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Kinetic models of conservative economies with wealth redistribution. (English) Zbl 1188.91115

Kinetic models for wealth distribution in a simple market economy are discussed. The models are based on the equation with taxation/redistribution \[ \frac{\partial f(v, t)}{\partial t}=Q_\epsilon(f, f)(v,t)+R^\epsilon_\chi(f)(v, t), \] where \(f=f(v, t)\) is the distribution of wealth \(v\in\mathbb{R}_+\) at time \(t\geq 0\), the bilinear operator \(Q_\epsilon\) accounts for taxation in trades, the differential operator \(R^\epsilon_\chi\) accounts for redistribution and (possible) additional taxation.
It is shown that in general the redistribution is able to modify the Pareto index, and that this modification can be quantified in terms of the redistribution operator.

MSC:

91B60 Trade models
82C40 Kinetic theory of gases in time-dependent statistical mechanics
35B40 Asymptotic behavior of solutions to PDEs
91B80 Applications of statistical and quantum mechanics to economics (econophysics)
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