On a kinetic model for a simple market economy

Stephane Cordier; Lorenzo Pareschi; Giuseppe Toscani

doi:10.1007/s10955-005-5456-0

On a kinetic model for a simple market economy

Stephane Cordier
, Lorenzo Pareschi
, Giuseppe Toscani

Research output: Contribution to journal › Article › peer-review

200 Scopus citations

Abstract

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.

Original language	English
Pages (from-to)	253-277
Number of pages	25
Journal	Journal of Statistical Physics
Volume	120
Issue number	1-2
DOIs	https://doi.org/10.1007/s10955-005-5456-0
State	Published - Jul 2005
Externally published	Yes

Keywords

Boltzmann equation
Econophysics
Pareto distribution
Wealth and income distributions

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10.1007/s10955-005-5456-0

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title = "On a kinetic model for a simple market economy",

abstract = "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.",

keywords = "Boltzmann equation, Econophysics, Pareto distribution, Wealth and income distributions",

author = "Stephane Cordier and Lorenzo Pareschi and Giuseppe Toscani",

note = "Funding Information: The authors acknowledge support from the IHP network HYKE “Hyperbolic and Kinetic Equations: Asymptotics, Numerics, Applications” HPRN-CT-2002-00282 funded by the EC., and from the Italian MIUR, project “Mathematical Problems of Kinetic Theories”. L. Pareschi thanks the Department of Mathematics and Applications, Mathematical Physics of Orleans (MAPMO) for the kind hospitality during his visit. The author thank the anonymous referees, for helpful suggestions and comments who led to a marked improvement of the paper.",

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AU - Cordier, Stephane

AU - Pareschi, Lorenzo

AU - Toscani, Giuseppe

N1 - Funding Information: The authors acknowledge support from the IHP network HYKE “Hyperbolic and Kinetic Equations: Asymptotics, Numerics, Applications” HPRN-CT-2002-00282 funded by the EC., and from the Italian MIUR, project “Mathematical Problems of Kinetic Theories”. L. Pareschi thanks the Department of Mathematics and Applications, Mathematical Physics of Orleans (MAPMO) for the kind hospitality during his visit. The author thank the anonymous referees, for helpful suggestions and comments who led to a marked improvement of the paper.

PY - 2005/7

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N2 - 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.

AB - 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.

KW - Boltzmann equation

KW - Econophysics

KW - Pareto distribution

KW - Wealth and income distributions

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DO - 10.1007/s10955-005-5456-0

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VL - 120

SP - 253

EP - 277

JO - Journal of Statistical Physics

JF - Journal of Statistical Physics

IS - 1-2

ER -

On a kinetic model for a simple market economy

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Keywords

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