Discrete kinetic models of complex socio-economic systems
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A major challenge for the theory of complex systems is the explanation of global features emerging from a whole of microscopic interactions. In socio-economic systems for example a large number of direct and indirect economic interactions occur between individuals, leading to important observable collective features, like the income distribution, the Gini index etc. We present here a class of discrete kinetic models (possibly equipped with a network structure) suitable for the description of micro-processes of money exchange, taxation and redistribution in a market society. We report recent results on issues like means-tested welfare policies, tax evasion and the effects of taxpayer audits, social mobility and economic inequality. Two examples of our findings are as follows. 1) Investigating the effects that different fiscal policies and differently weighted policies have on the long-run income distributions, we find that a policy of “taxing the rich much more than the poor" is not only less efficient than “cutting the welfare for the rich", but also leads to a reduction in the total tax revenue. It therefore avoids potentially painful cuts in the government budget. 2) Exploiting the structure of the differential equations, which involve several transition probabilities for the passage from an income class to another, we introduce a measure of social mobility. Together with the Gini index, this measure serves as a tool to explore the correlation between economic inequality and social mobility. In agreement with what is observed in real world situations the correlation turns out to be clearly negative: a lower mobility corresponds to a higher inequality.