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Unformatted text preview: Quasilinear Utility and Pareto Efficiency Todd Sarver Northwestern University Econ 3102 Fall 2011 Todd Sarver (Northwestern University) Quasilinear Utility and Pareto Efficiency Econ 3102 Fall 2011 1 / 8 Quasilinear Utility Consider adding monetary transfers to the model: Todd Sarver (Northwestern University) Quasilinear Utility and Pareto Efficiency Econ 3102 Fall 2011 2 / 8 Quasilinear Utility Consider adding monetary transfers to the model: Let t i be the transfer to individual i . If t i > , then money is being transfered to individual i . If t i < , then money is being transfered away from individual i . Todd Sarver (Northwestern University) Quasilinear Utility and Pareto Efficiency Econ 3102 Fall 2011 2 / 8 Quasilinear Utility Consider adding monetary transfers to the model: Let t i be the transfer to individual i . If t i > , then money is being transfered to individual i . If t i < , then money is being transfered away from individual i . Feasibility constraint: We require that n i =1 t i = 0 . That is, money transfered to one individual must be funded by transferring money away from some other individuals. Todd Sarver (Northwestern University) Quasilinear Utility and Pareto Efficiency Econ 3102 Fall 2011 2 / 8 Quasilinear Utility Consider adding monetary transfers to the model: Let t i be the transfer to individual i . If t i > , then money is being transfered to individual i . If t i < , then money is being transfered away from individual i . Feasibility constraint: We require that n i =1 t i = 0 . That is, money transfered to one individual must be funded by transferring money away from some other individuals. Definition A utility function u i is quasilinear in monetary transfers if it takes the form u i ( t i ,A ) = t i + v i ( A ) , where v i is some function that assigns a value to each alternative A . Todd Sarver (Northwestern University) Quasilinear Utility and Pareto Efficiency Econ 3102 Fall 2011 2 / 8 Quasilinear Utility: Bigger Pie Pareto Improvement Theorem Consider any set of transfers t 1 ,t 2 ,...,t n and any alternative A . Suppose there exists another alternative B such that n i =1 v i ( B ) > n i =1 v i ( A ) . Then, there exist a new set of transfers t 1 , t 2 ,..., t n such that the allocation ( t 1 ,..., t n ,B ) is a Pareto improvement of ( t 1 ,...,t n ,A ) . Todd Sarver (Northwestern University) Quasilinear Utility and Pareto Efficiency Econ 3102 Fall 2011 3 / 8 Quasilinear Utility: Bigger Pie Pareto Improvement Theorem Consider any set of transfers t 1 ,t 2 ,...,t n and any alternative A . Suppose there exists another alternative B such that n i =1 v i ( B ) > n i =1 v i ( A ) ....
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This note was uploaded on 01/03/2012 for the course ECON 3102 taught by Professor Sarver during the Spring '08 term at Northwestern.
 Spring '08
 SARVER
 Microeconomics, Utility

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