Abstract
In our recently proposed stochastic version of discretized kinetic theory, the exchange of wealth in a society is modelled through a large system of Langevin equations. The deterministic part of the equations is based on non-linear transition probabilities between income classes. The noise terms can be additive, multiplicative or mixed, both with white or Ornstein–Uhlenbeck spectrum. The most important measured correlations are those between Gini inequality index G and social mobility M, between total income and G, and between M and total income. We describe numerical results concerning these correlations and a quantity which gives average stochastic deviations from the equilibrium solutions in dependence on the noise amplitude.
Highlights
Wealth exchange models [1,2] are used in the context of economic theory and econophysics [3,4] to describe in a simplified way the individual economic interactions occurring in a society
Fluctuations should be taken into account in the models. This is in some sense done in economic agent-based models [5,6] which are essentially computer simulations of economic systems based on a population sample
The transitions are the consequence of economic interactions which occur with certain probabilities defined by the model and depend on several parameters
Summary
Wealth exchange models [1,2] are used in the context of economic theory and econophysics [3,4] to describe in a simplified way the individual economic interactions occurring in a society They allow to predict emerging collective features like the income distribution, the Gini index or the Pareto exponent. We present extensive statistical results, almost all relative to a stochastic model with multiplicative noise They concern quantities which are of major interest for real world economies and whose values today constitute a widespread object of concern [13,14].
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