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.

Graphical abstract

中文翻译：

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投资/税收/再分配模型的重要性

摘要

具有年度财富投资和税收的代理模型会在跨界回归/累进税收时出现一个关键的阶段过渡。对于回归的情况，社会的最终命运是一种崩溃的格局，在这种格局中，所有人口的财富最终都掌握在单个代理人手中，这种吸收状态自发地打破了代理人之间的对称性。对于累进税制，动态过程将永远持续进行，所有代理商之间分配的财富会发生波动。对称性没有破坏。阶次参数是平均值m = -log log w ₁，其中w ₁是最富有的代理的财富份额，在崩溃阶段消失。参数p控制税收累进性（p > 0）或回归性（p <0），并且在传统的平衡相变中，温度起着相同的作用，p = p _c = 0是临界转变点。同样，由人口支付的总税收的给定部分在所有主体之间进行统一重新分配，此过程在均衡相变中起着统一外部场h的相同作用。在此，详细研究了阶数参数m随p和h的变化的临界度。

图形概要