note13 - Microeconomic Theory Econ 101A Fall 2008 GSI Eva...

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Unformatted text preview: Microeconomic Theory Econ 101A Fall 2008 GSI: Eva Vivalt Section Notes 14: Pareto Optimality and Public Goods 1 Pareto Optimality 1.1 Definition Say we have 2 agents. A set of actions ( a P 1 ,a P 2 ) is “Pareto optimal” or “Pareto efficient” if there is no other feasible set of actions ( a 1 ,a 2 ) s.t. either: U 1 ( a 1 ,a 2 ) ≥ U 1 ( a P 1 ,a P 2 ) and U 2 ( a 1 ,a 2 ) > U 2 ( a P 1 ,a P 2 ) or U 1 ( a 1 ,a 2 ) > U 1 ( a P 1 ,a P 2 ) and U 2 ( a 1 ,a 2 ) ≥ U 2 ( a P 1 ,a P 2 ) In other words, there is no way to adjust things from a Pareto optimum that makes any one person strictly better off while leaving everyone else at least as well off as they already were. An equivalent formulation is that for any feasible set of actions ( a 1 ,a 2 ): U 1 ( a 1 ,a 2 ) > U 1 ( a P 1 ,a P 2 )- - > U 2 ( a 1 ,a 2 ) < U 2 ( a P 1 ,a P 2 ) for a Pareto optimum ( a P 1 ,a P 2 ). This says that any set of actions that makes one person strictly better off must make someone else strictly worse off.must make someone else strictly worse off....
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note13 - Microeconomic Theory Econ 101A Fall 2008 GSI Eva...

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