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

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

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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

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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 > 0 , then money is being transfered to individual i . If t i < 0 , 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

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Quasilinear Utility Consider adding monetary transfers to the model: Let t i be the transfer to individual i . If t i > 0 , then money is being transfered to individual i . If t i < 0 , 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 > 0 , then money is being transfered to individual i . If t i < 0 , 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

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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 ˆ t 1 , ˆ t 2 , . . . , ˆ t n such that the allocation ( ˆ t 1 , . . . , ˆ 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 ) . Then, there exist a new set of transfers ˆ t 1 , ˆ t 2 , . . . , ˆ t n such that the allocation ( ˆ t 1 , . . . , ˆ t n , B ) is a Pareto improvement of ( t 1 , . . . , t n , A ) . Intuition Think of n i =1 v i ( A ) as the size of the utility “pie”, which is to be divided between the individuals. Since utility is quasilinear, we can use monetary transfers to divide this pie any way we see fit.

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