Section-5-Quasilinear-Utility-and-Pareto-Efficiency-slides

Section-5-Quasilinear-Utility-and-Pareto-Efficiency-slides...

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Unformatted text preview: Quasilinear Utility and Pareto Efficiency Todd Sarver Northwestern University Econ 310-2 Fall 2011 Todd Sarver (Northwestern University) Quasilinear Utility and Pareto Efficiency Econ 310-2 Fall 2011 1 / 8 Quasilinear Utility Consider adding monetary transfers to the model: Todd Sarver (Northwestern University) Quasilinear Utility and Pareto Efficiency Econ 310-2 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 310-2 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 310-2 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 310-2 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 310-2 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 310-2 taught by Professor Sarver during the Spring '08 term at Northwestern.

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Section-5-Quasilinear-Utility-and-Pareto-Efficiency-slides...

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