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The Equilibrium ManifoldPostmodern Developments in the Theory of General Economic Equilibrium$
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Yves Balasko

Print publication date: 2009

Print ISBN-13: 9780262026543

Published to MIT Press Scholarship Online: August 2013

DOI: 10.7551/mitpress/9780262026543.001.0001

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The Equilibrium Manifold and the Natural Projection

The Equilibrium Manifold and the Natural Projection

Chapter:
(p.20) (p.21) 2 The Equilibrium Manifold and the Natural Projection
Source:
The Equilibrium Manifold
Author(s):

Yves Balasko

Publisher:
The MIT Press
DOI:10.7551/mitpress/9780262026543.003.0039

This chapter introduces the concept of the equilibrium manifold as a tool for the study of properties that might not be satisfied by all equilibria. The equilibrium manifold leads to the related concept of natural projection, a map from the equilibrium manifold into the space of economies. It then shows that the natural projection is smooth and proper, which suffices for this map to define a structure that is known in mathematics as a ramified covering. The results of Debreu (1970) then become straightforward consequences of this structure.

Keywords:   equilibrium manifold, natural projection, economies, ramified covering

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