A UNIFIED TREATMENT OF FINITE AND INFINITE ECONOMIES - LIMITED ARBITRAGE IS NECESSARY AND SUFFICIENT FOR THE EXISTENCE OF EQUILIBRIUM AND THE CORE

A single condition, limited arbitrage, is shown to be necessary and su fficient for the existence of a competitive equilibrium and the core i n economies with any number of markets, finite or infinite, with or wi thout short sales. This extends earlier results of Chichilnisky [8] fo r finite economies. This unification of finite and infinite economies is achieved by proving that in Hilbert spaces limited arbitrage is nec essary and sufficient for the compactness of the Pareto frontier. Limi ted arbitrage has also been shown to be necessary and sufficient for a resolution of the social choice paradox [9], [10], [12], [13], [14].