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Unformatted text preview: Economics 310-2 Spring 2009 Professor Jeff Ely Problem Set 4 Due April 27 1. ( Tragedy of the Commons ) There are n farmers who share access to a common plot of land. Each farmer has one cow and uses the land for grazing. The problem for the farmers is to determine how many hours each farmer will be able to use the land. Thus, an alternative is a list ( h 1 ,h 2 ,...,h n ) where h i denotes the number of hours that farmer i will be allowed to let his cow graze. Farmer i ’s valuation function is as follows. Farmer i has a value v i and if farmer i ’s cow grazes for h i hours, then farmer i ’s valuation is qh i v i where q is the quality of the land. The quality of the land in turn depends on how much it is being used. In particular, if H = ∑ j h j is the total number of cow-hours of grazing, the quality of the land is q ( H ) = 10- H (in other words, each additinal hour a farmer allows his cow to graze lowers the quality of the land by one unit)....
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