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Implementing a Generalized Cobb Model for Production Functions

Authors:
Alina Andreica
Florina Covaci

Keywords: Cobb-Douglas model; generalized production functions; symbolic modelling; Buchberger algorithm; generic implementations

Abstract:
The paper proposes an extension of Cobb-Douglas model for production functions applicable in multi-product and regional contexts and a combined symbolic & numeric method for solving the system. In this respect, we propose a new application of Buchberger’s algorithm for computing Gröbner basis in simplifying the polynomial set that is obtained by modelling economic production systems. We present our Mathematica categorical implementation of Gröbner basis algorithm that can be applied for performing necessary computations. We apply Gröbner basis algorithm for some specific production function cases proposed in the economic literature and discuss the results. We consider that Gröbner basis algorithm is important in processing (according to various variable orderings) the polynomial set that is constructed and in synthesizing the most important economic characteristics taken into account by the model. Further on, numeric methods can be applied if necessary. We also note the importance of generic implementations of Buchberger’s algorithm, which can be easy adapted for various domains.

Pages: 55 to 60

Copyright: Copyright (c) IARIA, 2013

Publication date: September 29, 2013

Published in: conference

ISSN: 2308-4499

ISBN: 978-1-61208-290-5

Location: Porto, Portugal

Dates: from September 29, 2013 to October 3, 2013