Stability of Pareto-Zipf Law in Non-Stationary Economies

TL;DR

This paper demonstrates that Pareto-Zipf power laws in wealth and market returns remain stable in non-stationary economies modeled by generalized Lotka-Volterra systems, with an invariant exponent around 1.4.

Contribution

It introduces a generalized Lotka-Volterra model showing the stability of Pareto-Zipf laws in dynamic economic systems with a fixed exponent.

Findings

Power laws in wealth and returns are invariant to total wealth changes.

The exponent alpha is approximately 1.4, reflecting social and biological constraints.

The model applies to non-stationary, stochastic economic systems.

Abstract

Generalized Lotka-Volterra (GLV) models extending the (70 year old) logistic equation to stochastic systems consisting of a multitude of competing auto-catalytic components lead to power distribution laws of the (100 year old) Pareto-Zipf type. In particular, when applied to economic systems, GLV leads to power laws in the relative individual wealth distribution and in the market returns. These power laws and their exponent alpha are invariant to arbitrary variations in the total wealth of the system and to other endogenous and exogenous factors. The measured value of the exponent alpha = 1.4 is related to built-in human social and biological constraints.