Inelastically scattering particles and wealth distribution in an open economy

2003/11/30 by Frantisek Slanina, František Slanina · 2 citations
Economics, Econometrics and Finance · Mathematics · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Analogy #Complex Systems and Time Series Analysis #Distribution (mathematics) #Distribution function #Exponent #Function (biology) #Inelastic scattering #Limit (mathematics) #Mathematical analysis #Mathematical physics #Mathematics #Pareto distribution #Physics #Power function #Power law #Quantum mechanics #Scaling #Scattering #Statistical physics #Theoretical and Computational Physics #cond-mat.dis-nn #cond-mat.stat-mech #q-fin.GN

paper · pdf · doi:10.1103/physreve.69.046102

published as Phys. Rev. E 69, 046102 (2004) · 8 pages 5 figures

arxiv created 2003/12/17 · openalex publication_date 2004/04/14 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

Using the analogy with inelastic granular gases we introduce a model for wealth exchange in society. The dynamics is governed by a kinetic equation, which allows for self-similar solutions. The scaling function has a power-law tail, the exponent being given by a transcendental equation. In the limit of continuous trading, a closed form of the wealth distribution is calculated analytically.

Citations

• Wealth condensation in pareto macroeconomies
• Self-similarity in random collision processes
• Statistical mechanics of money: how saving propensity affects its distribution
• Stable equilibrium based on Lévy statistics: Stochastic collision models approach
• From gene families and genera to incomes and internet file sizes: Why power laws are so common in nature
• Emergence of scaling in random networks
• Scaling, multiscaling, and nontrivial exponents in inelastic collision processes
• Stochastic Maps, Wealth Distribution in Random Asset Exchange Models and the Marginal Utility of Relative Wealth
• Statistical mechanics of money
• Nontrivial velocity distributions in inelastic gases
• Multiscaling in inelastic collisions

Cited by

• Central limit theorem for a class of one-dimensional kinetic equations
• Dynamics of three-agent games