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Unformatted text preview: Economics 3102 Spring 2009 Professor Jeff Ely Problem Set 2 Due Monday April 13 1. Two roomates Xavier and Yolanda share an apartment with lovely shag carpeting. Neither of them owns a vacuum cleaner. In order to keep the carpet clean, they must enlist the services of their neighbor Zeke. If Zeke spends a total of h hours a day vacuuming their carpet, Xavier and Yolanda would obtain value v x ( h ) and v y ( h ) respectively, where v x ( h ) = 3 h h 2 v y ( h ) = 2 h 3 h 2 Zeke’s value, on the other hand is negative v z ( h ) = h 2 (vacuuming is a chore for Zeke and since it is not his apartment he gets no benefit from the clean carpet.) So consider the problem of deciding how many hours h Zeke should spend cleaning the carpet. Any h ≥ 0 is a possible alternative. (a) Suppose to begin with there is no money, so that the agents utility functions are just their value functions v x , v y , v z . With these preferences, what levels of h are Pareto efficient?...
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 Spring '08
 Witte
 Economics, Macroeconomics, Game Theory, Trigraph, Pareto Efficient, utilitarian solution h∗

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