On the Mas-Colell-Richard equilibrium theorem

A. Mas-Colell and S. F. Richard (J. Econ. Theory 53 (1991), 1-11) published a remarkable infinite dimensional equilibrium existence theorem for exchange economies that encompasses all the currently available important equilibrium results as corollaries. To prove this theorem, the authors utilized in an ingenious way the lattice structure of Riesz spaces. However, in two critical steps during the proof of the theorem. there is an ''obvious'' claim used by the authors which may fail to be true. In this note, we present an example where this ''obvious'' conclusion is false. We also indicate how one can correct the proof of this truly outstanding equilibrium existence theorem. (C) 1997 Academic Press.