5 - Limit theorems for the core

Abstract

This chapter describes the limit theorems for the core. In the case of a limit, or continuum economy, the core C (E) and the competitive equilibria W (E) coincide. In an economy with a continuum of agents, where individuals acting in isolation are, indeed, of no importance, one has coincidence of the core and the competitive allocations. Core allocations in large economies are nearly competitive allocations. For any such allocation, there is a price system under which individuals in the economy, acting as price takers, would choose a bundle close to the bundle they receive in that allocation. This leads to a more precise formulation of Edgeworth's idea that the core shrinks as economies become large.