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Unformatted text preview: Economics 201B Handout on Core Convergence Core convergence theorems assert that, for economies with a large number of agents, core allocations are approximately competitive. The particular sense of approximate competitiveness depends on our assumptions, particu- larly our assumptions about preferences. There are three motivations for the study of the core. The first two relate to what the core convergence results tell us about Walrasian equilibrium, and are normative in character. The fact that Walrasian allocations lie in the core is an important strengthening of the First Welfare Theorem. This is a strong stability property of Walrasian equilibrium: no group of individuals would choose to upset the equilibrium by recontracting among themselves. It has a further normative significance. If we are satisfied that the distribu- tion of initial endowments has been done in an equitable manner, no group can object that it is treated unfairly at a core allocation. Since Walrasian allocations lie in the core, they possess this desirable group fairness property. This strengthening of the First Welfare Theorem requires no assumptions on the economy beyond those limited assumptions required for the First Welfare Theorem itself. The second motivation concerns the relationship of the core convergence theorems to the Second Welfare Theorem, which asserts, under appropriate hypotheses, that any Pareto optimal allocation is a Walrasian equilibrium with transfers. The core convergence theorems assert that core allocations of large economies are nearly Walrasian without any transfers. 1 This is a strong unbiasedness property of Walrasian equilibrium: if a social planner were to insist that only Walrasian outcomes were to be permitted, that insis- tence by itself would not substantially narrow the range of possible outcomes beyond the narrowing that occurs in the core. The insistence would have no hidden implications for the welfare of different groups beyond whatever...
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- Spring '06