In finite dimensional economies, it was proven by Werner [Werner, J., 1987.
Arbitrage and the existence of competitive equilibrium. Econometrica 55, 1
403-1418.], that if there exists a no-arbitrage price (equivalently, under
standard assumptions on agents' utilities, if aggregate demand exists for s
ome price), then there exists an equilibrium. This result does not generali
ze to the infinite dimension. The purpose of this paper is to propose a "ut
ility weight" interpretation of the notion of "of no-arbitrage]price". We d
efine "fair utility weight vectors" as utility weight vectors for which the
representative agent problem has a unique solution. They correspond to no-
arbitrage prices. The assumption that there exists a Pareto-optimum, can be
viewed as the equivalent of the assumption of existence of aggregate deman
d. We may then define in the space of utility weight vector, the excess uti
lity correspondence, which has the properties of an excess demand correspon
dence. We use a generalized version of Gale-Nikaido-Debreu's lemma to prove
the existence of an equilibrium. (C) 2000 Elsevier Science S.A. All rights
reserved.