In search of a new economic model determined by logistic growth

TL;DR

This paper develops a new economic growth model based on logistic growth assumptions, deriving novel production functions and wage share concepts, and analyzing their empirical validity and implications for profit maximization and Bowley's law.

Contribution

It introduces a logistic growth-based economic model extending Sato's work, with new functions and insights into wage share and Bowley's law.

Findings

New production functions fit economic data reasonably well

Profit maximization problem is solved using the new functions

Bowley's law no longer holds in post-1960 data

Abstract

In this paper we extend the work by Ryuzo 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. It is employed to derive new production functions and introduce a new 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 maximization 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 post-1960 data.