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In search of a new economic model determined by logistic growth

Part of: Partial differential equations on manifolds; differential operators Variational problems in infinite-dimensional spaces Mathematical economics

Published online by Cambridge University Press:  27 March 2019

R. G. SMIRNOV  and
K. WANG
R. G. SMIRNOV*
Affiliation:
Department of Mathematics and Statistics, Dalhousie University, Halifax, Nova Scotia, B3H 3J5, Canada e-mails: Roman.Smirnov@dal.ca; kunpengwang@dal.ca
K. WANG
Affiliation:
Department of Mathematics and Statistics, Dalhousie University, Halifax, Nova Scotia, B3H 3J5, Canada e-mails: Roman.Smirnov@dal.ca; kunpengwang@dal.ca
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Abstract

In this paper, we extend the work by Sato devoted to the development of economic growth models within the framework of the Lie group theory. We propose a new growth model based on the assumption of logistic growth in factors and derive the corresponding production functions, as well as a compatible notion of wage share. In the process, it is shown that the new functions compare reasonably well against relevant economic data. The corresponding problem of maximisation of profit under conditions of perfect competition is solved with the aid of one of these functions. In addition, it is explained in reasonably rigorous mathematical terms why Bowley’s law no longer holds true in the post-1960 data.

Keywords

Growth modelsgroup actionsinvariance and symmetry propertiesmathematical modelling in economicsproduction functions

MSC classification

Primary: 58E40: Group actions
Secondary: 58J70: Invariance and symmetry properties 91B62: Growth models
Type
Papers
Information
European Journal of Applied Mathematics , Volume 31 , Issue 2 , April 2020 , pp. 339 - 368
Copyright
© Cambridge University Press 2019 

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