201Lecture132006 - Economics 201BSecond Half Lecture 13...

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Economics 201B–Second Half Lecture 13 Justifying (or Undermining) the Price-Taking Assump- tion Many formulations: Core, Ostroy’s No Surplus Condition, Bar- gaining Set, Shapley-Shubik Market Games (noncooperative), other noncooperative games Core is the most commonly used. The core is the set of all allocations such that no coalition (set of agents) can improve on or block the allocation (make all of its members better oF) by seceding from the economy and only trading among its members. Core is institution-free; no mention of prices. “Core convergence” means roughly that For economies with a large number of agents, core allocations are “approximately Walrasian.” “Approximately Walrasian” means diFerent things in diFerent contexts, depending on what we are willing to assume. Three motivations for the study of the core : Walrasian allocations lie in the core : Important strength- ening of ±irst Welfare Theorem, under same minimal as- sumptions as ±irst Welfare Theorem. (Positive): Strong stability property of Walrasian equi- librium: no group of individuals would choose to upset the equilibrium by recontracting among themselves. 1
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(Normative): If distribution of initial endowments is eq- uitable, no group is treated unfairly at a core allocation. Since Walrasian allocations lie in the core, this is a Group Fairness Property of Walrasian Equilibrium. Core Convergence strengthens Second Welfare Theorem Second Welfare Theorem says every Pareto Optimum is a Walrasian Equilibria with Transfers. Core convergence asserts that core allocations of large economies are nearly Walrasian without transfers. One version states that core allocations can be realized as exact Walrasian equilibrium with small income transfers. Strong “unbiasedness” property of Walrasian equilib- rium · Restricting to Walrasian outcomes does not narrow possible outcomes beyond narrowing occurring in the core.
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201Lecture132006 - Economics 201BSecond Half Lecture 13...

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