dorsal/arxiv
View SchemaKinetic theory models for the distribution of wealth: power law from overlap of exponentials
| Authors | Marco Patriarca, Anirban Chakraborti, Kimmo Kaski, Guido Germano |
|---|---|
| Categories | |
| ArXiv ID | physics/0504153 |
| URL | https://arxiv.org/abs/physics/0504153 |
| DOI | 10.1007/88-470-0389-X_10 |
| Journal | New Economic Windows 2, 93-110, 2005 |
Abstract
Various multi-agent models of wealth distributions defined by microscopic laws regulating the trades, with or without a saving criterion, are reviewed. We discuss and clarify the equilibrium properties of the model with constant global saving propensity, resulting in Gamma distributions, and their equivalence to the Maxwell-Boltzmann kinetic energy distribution for a system of molecules in an effective number of dimensions $D_\lambda$, related to the saving propensity $\lambda$ [M. Patriarca, A. Chakraborti, and K. Kaski, Phys. Rev. E 70 (2004) 016104]. We use these results to analyze the model in which the individual saving propensities of the agents are quenched random variables, and the tail of the equilibrium wealth distribution exhibits a Pareto law $f(x) \propto x^{-\alpha -1}$ with an exponent $\alpha=1$ [A. Chatterjee, B. K. Chakrabarti, and S. S. Manna, Physica Scripta T106 (2003) 367]. Here, we show that the observed Pareto power law can be explained as arising from the overlap of the Maxwell-Boltzmann distributions associated to the various agents, which reach an equilibrium state characterized by their individual Gamma distributions. We also consider the influence of different types of saving propensity distributions on the equilibrium state.
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"abstract": "Various multi-agent models of wealth distributions defined by microscopic\nlaws regulating the trades, with or without a saving criterion, are reviewed.\nWe discuss and clarify the equilibrium properties of the model with constant\nglobal saving propensity, resulting in Gamma distributions, and their\nequivalence to the Maxwell-Boltzmann kinetic energy distribution for a system\nof molecules in an effective number of dimensions $D_\\lambda$, related to the\nsaving propensity $\\lambda$ [M. Patriarca, A. Chakraborti, and K. Kaski, Phys.\nRev. E 70 (2004) 016104]. We use these results to analyze the model in which\nthe individual saving propensities of the agents are quenched random variables,\nand the tail of the equilibrium wealth distribution exhibits a Pareto law $f(x)\n\\propto x^{-\\alpha -1}$ with an exponent $\\alpha=1$ [A. Chatterjee, B. K.\nChakrabarti, and S. S. Manna, Physica Scripta T106 (2003) 367]. Here, we show\nthat the observed Pareto power law can be explained as arising from the overlap\nof the Maxwell-Boltzmann distributions associated to the various agents, which\nreach an equilibrium state characterized by their individual Gamma\ndistributions. We also consider the influence of different types of saving\npropensity distributions on the equilibrium state.",
"arxiv_id": "physics/0504153",
"authors": [
"Marco Patriarca",
"Anirban Chakraborti",
"Kimmo Kaski",
"Guido Germano"
],
"categories": [
"physics.soc-ph",
"q-fin.GN"
],
"doi": "10.1007/88-470-0389-X_10",
"journal_ref": "New Economic Windows 2, 93-110, 2005",
"title": "Kinetic theory models for the distribution of wealth: power law from overlap of exponentials",
"url": "https://arxiv.org/abs/physics/0504153"
},
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