Cones with Semi-interior Points and Equilibrium

Achille Basile (), Maria Graziano, Maria Papadaki () and Ioannis A. Polyrakis ()
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Maria Papadaki: National Technical University of Athens
Ioannis A. Polyrakis: National Technical University of Athens

CSEF Working Papers from Centre for Studies in Economics and Finance (CSEF), University of Naples, Italy

Abstract: We study exchange economies in ordered normed spaces (X, ||.||) where agents have possibly different consumption sets. We define the notion of semi-interior point of the positive cone X+ of X, a notion weaker than the one of interior point. We prove that if X+ has semi-interior points, then the second welfare theorem holds true and a quasi equilibrium allocation exists. In both cases the supporting price is continuous with respect to a new norm |||.||| on X which is strongly related with the initial norm and the ordering, and in some sense can be considered as an extension of the norm adopted in classical equilibrium models. Many examples of cones in normed and Banach spaces with semi-interior points but with empty interior are provided, showing that this class of cones is a rich one. We also consider spaces ordered by strongly reflexive cones where we prove the existence of a quasi equilibrium without the closedness condition (i.e. without the condition that the utility space is closed). The results in the case of semi-interior points derive from those concerning the case of ordering cones with nonempty interior.

Keywords: cones; equilibrium; ordered spaces; second welfare theorem; strongly reflexive cones (search for similar items in EconPapers)
JEL-codes: C62 D51 (search for similar items in EconPapers)
Date: 2016-05-17
New Economics Papers: this item is included in nep-upt
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Citations: View citations in EconPapers (1)

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Related works:
Journal Article: Cones with semi-interior points and equilibrium (2017)
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