Economic Equilibrium under Deformation of the Economy.
STANFORD UNIV CALIF DEPT OF OPERATIONS RESEARCH
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A description of economic deformations and the computation of equilibrium paths is the central theme of this study. A general mathematical framework for modeling economies under deformation is developed by expanding Herbert Scarfs original activity analysis formulation to include uncountable unit activity sets, unbounded multi-valued demand correspondences, and tax and revenue systems similar to those introduced by John Shoven and John Whalley. Deformations of virtually all economic constructs are allowed in this general model. The computation of equilibrium paths is accomplished by a simplicial pivot algorithm designed along the lines of the homotopy-type fixed point technoiques pioneered by Curtis Eaves. The dimension normally used to refine piecewise linear approximations now serves as the index of the economic deformation. To make this approach viable in practice, a new family of triangulations of Euclidean space is fashioned out of two conventional triangulations invented by Michael Todd. The geometry of these triangulations can be dynamically altered by the algorithm as it attempts to maintain uniform approximation error along the equilibrium path. The economic model and computational algorithm are translated into a set of computer routines which generate explicity numerical approximations to equilibrium paths for a variety of examples.
- Economics and Cost Analysis
- Theoretical Mathematics