Investment/taxation/redistribution model criticality
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THE EUROPEAN PHYSICAL JOURNAL B
Regular Article
Investment/taxation/redistribution model criticality Paulo Murilo Castro de Oliveira 1,2,a 1 2
Instituto de F´ısica, Universidade Federal Fluminense, Niter´ oi, RJ 24210-340, Brazil Instituto Nacional de Ciˆencia e Tecnologia – Sistemas Complexos, Rio de Janeiro, Brazil Received 20 June 2020 / Received in final form 26 August 2020 / Accepted 8 September 2020 Published online 12 October 2020 c EDP Sciences / Societ`
a Italiana di Fisica / Springer-Verlag GmbH Germany, part of Springer Nature, 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 = −h log w1 i, 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 = pc = 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.
1 Introduction In society, individuals invest their working potential and/or capital. They also pay taxes. As a result, their wealths fluctuate in time. Taxation rule is progressive when the tax rate is larger for rich than poor people, otherwise it is regressive. In [1], the evolution of such a society is modeled applying the same rule to all individuals. Hereafter, we refer only to this computer model, not social, political or economic opinions. The reader of course can interpret the results within his/her economic point of view, or face the vast Economics literature on the subject, but this is not the purpose here. The purpose is restricted to the analysis of the phase transition exhibited by the model, according to the traditional research field of critical phenomena. In the model, regressive taxation breaks the symmetry among individuals, one of them eventually owns alone the whole population wealth. The economic evolution ceases. Progressive taxation, on the other hand, preserves forever the economic time evolution, any poor individual can become rich or vice-versa. Progressive taxation also avoids large inequalities. Different ingredients can be included in the model, in order to test different properties under the Economics point of view. For instance saturation of
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