Production equilibria

This paper studies production economies in a commodity space that is an ordered locally convex space. We establish a general theorem on the existence of equilibrium without requiring that the commodity space or its dual be a vector lattice. Such commodity spaces arise in models of portfolio trading...

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Bibliographic Details
Published in:Journal of mathematical economics 2006-08, Vol.42 (4), p.406-421
Main Authors: Aliprantis, Charalambos D., Florenzano, Monique, Tourky, Rabee
Format: Article
Language:English
Subjects:
Commodities
Commodity markets
Economic equilibrium
Economics and Finance
Edgeworth equilibrium
Equilibrium
Functional Analysis
Humanities and Social Sciences
Lattice theory
Mathematical economics
Mathematics
Production economics
Production economies
Properness
Riesz–Kantorovich functional
Studies
Sup-convolution
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Summary:This paper studies production economies in a commodity space that is an ordered locally convex space. We establish a general theorem on the existence of equilibrium without requiring that the commodity space or its dual be a vector lattice. Such commodity spaces arise in models of portfolio trading where the absence of some option usually means the absence of a vector lattice structure. The conditions on preferences and production sets are at least as general as those imposed in the literature dealing with vector lattice commodity spaces. The main assumption on the order structure is that the Riesz–Kantorovich functionals satisfy a uniform properness condition that can be formulated in terms of a duality property that is readily checked. This condition is satisfied in a vector lattice commodity space but there are many examples of other commodity spaces that satisfy the condition, which are not vector lattices, have no order unit, and do not have either the decomposition property or its approximate versions.
ISSN:0304-4068
1873-1538
DOI:10.1016/j.jmateco.2006.04.006