Core and Walrasian equilibria when agents' characteristics are extremely dispersed

Summary.

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.