It is shown that core-Walras equivalence fails whenever the commodity space is a non-separable Banach space. The interpretation is that a large number of agents guarantees core-Walras equivalence only if there is actually a large number of agents relative to the size of the commodity space. Otherwise a large number of agents means that agents' characteristics may be extremely dispersed, so that the standard theory of perfect competition fails. Supplementing the core-Walras non-equivalence result, it is shown that in the framework of economies with weakly compact consumption sets – as developed by Khan and Yannelis (1991) – the core is always non-empty, even if consumption sets are non-separable. Copyright Springer-Verlag Berlin Heidelberg 2003Keywords and Phrases: Non-separable commodity space, Measure space of agents, Core, Walrasian equilibrium, Core-Walras equivalence., JEL Classification Numbers: C62, C71, D41, D50.,
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