Regular Article

Investment/taxation/redistribution model criticality

¹ Instituto de Física, Universidade Federal Fluminense, Niterói, RJ 24210-340, Brazil
² Instituto Nacional de Ciência e Tecnologia – Sistemas Complexos, Rio de Janeiro, Brazil

^a e-mail: pmco@if.uff.br

Received: 20 June 2020
Received in final form: 26 August 2020
Accepted: 8 September 2020
Published online: 12 October 2020

Abstract

An agent model with annual wealth investment and taxation presents a critical phase transition when one crosses the frontier regressive/progressive taxation. For the regressive case the final destiny of the society is a collapsed configuration in which all population wealth eventually remains in hands of a single agent, an absorbing state spontaneously breaking the symmetry among agents. For progressive taxation, the dynamic process continues forever with fluctuating wealths distributed among all agents; symmetry is not broken. The order parameter is the average m = −⟨logw₁⟩, where w₁ is the wealth share of the richest agent, vanishing at the collapsed phase. A parameter p controls the taxation progressiveness (p > 0) or regressiveness (p < 0) and plays the same role of the temperature in traditional, equilibrium phase transitions, p = p_c = 0 being the critical transition point. Also, a given fraction of the total taxes paid by the population is uniformly redistributed among all agents, this procedure playing the same role of a uniform external field h in equilibrium phase transitions. Here, the transition criticality of the order parameter m as a function of p and h is studied in detail.