Equilibria in large economies with a separable Banach commodity space and non-ordered preferences

• Published in: Journal of mathematical economics Vol. 39; no. 8; pp. 863 - 889
• Main Author: Filipe Martins-da-Rocha, V
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier B.V 01.11.2003; Elsevier; Elsevier Sequoia S.A
• Series: Journal of Mathematical Economics
• Subjects: Commodities; Discretization of measurable correspondences; Economic size; Economic theory; Economics; Equilibrium; Mathematical methods; Mathematical models; Measure space of agents; Non-ordered but convex preferences; Partially ordered but non-convex preferences; Separable Banach commodity spaces; Studies; D51; Non-ordered but convex preferences; Separable Banach commodity spaces; Partially ordered but non-convex preferences; Measure space of agents; Discretization of measurable correspondences; C62
• ISSN: 0304-4068; 1873-1538
• DOI: 10.1016/S0304-4068(03)00004-1

The purpose of this paper is to provide an existence result of equilibria for economies with a measure space of agents, a non-trivial production sector and an infinite dimensional commodity space. The commodity space is modeled by an ordered separable Banach space whose positive cone has a non-empty interior. The discretization approach proposed in this paper, allows us to extend the existence results in Khan and Yannelis [Equilibrium in markets with a continuum of agents and commodities. In: Khan, M.A., Yannelis, N.C. (Eds.), Equilibrium Theory in Infinite Dimensional Spaces. Springer, Berlin, 1991] and Podczeck [Economic Theory 9 (1997) 585] to economies with a non-trivial production sector and with possibly non-ordered but convex preferences as well as partially ordered (possibly incomplete) but non-convex preferences.