Abstract
We discuss a framework for the microscopic modelling of taxation and redistribution processes in a closed trading market society. For a prototype model and some variants of it, we examine the emergence of income distribution curves which exhibit “fat” power-law tails as the real world ones. We also incorporate tax evasion into the models and we investigate, in particular, its effect on the income profiles. Our findings are in agreement with the expectation that a fair fiscal policy and individual correctness are effective tools towards the overcoming of social inequalities.
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Notes
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1 The text of the conference can be found under the title “The Relations of Applied Mathematics” e.g. in the volume Physics for a New Century. Papers presented at the 1904 St. Louis Congress, edited by Katherine Russell Sopka, Tomash Publishers/Amer. Inst. of Physics (1986), pp. 267–279.
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2 As will be clear in the sequel, we consider here also interactions with a nonlinear adaptive nature. Moreover, a single interaction does not lead here to a change of class of individuals as was the case in [5].
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3 The reason why individuals of the n-th class constitute an exception is a technical one: if an individual of the n-th class would receive some money, the possibility would arise for him to advance to a higher class, which is impossible.
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4 Since the number of individuals is constant in time and only a finite number of income classes is scheduled, if a tail is expected in the asymptotic distribution, the global income cannot be too high.
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5 We are taking into account also other evasion forms in work in progress.
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Bertotti, M.L., Modanese, G. (2014). Mathematical Models for Socio-economic Problems. In: Celletti, A., Locatelli, U., Ruggeri, T., Strickland, E. (eds) Mathematical Models and Methods for Planet Earth. Springer INdAM Series, vol 6. Springer, Cham. https://doi.org/10.1007/978-3-319-02657-2_10
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