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Question: hi i need help on i ii and iii thank...

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S19 Prof. Stahl 359M Environmental Economics HW 1 1. A small village of 1000 families in Outer Bodiva has a single coal burning factory that pollutes the air. A Peace Corps volunteer suggests a project that would install smokestack filters and significantly reduce the air pollution. The project will require 2000 hours of labor. If the project is undertaken, each family will enjoy a gross benefit of y, measured in hours of labor Assume that y 1 for 500 of the families, and y - 5 for the other 500 families. Also assume that these benefits are private: no one knows anyone elses true benefit a) A village elder suggests that every family should be required to contribute equally to the project (i.e. 2 hours each). Will this proposal win a b) Another village elder suggests that every family be asked to submit a sealed ballot that indicates an amount of labor the family is willing to commit to the project. If the total of the commitments is at least 2000 hours, the project is undertaken; otherwise it is abandoned. If the total of the commitments, X -x, exceeds 2000 hours, then each family is required to fulfill only the fraction 2000/x of its commitment. Note that if every family volunteers its total benefit (Ci.e. xy), then in the end each family will be obligated to provide 2/3 of y (i) Prove that it is not rational for every family to report truthfully (ie. set x y). Hint: take the point of view of one family (say family i), and assume that all other families report truthfully. Then, show that the rational decision of family i is x0.] (i) Suppose that after much discussion in the village, everyone agrees that everyone should contribute at least I hour. It is also realized that half the families will contribute no more than I hour, implying that the other 500 families need to contribute 1500 hours in total, which can be accomplished by each contributing 3 hours. Show that it is rational for every family to do this; that is, if family i believes all other families will contribute according to this suggestion, then it is rational for family i to contribute 1 hour ify-1, and contribute 3 hours if y-s. (iii) An alternative scenario is that a village leader suggests that the cost of this project should be born only by those who benefit the most, and that each family should contribute either 0 or 4 hours. Show that it is rational for every family to do this; that is, if family i believes all other families will contribute according to this suggestion, then it is rational for family i to contribute 0 hours if y I, and contribute 4 hours if y- (iv) Compare the fairmess of schemes (i) and (ii) in terms of hours contributed and net benefits (y-x). Hi, I need help on (I), (II) and (III). Thank you.
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