Inconsequential arbitrage

We introduce the concept of inconsequential arbitrage and, in the context o f a model allowing short-sales and half-lines in indifference surfaces, pro ve that inconsequential arbitrage is sufficient for existence of equilibriu m. Moreover, with a slightly stronger condition of nonsatiation than that r equired for existence of equilibrium and with a mild uniformity condition o n arbitrage opportunities, we show that inconsequential arbitrage, the exis tence of a Pareto optimal allocation, and compactness of the set of utility possibilities are equivalent. Thus, when all equilibria are Pareto optimal - for example, when local nonsatiation holds - inconsequential arbitrage i s necessary and sufficient for existence of an equilibrium. By further stre ngthening our nonsatiation condition, we obtain a second welfare theorem fo r exchange economies allowing short sales. Finally, we compare inconsequential arbitrage to the conditions limiting ar bitrage of Hart [Hart, O.D., 1974. J. Econ. Theory 9, 293-311], Werner [Wer ner, J., 1987. Econometrica 55, abs 1403-1418], Dana et al. [Dana, R.A., Le Van, C., Magnien, E, 1999. J. Econ. Theory 87, 169-193] and Allouch [Allou ch, N., 1999. Equilibrium and no market arbitrage. CERMSEM, Universite de P aris I]. For example, we show that the condition of Hart (translated to a g eneral equilibrium setting) and the condition of werner are equivalent. We then show that the Hart/Werner conditions imply inconsequential arbitrage. To highlight the extent to which we extend Hart and Werner, we construct an example of an exchange economy in which inconsequential arbitrage holds (a nd is necessary and sufficient for existence), while the Hart/Werner condit ions do not hold. (C) 2000 Elsevier Science S.A. All rights reserved.