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The Catastrophe Map of a Two Period Production Model with Uncertainty
Department of Statistics, University College London, London, UK;Department of Mathematics, University of Sussex, East Sussex, UK
- 1 Department of Statistics, University College London, London, UK;Department of Mathematics, University of Sussex, East Sussex, UK
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Abstract
This paper shows existence and efficiency of equilibria of a two period production model with uncertainty as a consequence of the catastrophe map being smooth and proper. Its inverse mapping defines a finite covering implying finiteness of equilibria. Beyond the extraction of local equilibrium information of the model, the catastrophe map renders itself well for a global study of the equilibrium set. It is shown that the equilibrium set has the structure of a smooth submanifold of the Euclidean space which is diffeomorphic to the sphere implying connectedness, simple connectedness, and contractibility.
KeywordsDifferential TopologylGeneral EquilibriumUncertaintyProduction
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