Pareto Law in a Kinetic Model of Market with Random Saving Propensity

By Arnab Chatterjee, Bikas K. Chakrabarti, S. S. Manna. 2003

286 citations recorded by the source corpus.

We have numerically simulated the ideal-gas models of trading markets, where each agent is identified with a gas molecule and each trading as an elastic or money-conserving two-body collision. Unlike in the ideal gas, we introduce (quenched) saving propensity of the agents, distributed widely between the agents (0⩽λ<1). The system remarkably self-organizes to a critical Pareto distribution of money P(m)∼m−(ν+1) with ν≃1. We analyze the robustness (universality) of the distribution in the model. We also argue that although the fractional saving ingredient is a bit unnatural one in the context of gas models, our model is the simplest so far, showing self-organized criticality, and combines two century-old distributions: Gibbs (1901) and Pareto (1897) distributions.

Subfields: Condensed Matter Physics, Economics and Econometrics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/8bde315d73abb9fad4ac01f1d539b0948f7e738a

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Citations in the corpus

Econophysics: Empirical facts and agent-based models (2009, unknown): “…that the marginal distribution f(x) can be resolved as an overlap of individual Gamma distributions with λ-dependent parameters; furthermore, the mode and the average value of the distributions fi(x) both diverge for λ→ 1 as 〈x(λ)〉 ∼ 1/(1−λ) (Chatterjee et al. (2004); Patriarca et al. (2005)).”
The Inequality Process as a wealth maximizing process (2005, methodology): “Conclusions But for their respective stochastic drivers of wealth exchange between particles the One Parameter Inequality Process (OPIP) (2a,b) and [2-23] and the Saved Wealth Model (SWM) of Chakraborti and Chakrabarti (1a,b) and [24-30] are isomorphic stochastic binary interacting particle systems.”
Econophysics review: II. Agent-based models (2011, unknown): “The figure confirms the importance of agents with close to 1 for producing a power-law probability distribution (Chatterjee et al. 2004, Heinsalu et al. 2009).”
Fokker–Planck equations in the modeling of socio-economic phenomena (2017, background): “Economics is, by far, one of the human behaviors to which methods borrowed from statistical mechanics for particle systems have been systematically applied[16, 29, 30, 31, 32, 36, 42, 63, 67, 90] (cf.”
Kinetic models of conservative economies with wealth redistribution (2009, background): “This concept has been introduced in [6], where a fixed saving rate for all agents has been proposed, and generalized in [7] by introducing a individual saving rate.”
Colloquium: Statistical mechanics of money, wealth, and income (2009, methodology): “hakrabarti, 2005) and related papers, the case of random saving propensity was studied. In these models, the agents are assigned random parameters λ drawn from a uniform distribution between 0 and 1 (Chatterjee, Chakrabarti, and Manna, 2004). It was found that this model produces a power-law tail P(”
On Steady Distributions of Kinetic Models of Conservative Economies (2008, methodology): “Mainly two variants to introduce saving propensities have been studied: In the first, all agents have the same fixed saving factor [11], while in the second, the saving propensity has a quenched random distribution [12].”