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Market Failures and Equilibria in Banach Lattices: New Tangent and Normal Cones

Jean-Marc Bonnisseau () and Matías Fuentes
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Matías Fuentes: UNSAM - Universidad Nacional de San Martin

Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) from HAL

Abstract: In this paper, we consider an economy with infinitely many commodities and market failures such as increasing returns to scale and external effects or other regarding preferences. The commodity space is a Banach lattice possibly without interior points in the positive cone in order to include most of the relevant commodity spaces in economics. We propose a new definition of the marginal pricing rule through a new tangent cone to the production set at a point of its (non-smooth) boundary. The major contribution is the unification of many previous works with convex or non-convex production sets, smooth or non-smooth, for the competitive equilibria and for the marginal pricing equilibria, with or without external effects, in finite-dimensional spaces as well as in infinite-dimensional spaces. In order to prove the existence of a marginal pricing equilibria, we also provide a suitable properness condition on non-convex technologies to deal with the emptiness of the interior of the positive cone.

Keywords: Marginal pricing rule; Banach lattices; Market failures; Properness; General equilibrium (search for similar items in EconPapers)
Date: 2020-02
Note: View the original document on HAL open archive server: https://halshs.archives-ouvertes.fr/halshs-02344270
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Published in Journal of Optimization Theory and Applications, Springer Verlag, 2020, 184, pp.338-367. ⟨10.1007/s10957-019-01593-w⟩

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Journal Article: Market Failures and Equilibria in Banach Lattices: New Tangent and Normal Cones (2020) Downloads
Working Paper: Market Failures and Equilibria in Banach Lattices: New Tangent and Normal Cones (2020)
Working Paper: Market Failures and Equilibria in Banach Lattices: New Tangent and Normal Cones (2020)
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Persistent link: https://EconPapers.repec.org/RePEc:hal:cesptp:halshs-02344270

DOI: 10.1007/s10957-019-01593-w

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