Applied Mathematics
Volume 4, Issue 8 (August 2013)
ISSN Print: 2152-7385 ISSN Online: 2152-7393
Google-based Impact Factor: 0.58 Citations
The Catastrophe Map of a Two Period Production Model with Uncertainty ()
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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.
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