Equilibria in security markets with a continuum of agents
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We prove the existence of a competitive equilibrium for exchange economies with a measure space of agents and for which the commodity space is ` p, 1 < p < +∞. A vector x = (xn) in ` p may be interpreted as a security which promises to deliver xn units of numeraire at state (or date) n. Under assumptions imposing uniform bounds on marginal rates of substitution, positive results on core-Walras equivalence were established in Rustichini–Yannelis  and Podczeck . In this paper we prove that under similar assumptions on marginal rates of substitution, the set of competitive equilibria (and thus the core) is non-empty.