The Marginal Pricing Rule in Economies with Infinitely Many Commodities

The Marginal Pricing Rule in Economies with Infinitely Many Commodities Clarke's normal cone appears as the right tool to define the marginal pricing rule in finite dimensional commodity space since it allows to consider in the same framework convex, smooth as well as nonsmooth nonconvex production sets. Furthermore it has nice continuity and convexity properties. But it is not well adapted for economies with infinitely many commodities since it does satisfy minimal continuity properties. In this paper, we propose an alternative definition of the marginal pricing rule. It allows us to prove the second welfare theorem and the existence of marginal pricing equilibria for economies with several producers under assumptions similar to the one used for economies with a finite set of commodities. Our approach is sufficiently general to take into account the convex and the smooth cases for which our definition of the marginal pricing rule coincides with the one given by the Clarke's normal cone or the normal cone of convex analysis. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Positivity Springer Journals

The Marginal Pricing Rule in Economies with Infinitely Many Commodities

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Publisher
Springer Journals
Copyright
Copyright © 2002 by Kluwer Academic Publishers
Subject
Mathematics; Fourier Analysis; Operator Theory; Potential Theory; Calculus of Variations and Optimal Control; Optimization; Econometrics
ISSN
1385-1292
eISSN
1572-9281
D.O.I.
10.1023/A:1020253122955
Publisher site
See Article on Publisher Site

Abstract

Clarke's normal cone appears as the right tool to define the marginal pricing rule in finite dimensional commodity space since it allows to consider in the same framework convex, smooth as well as nonsmooth nonconvex production sets. Furthermore it has nice continuity and convexity properties. But it is not well adapted for economies with infinitely many commodities since it does satisfy minimal continuity properties. In this paper, we propose an alternative definition of the marginal pricing rule. It allows us to prove the second welfare theorem and the existence of marginal pricing equilibria for economies with several producers under assumptions similar to the one used for economies with a finite set of commodities. Our approach is sufficiently general to take into account the convex and the smooth cases for which our definition of the marginal pricing rule coincides with the one given by the Clarke's normal cone or the normal cone of convex analysis.

Journal

PositivitySpringer Journals

Published: Oct 12, 2004

References

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