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Unformatted text preview: Econ 440 October 2007 Peter Norman Homework3 1. Consider a world with three alternatives f x; y; z g and three agents f 1 ; 2 ; 3 g : (a) Construct a preference pro&le that generates a Voting cycle (Condurcet cycle). (b) Consider the following sequential game. In stage 1 there is a vote between x and y: Then, in the second stage there is a vote between z and the winning alternative of the &rst stage vote. Assume that each agent vote as if she is pivotal (eg. elimination of weakly dominant strategies). What is the winning policy? (c) Do the same thing as in part b, but assume that the &rst stage vote is between x and z: . (d) Do the same thing as in parts b and c, but assume that the &rst stage vote is between y and z: (e) Suppose that agent 1 can decide on which two alternatives to vote on in stage 1. What will happen? Why is this interesting from the point of view of understanding the role of legislative procedures? 2. Consider an economy with three agents, A; B; C , a private and a public good. Suppose preferences are given by U A ( x; y ) ; U B ( x; y ) and U C ( x; y ) and that each agents is endowed with one unit f the private good. The private good can be turned into the public good on a one-to-one basis (just like weve alwaysgood....
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