On Core-Walras (Non-) Equivalence for Economies with a Large Commodity Space

Addressing a question raised by Tourky and Yannelis (1998), we show that given any non-separable Banach space as commodity space and giben any atomless measure space of agents, there is an economy fulfilling the usual standard assumptions but having a core allocation not supportable as a Walrasion equilibrium, and in fact, having no Walrasian equilibria at all. We shall also consider the framework of economies with weakly compact consuption sets as developed by Khan and Yannelis (1991). We prove that in this setting the core of an economy with a measure space of traders is non-empty, regardless of wheter or not the commodity space is separable. On the other hand, we show that when the commodity space contains weakly compact subsets that are non-separable, than, again, there are atomless economies for which core-Walras equivalence fails. Thus, in particular, for very large commodity spaces the notion of the core seems to be more robust than that of a Walrasian equilibrium.