Abstract
A condition of limited arbitrage is defined on the endowments and the preferences of the traders in an Arrow-Debreu economy. Theorem 1 establishes that limited arbitrage is necessary and sufficient for the existence of the competitive equilibrium in markets with or without short sales. Limited arbitrage bounds utility arbitrages. the diversity of the traders in the economy, and the gains from trade which they can afford from initial endowments (Proposition 2); it is related to but nonetheless different from the no-arbitrage condition used in finance. Theorem 2 establishes that an Arrow-Debreu economy has a competitive equilibrium if and only if every one of its subeconomies with N I traders does, where N is the number of commodities. Limited arbitrage has been shown elsewhere to be equivalent to the existence of the core [16], to the contractibility of spaces of preferences and to the existence of continuous anonymous social choice rules which respect unanimity.
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