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Gibbs versus non-Gibbs distributions in money dynamics

Author

Listed:
  • Patriarca, Marco
  • Chakraborti, Anirban
  • Kaski, Kimmo

Abstract

We review a simple model of closed economy, where the economic agents make money transactions and a saving criterion is present. We observe the Gibbs distribution for zero saving propensity, and non-Gibbs distributions otherwise. While the exact solution in the case of zero saving propensity is already known to be given by the Gibbs distribution, here we provide the explicit analytical form of the equilibrium distribution for the general case of nonzero saving propensity. We verify it through comparison with numerical data and show that it can be cast in the form of a gamma-distribution.

Suggested Citation

  • Patriarca, Marco & Chakraborti, Anirban & Kaski, Kimmo, 2004. "Gibbs versus non-Gibbs distributions in money dynamics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 340(1), pages 334-339.
    • Handle: RePEc:eee:phsmap:v:340:y:2004:i:1:p:334-339
    DOI: 10.1016/j.physa.2004.04.024
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    Citations

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    Cited by:

    1. Carmen Pellicer-Lostao & Ricardo Lopez-Ruiz, 2009. "Economic Models with Chaotic Money Exchange," Papers 0901.1038, arXiv.org.
    2. D. S. Quevedo & C. J. Quimbay, 2019. "Piketty's second fundamental law of capitalism as an emergent property in a kinetic wealth-exchange model of economic growth," Papers 1903.00952, arXiv.org, revised Mar 2019.
    3. Maciej Jagielski & Ryszard Kutner, 2013. "Modelling the income distribution in the European Union: An application for the initial analysis of the recent worldwide financial crisis," Papers 1312.2362, arXiv.org.
    4. Ausloos, Marcel & Pe¸kalski, Andrzej, 2007. "Model of wealth and goods dynamics in a closed market," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 373(C), pages 560-568.
    5. Huang, Jing & Wang, Yougui, 2014. "The time-dependent characteristics of relative mobility," Economic Modelling, Elsevier, vol. 37(C), pages 291-295.
    6. Patriarca, Marco & Chakraborti, Anirban & Germano, Guido, 2006. "Influence of saving propensity on the power-law tail of the wealth distribution," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 369(2), pages 723-736.

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