In search of a new economic model determined by logistic growth

Abstract

In this paper 1 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 impact of the economy financialization on the level of economic development of the associate EU member states

“…In particular, Smirnov and Wang (2018) proposed a new (logistic) growth model, which is anatural continuation of previous research on economic growth.…”

Corruption and money laundering: You scratch my back, i’ll scratch yours

“…In other words, market saturation triggers maximum capital capacity. Empirically (Aoki & Yoshikawa, 2002;Girdzijauskas et al, 2012;Smirnov & Wang, 2019), researchers have shown that by extending the Sato exponential growth model, it is possible to derive a logistic model to replace the traditional Cobb-Douglas production function, that better fits the data.…”

The Hamiltonian approach to the problem of derivation of production functions in economic growth theory

“…Recall, Sato [3] (see also pp. 4-5 in [5]) employed Lie group theory methods to derive the Cobb-Douglas function as an invariant of a one parameter group action determined by exponential growth in labor, capital, and production. His other goal was to resolve the Solow-Stigler controversy [3,18] that can be described as the observation that the increase of output is not proportional to the growth of labor and capital in the production function, which, in turn, implies that the technical progress should also be taken into the account in the development of any growth model.…”

“…To show the workings of the Hamiltonian formalism in the study of technical progress and production functions in economics, let us recall first that symmetry methods have already proven to be a very powerful tool in this context, which was demonstrated by Sato [3] (see also Sato and Ramachandran [4], the relevant references in [5], and, for example, Perets and Yashiv [6]). In particular, the authors in [5] have extended Sato's approach to derive a new family of production functions under the assumption of logistic growth in factors. It is our contention that the theory can be further developed at this point by recasting its setting within a Hamiltonian framework.…”

“…It is our contention that the theory can be further developed at this point by recasting its setting within a Hamiltonian framework. More specifically, we will redefine the existing models [3,5] and introduce a new one by presenting them as special cases of the general n-dimensional Lotka-Volterra model in population dynamics (see, for example, Kerner [7] and the relevant references therein). This model is given by the following formula:…”