In this paper, we consider a simple kinetic model of economy involving both exchanges between agents and speculative trading. We show that the kinetic model admits non trivial quasi-stationary states with power law tails of Pareto type. In order to do this we consider a suitable asymptotic limit of the model yielding a Fokker-Planck equation for the distribution of wealth among individuals. For this equation the stationary state can be easily derived and shows a Pareto power law tail. Numerical results confirm the previous analysis.
Publié le : 2004-12-21
Classification:
wealth and income distributions,
Fokker Planck model,
Monte Carlo simulations,
Pareto distribution,
Econophysics,
Boltzmann equation,
[MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP],
[SHS.ECO]Humanities and Social Sciences/Economies and finances
@article{hal-00003648,
author = {Cordier, St\'ephane and Pareschi, Lorenzo and Toscani, Giuseppe},
title = {On a kinetic model for a simple market economy},
journal = {HAL},
volume = {2004},
number = {0},
year = {2004},
language = {en},
url = {http://dml.mathdoc.fr/item/hal-00003648}
}
Cordier, Stéphane; Pareschi, Lorenzo; Toscani, Giuseppe. On a kinetic model for a simple market economy. HAL, Tome 2004 (2004) no. 0, . http://gdmltest.u-ga.fr/item/hal-00003648/