In search of a new economic model determined by logistic growth

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...

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Published inEuropean journal of applied mathematics Vol. 31; no. 2; pp. 339 - 368
Main Authors SMIRNOV, R. G., WANG, K.
Format Journal Article
LanguageEnglish
Published Cambridge Cambridge University Press 01.04.2020
Subjects
Applied mathematics
Economic analysis
Economic development
Economic models
Group theory
Growth models
Lie groups
Mathematical analysis
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ISSN0956-7925
1469-4425
DOI10.1017/S0956792519000081

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Summary: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.
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ISSN:0956-7925
1469-4425
DOI:10.1017/S0956792519000081