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Taxation and Redistribution against Inequality: A Mathematical Model

Reducing inequality is a tremendously important sustainable development goal. Albeit providing stylised frames for modelling, also mathematics can contribute to understanding and explaining the emergence of collective patterns in complex socio-economic systems. It can then effectively help to identify actions and measures to be taken and support policy-makers towards adoption of conceivable welfare measures aimed at halting the growth of inequality. Based on these assumptions, we here discuss some variants of a mathematical “micro-to-macro” model for the dynamics of taxation and redistribution processes in a closed trading market society. The model has an exploratory character resulting from possible tuning of various parameters involved: through its analysis, one can foresee the consequences on the long-run income distributions of different fiscal policies and differently weighted welfare policies, interventions, and subsidy provision, as well as the impact of the extent of tax evasion. In short, the model shows that in the long term redistributive policy results in a lower level of economic inequality in society.