Abstract

Solution of an Economic Model using Dynamic Deformation Procedure

Author(s): R.S. Patel and J.K. Verma

Since most of the economic problems are related to the optimization problems, therefore the tech-niques of the Dantzig[1] can be applied, to all such economic problems in which these problems corresponds to linear form under some constraints conditions. Many nonlinear variety of economic problems are solved by the non-linear techniquesbased on the quadratic programming method under the Kuhn-Tucker[10] conditions.Scarf developed a finite algorithm based on the subdivision of the simplex into finite subsets called primitivesets, then utilizing the Lemke complementarity pivoting procedure he provided the first constructive proof to Brouwer's fixed point theorem. Scarf's work attracted many others researchers. Thereafter, many important refinement and extensions to his algorithm were developed with the help of triangulation of simplex carried by Kuhn[7], Todd[21], Eaves [2] and Merril [16] etc. However, algorithm developed by Freudenthal[5], Kuhn[7,8],Todd [21] etc. were the extension of the Scarf's algo-rithm to have better approximation of the fixed point of a continuous mapping from a simplex into itself. Whereas Merril[16], Eaves[2], Eaves and Saigal [3] etc. developed several algorithms for points to set mapping or semi con-tinuous mapping.In this paper we have tried to give adynamic manifold construction process to find the solution of different type of economic problems.

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