In this paper, we introduce a statistical equilibrium model to describe the properties of a large collection of competitive interacting firms. The interaction mechanism is essentially based on the notion of classical competition, i.e. the tendency for competition to equalize profit rates across and within sectors.

The classical competition framework essentially describes a negative feedback mechanism: the sectors or industries which generate above-average profits attract more capital than the other sectors. The concentration of capital raises output and lowers prices, ultimately giving an incentive to leave the sector, thereby increasing profit rates for the remaining firms. The continuing shocks in terms of technological innovations and changing tastes, for instance, render a complete elimination of differences in profits among the sectors a very improbable event, even in the long run.

The detailed specification of the interaction mechanism among competitive firms is a demanding task. We take the position that this complex environment might be described in the context of a statistical equilibrium model. Within the concept of classical competition, the incessant movement of capital to equalize profit rates might be decomposed into two aspects: a measure of central tendency towards an average profit rate, and a measure of dispersion around the average, which accounts for the complex movements of capital and the interactions among firms. Essentially, the system of competitive firms is described using two macroscopic constrains: the existence of a profit rate, m, to which the economy as a whole tends to converge, and a general measure of dispersion, given by the a-th central moment around m, E[|(x-m)/sigma|^a] = 1, which accounts for the non-elimination of differences in profit rates among firms, due to the complexity of the competitive environment.

The model predicts a Subbotin or exponential power distribution of profit rates. The equilibrium distribution is derived from a properly constructed diffusion process, which might be used to describe the dynamics of the profit rates, and not just their equilibrium properties. In the paper we developed such theory, which leads to a simple stochastic process of competitive firm dynamics.

• Legal notice:
  

  Copyright (c) Pielaszek Research, all rights reserved.
  The above materials, including auxiliary resources, are subject to Publisher's copyright and the Author(s) intellectual rights. Without limiting Author(s) rights under respective Copyright Transfer Agreement, no part of the above documents may be reproduced without the express written permission of Pielaszek Research, the Publisher. Express permission from the Author(s) is required to use the above materials for academic purposes, such as lectures or scientific presentations.
  In every case, proper references including Author(s) name(s) and URL of this webpage: https://science24.com/paper/14790 must be provided.

1. System size and network effects in a probabilistic herding model 
2. Hierarchical networks effects in a financial herding model