Existence of Competitive Equilibrium in Unbounded Exchange Economies with Satiation: A Note

Abstract

In this note, we extend the result of Sato (2010) to economies with unbounded-from-below choice sets: we prove the existence of a competitive equilibrium (to be exact, a quasi-equilibrium) by assuming “boundary satiation” introduced in Sato (2010) and the “strong compactness of the individually rational utility set” introduced in Martins-da-Rocha and Monteiro (2009). As a result, we obtain a new equilibrium existence theorem that can be applied to the case in which choice sets are unbounded from below and satiation occurs only inside the set of individually attainable choices. We also investigate the relationships between boundary satiation and some other conditions concerning satiation provided in the literature.

Keywords: Satiation, Unbounded-from-below choice sets, Individually rational utility set, Competitive equilibrium

JEL Classification: C62, D50