Second Welfare Theorem
Second Welfare TheoremEcon 2100Fall 2018Lecture 18, October 31 (boo)Outline1Second Welfare TheoremFrom Last ClassWe want to state a prove a Theorem that says that any Pareto optimalallocation is (part of) a competitive will entail nding the prices that make that allocation an , we had to change the de nition of equilibrium to deal with an economy fXi;%i; !igIi=1;fYjgJj=1 , an allocationx ;y and a pricevectorp are a price equilibrium with transfers if there exists a vector ofwealth levelsw2RLwithIXi=1wi=p IXi=1!i+JXj=1p y jsuch that:1. For eachj=1; :::;J:p yj p y jfor allyj2Yj;2. For eachi=1; :::;I:x i%ixifor allxi2fxi2Xi:p xi wig; i IPi=1!i+JPj=1y j,withpl=0 if the inequlity is strict for x the boundary issues, we make another small nitionGiven an economyfXi;%igIi=1;fYjgJj=1; !, an allocationx ;y and a price vectorp constitute a quasi-equilibrium with transfers if there exists a vector of wealthlevelsw= (w1;w2; :::;wI)withIXi=1wi=p !
Second Welfare Theorem: Preliminaries We have seen a few counterexamples to a possible second welfare theorem, and ways in which we can deal with these.
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