In this paper we first give an existence of equilibrium theorem with unbounded below consumption sets, by the demand approach, assuming only that the individually rational utility set is compact. vVe then classify different notions of absence of arbitrage and give conditions under which they are equivalent to the existence of an equilibrium. SUR LES DIFFERENTES NOTIONS D'ARBITRAGE ET L'EXISTENCE DE L'EQUILIBRE Résumé•-Dans ce papier, d'abord nous donnons un théorème d'existence d'un équilibre avec des ensembles de consommation non bornés inférieurement par l'approche de la demande en suµµosant seulement que l'ensemble des utilités individuellement rationnelles est compact. Ensuite. nous classons les différentes notions d'absence d'arbitrage et donnons des conditions qui les rendent équivalentes à l'existence d'un équilibre.
We study the existence of equilibrium and rational bubbles in a Ramsey model with heterogeneous agents, borrowing constraints and endogenous labor.Applying a nonstandard fixed-point theorem by Gale and Mas-Colell's (1975), we prove the existence of equilibrium in a time-truncated bounded economy. A common argument shows this solution to be an equilibrium for any unbounded economy with the same fundamentals. Taking the limit of a sequence of truncated economies, we eventually obtain the existence of equilibrium in the Ramsey model.In the second part of the paper, we address the issue of rational bubbles and we prove that they never occur in a productive economy à la Ramsey.
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