A common origin of the power law distributions in models of market and earthquake

TL;DR

This paper demonstrates that power law distributions in both economic and geophysical models originate from a common mechanism involving the asymptotic behavior of log-normal distributions, enhancing understanding across disciplines.

Contribution

It reveals a unified origin of power laws in market and earthquake models, linking their asymptotic forms to the behavior of log-normal distributions.

Findings

Power laws emerge as asymptotic forms of log-normal distributions.

The same generic mechanism underlies power laws in economics and geophysics.

Understanding this origin aids in developing generalized models across fields.

Abstract

We show that there is a common mode of origin for the power laws observed in two different models: (i) the Pareto law for the distribution of money among the agents with random saving propensities in an ideal gas-like market model and (ii) the Gutenberg-Richter law for the distribution of overlaps in a fractal-overlap model for earthquakes. We find that the power laws appear as the asymptotic forms of ever-widening log-normal distributions for the agents' money and the overlap magnitude respectively. The identification of the generic origin of the power laws helps in better understanding and in developing generalized views of phenomena in such diverse areas as economics and geophysics.