Econ 337TA Session 2Jorge CatepillanJanuary 19, 2012Problem 1Young and old residents tend to have different preferences for local public services. Suppose that each oldperson has the utility functionUo= 2G+2xO, where G is consumption of a local public good and xo is an oldperson’s consumption of a private good. Similarly, the utility function for a young person isUy= 6G+ 2xy.Each old person has an initial endowment of 10 dollars and each young person has an endowment of 5 dollars.The marginal cost of producing the private good is assumed to be one. Any local government can produceG units of the local public good at a total cost ofNG2+N(4-N)2G, where N denotes the number ofresidents in its jurisdiction. Suppose that local governments set taxes by dividing the total cost of publicgoods equally among residents.a. Use Samuelson’s condition to determine the Pareto effcient level of G in acommunity with two oldpersons and two young persons.
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