TITLE:
The Catastrophe Map of a Two Period Production Model with Uncertainty
AUTHORS:
Pascal Stiefenhofer
KEYWORDS:
Differential Topologyl; General Equilibrium; Uncertainty; Production
JOURNAL NAME:
Applied Mathematics,
Vol.4 No.8A,
July
25,
2013
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.