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The Catastrophe Map of a Two Period Production Model with Uncertainty

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DOI: 10.4236/am.2013.48A016    3,719 Downloads   5,054 Views   Citations

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.

Conflicts of Interest

The authors declare no conflicts of interest.

Cite this paper

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.

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