Smooth economic analysis for general spaces of commodities

Accinelli, Elvio and Covarrubias, Enrique (2014): Smooth economic analysis for general spaces of commodities.

Abstract

This paper provides an extended framework to study general equilibrium theory with commodity spaces possibly of infinite dimensions. Our approach overcomes some difficulties found in the literature since it allows the study of the equilibrium when consumption sets may have an empty interior. It also overcomes the need for separable utilities or utilities that satisfy quadratic concavity. The results are based on restricting the mathematical notions of open neighborhoods, continuity, and derivatives at a point, to only those directions that lie within the positive cone. We prove in this setting ``directional'' equivalents of the Sard-Smale and Preimage Theorems. With these tools, we define the social equilibrium set and show that it is a directional Banach manifold. Together with a suitable definition of projection map, this framework allows a natural equivalent to infinite dimensions of the ``catastrophic'' approach to general economic equilibrium.

• Item Type: MPRA Paper
• Language: English
• Keywords: determinacy; equilibrium manifold: positive cone
• Subjects: C - Mathematical and Quantitative Methods > C6 - Mathematical Methods ; Programming Models ; Mathematical and Simulation Modeling > C62 - Existence and Stability Conditions of Equilibrium; D - Microeconomics > D5 - General Equilibrium and Disequilibrium > D51 - Exchange and Production Economies; D - Microeconomics > D5 - General Equilibrium and Disequilibrium > D53 - Financial Markets; G - Financial Economics > G1 - General Financial Markets > G12 - Asset Pricing ; Trading Volume ; Bond Interest Rates

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