lotery with random outcome X having cumulative distribution function

. Explain the interpretation of a utility function and why such a function should be increasing. is said that the utility function of a decision maker is given by Ua(x) = 2ax – x², x € R for some a > 0.For which lotteries with random outcomes X is the above function a utility function? Explain your answer and give an example of a lottery or specify a distibution of the random variable X for which the function mentioned in relation 2 is not a utility function. 3. Consider a decision maker with initial wealth 0 and this decision maker needs to play a lottery L having a random outcome X bounded above by a > 0. This means P(X < a) = 1. Is this decision maker risk averse or risk seeking for this particular lottery? Explain your answer and give the definion of riskaverse and risk seeking! 4. Let a > 0 be given and L a lotery with random outcome X having cumulative distribution function

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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4. Consider a society that has three individuals - 1,2 and 3 - and three alternatives - x, y and z. The society has a preference aggregation rule F. In year 2007, the profile of individual preferences were as follows: 1 2 3 X y Z y Z V It is known that the rule F satisfies Completeness, Transitivity, Anonymity, Unanimity and Independence of Irrelevant Alternatives. Also, in year 2007, F ranked x strictly above y. Now, we are in year 2008. The individual preferences have changed to: 1 2 3 Z y y X Z Z y X x (a) How does the society rank between y and x in 2008? Why? (b) How does the society rank between x and z in 2008? Why? (c) How does the society rank between y and z in 2008? Why? (d) What were the social preferences over all three alternatives in 2007?
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Q5
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Let vij be bidder i's valuation for object j, where i in {1,2,3} and j in {1,2}. Bidder i knows its valuation vi; but other bidders only know that vi; is drawn uniformly from [0, 100]. If bidder i wins object 1 at price p1 and object 2 at price p2, bidder i's payoff is v;1 If bidder i wins only object j at price p;, his payoff is vij – Pj. If bidder i does not win any object, his payoff is 0. The auction proceeds as follows. The initial prices are zero for both objects. All bidders sit in front of their computers and observe the prices for both items in real-time. Initially, all bidders are invited to enter the bidding race for both items. At any moment in time, each bidder has the option to withdraw from the bidding race for either object or both. If a bidder withdraws from the bidding for one object, he can no longer get back to the bidding for that object, but he can stay in the bidding race for the other object if he hasn't withdrawn from it previously. The price for an object…
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?
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