The Catastrophe Map of a Two Period Production Model with Uncertainty

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.

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P. Stiefenhofer, "The Catastrophe Map of a Two Period Production Model with Uncertainty," Applied Mathematics, Vol. 4 No. 8A, 2013, pp. 114-121. doi: 10.4236/am.2013.48A016.

Conflicts of Interest

The authors declare no conflicts of interest.

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