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Pramana

, Volume 71, Issue 2, pp 233–243 | Cite as

Gamma-distribution and wealth inequality

  • A. ChakrabortiEmail author
  • M. Patriarca
Article

Abstract

We discuss the equivalence between kinetic wealth-exchange models, in which agents exchange wealth during trades, and mechanical models of particles, exchanging energy during collisions. The universality of the underlying dynamics is shown both through a variational approach based on the minimization of the Boltzmann entropy and a microscopic analysis of the collision dynamics of molecules in a gas. In various relevant cases, the equilibrium distribution is well-approximated by a gamma-distribution with suitably defined temperature and number of dimensions. This in turn allows one to quantify the inequalities observed in the wealth distributions and suggests that their origin should be traced back to very general underlying mechanisms, for instance, the fact that smaller the fraction of the relevant quantity (e.g. wealth) that agent can exchange during an interaction, the closer the corresponding equilibrium distribution is to a fair distribution.

Keywords

Gamma distribution wealth inequality 

PACS Nos

89.65.Gh 87.23.Ge 02.50.-r 

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References

  1. [1]
    V Pareto, Cours d’economie politique (Rouge, Lausanne, 1897)Google Scholar
  2. [2]
    V Pareto, Cours d’economie politique, Reprinted as a volume of Oeuvres Completes (Droz, Geneva, 1971)Google Scholar
  3. [3]
    V Pareto, Manual of political economy (Kellag, New York, 1971)Google Scholar
  4. [4]
    R Gibrat, Les Inégalités Economiques (Sirey, 1931)Google Scholar
  5. [5]
    J Angle, The surplus theory of social stratification and the size distribution of personal wealth, in: Proceedings of the American Social Statistical Association, Social Statistics Section, Alexandria, VA, 1983, p. 395.Google Scholar
  6. [6]
    J Angle, Social Forces 65, 293 (1986), http://www.jstor.org CrossRefGoogle Scholar
  7. [7]
    E Bennati, La simulazione statistica nell’analisi della distribuzione del reddito: modelli realistici e metodo di Monte Carlo (ETS Editrice, Pisa, 1988)Google Scholar
  8. [8]
    E Bennati, Rivista Internazionale di Scienze Economiche e Commerciali 35, 735 (1988)Google Scholar
  9. [9]
    E Bennati, Il metodo Monte Carlo nell’analisi economica, Rassegna di lavori dell’ISCO X (1993) 31Google Scholar
  10. [10]
    A Chakraborti and B K Chakrabarti, Eur. Phys. J. B17, 167 (2000)ADSGoogle Scholar
  11. [11]
    M Patriarca, A Chakraborti and K Kaski, Phys. Rev. E70, 016104 (2004)Google Scholar
  12. [12]
    M Patriarca, A Chakraborti and K Kaski, Physica A340, 334 (2004)ADSMathSciNetGoogle Scholar
  13. [13]
    A Dragulescu and V M Yakovenko, Eur. Phys. J. B17, 723 (2000)ADSGoogle Scholar
  14. [14]
    J Angle, J. Math. Sociol. 18, 27 (1993)zbMATHGoogle Scholar
  15. [15]
    A Chakraborti, Int. J. Mod. Phys. C13, 1315 (2002)ADSGoogle Scholar
  16. [16]
    J Angle, J. Math. Sociol. 26, 217 (2002)zbMATHCrossRefGoogle Scholar
  17. [17]
    P K Mohanty, Phys. Rev. E74(1), 011117 (2006)Google Scholar
  18. [17a]
    P K Mohanty, private communicationGoogle Scholar
  19. [18]
    D Dhar and A Chakraborti, in preparation (2008)Google Scholar
  20. [19]
    M Patriarca, A Chakraborti, K Kaski and G Germano, Kinetic theory models for the distribution of wealth: Power law from overlap of exponentials, in: A Chatterjee, S Yarlagadda and B K Chakrabarti (eds), Econophysics of wealth distributions (Springer, 2005) p. 93, arXiv.org: physics/0504153Google Scholar
  21. [20]
    J Mimkes and G Willis, Lagrange principle of wealth distribution, in: A Chatterjee, S Yarlagadda and B K Chakrabarti (eds), Econophysics of wealth distributions (Springer, 2005) p. 61Google Scholar
  22. [21]
    J Mimkes and Y Aruka, Carnot process of wealth distribution, in: A Chatterjee, S Yarlagadda and B K Chakrabarti (eds), Econophysics of wealth distributions (Springer, 2005) p. 70Google Scholar
  23. [22]
    E W Weisstein, Hypersphere. From mathworld — A Wolfram web resource, http://mathworld.wolfram.com/Hypersphere.html

Copyright information

© Indian Academy of Sciences 2008

Authors and Affiliations

  1. 1.Department of PhysicsBanaras Hindu UniversityVaranasiIndia
  2. 2.National Institute of Chemical Physics and BiophysicsTallinEstonia

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