The Core Configuration. Exchange Economy With Utility Maximization

The classic theorem on the core of the pure exchange economy is that the core allocations convergence to Walras equilibrium.The purpose of this paper is to clarify the meaning of conclusion that approximate core allocations are demand-like by relating that conclusion of utility maximization,i.e the core allocations almost maximize the utility over the agents' budget sets.We first show an inequality that measures the distance from approximate core allocations to the demand set under some price vector.Secondly,we prove that these price vectors in the sequence of economies contained in a compact set.Thirdly,we make the conclusion that the utility of the approximate core allcations convergences to the utility of demand set. Finally,we give the rate of the convergence.