An Economic Model of Coupled Exponential Maps

TL;DR

This paper develops an economic model using coupled exponential maps to analyze how local interactions influence wealth distribution and statistical behaviors like Pareto or Boltzmann-Gibbs regimes.

Contribution

It introduces a novel coupled map model with local interactions that can reproduce different statistical regimes in economic systems.

Findings

System exhibits Pareto and Boltzmann-Gibbs behaviors depending on parameters

Regions of parameter space for different statistical behaviors are identified

Mean wealth, standard deviation, and Gini coefficient are computed

Abstract

In this work, an ensemble of economic interacting agents is considered. The agents are arranged in a linear array where only local couplings are allowed. The deterministic dynamics of each agent is given by a map. This map is expressed by two factors. The first one is a linear term that models the expansion of the agent's economy and that is controlled by the {\it growth capacity parameter}. The second one is an inhibition exponential term that is regulated by the {\it local environmental pressure}. Depending on the parameter setting, the system can display Pareto or Boltzmann-Gibbs behavior in the asymptotic dynamical regime. The regions of parameter space where the system exhibits one of these two statistical behaviors are delimited. Other properties of the system, such as the mean wealth, the standard deviation and the Gini coefficient, are also calculated.