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 = 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.
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References
P.M.C. de Oliveira, Europhys. Lett. 119, 40007 (2017) and references therein
M. Levy, J. Econ. Theory 110, 42 (2003)
J.-P. Bouchaud, M. Mézard, Physica A 282, 536 (2000)
P.M.C. de Oliveira, Physica A 537, 122588 (2020)
C.N. Yang, Phys. Rev. 85, 808 (1952)
D.B. Abraham, Phys. Lett. A 43, 163 (1973)
J.R.L. de Almeida, D.J. Thouless, J. Phys. A 11, 983 (1978)
J.R.L. de Almeida, R.C. Jones, J.M. Kosterlitz, D.J. Thouless, J. Phys. C 11, L871 (1978)
D. Sherrington, S. Kirkpatrick, Phys. Rev. Lett. 35, 1972 (1975)
S. Kirkpatrick, D. Sherrington, Phys. Rev. B 17, 4384 (1978)
M. Mézard, G. Parisi, M. Virasoro,Spin Glass Theory and Beyond (World Scientific, Singapore 1987)
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de Oliveira, P.M.C. Investment/taxation/redistribution model criticality. Eur. Phys. J. B 93, 196 (2020). https://doi.org/10.1140/epjb/e2020-10308-x
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DOI: https://doi.org/10.1140/epjb/e2020-10308-x