Department of Economics University of Vienna on Core-walras Equivalence in Banach Spaces When

The paper studies the core-Walras equivalence problem in the commodity space framework of Banach spaces, allocations being defined as Pettis integrable functions. In particular, a core-Walras equivalence result for a certain class of commodity spaces is established, without requiring that the commodity space be separable. The class covered by this result includes the Lp(μ) spaces, 1 ≤ p < ∞, μ being σ -finite. On the other hand, responding to objections made against some recent core-Walras nonequivalence results in the Bochner integrable allocations setting, it is shown that these latter results carry over to the Pettis integrable allocations setting, unless additional restrictions on the heterogeneity of agents’ preferences are in force.