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Wealth condensation in a multiplicative random asset exchange model

  • C. F. Moukarzel
  • S. Gonçalves
  • J. R. Iglesias
  • M. Rodríguez-Achach
  • R. Huerta-Quintanilla
Article

Abstract.

Random Asset Exchange (RAE) models, despite a number of simplifying assumptions, serve the purpose of establishing direct relationships between microscopic exchange mechanisms and observed economical data. In this work a conservative multiplicative RAE model is discussed in which, at each timestep, two agents “bet” for a fraction f of the poorest agent's wealth. When the poorest agent wins the bet with probability p, we show that, in a well defined region of the (p,f) phase space, there is wealth condensation. This means that all wealth ends up owned by only one agent, in the long run. We derive the condensation conditions analytically by two different procedures, and find results in accordance with previous numerical estimates. In the non-condensed phase, the equilibrium wealth distribution is a power law for small wealths. The associated exponent is derived analytically and it is found that it tends to -1 on the condensation interface. I turns out that wealth condensation happens also for values of p much larger than 0.5, that is under microscopic exchange rules that, apparently, favor the poor. We argue that the observed “rich get richer” effect is enhanced by the multiplicative character of the dynamics.

Keywords

European Physical Journal Special Topic Wealth Distribution Microscopic Exchange Multiplicative Character Poor Agent 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. J. Angle, Social Forces 65, 293 (1986) CrossRefGoogle Scholar
  2. V. Pareto, Cours d'Économie Politique (1897) Google Scholar
  3. H. Aoyama, W. Souma, Y. Fujiwara, Physica A 324, 352 (2003) zbMATHCrossRefADSMathSciNetGoogle Scholar
  4. M. Nirei, W. Souma, Two factor model of income distribution dynamics (2004) Google Scholar
  5. F. Clementi, M. Gallegati, Physica A 350, 427 (2005) CrossRefADSGoogle Scholar
  6. S. Sinha, Physica A 359, 555 (2006) CrossRefADSGoogle Scholar
  7. Statistics from Brazilian Economy, http://www.ibge.gov.br/home/estatistica/populacao/ trabalhoerendimento/pnad99/sintese/grafico.shtm (1999) Google Scholar
  8. A. Dragulescu, V.M. Yakovenko, Eur. Phys. J. B 17, 723 (2000) CrossRefADSGoogle Scholar
  9. A. Dragulescu, V.M. Yakovenko, Eur. Phys. J. B 20, 585 (2001) CrossRefADSGoogle Scholar
  10. A. Dragulescu, V.M. Yakovenko, Physica A 299, 213 (2001) zbMATHCrossRefADSGoogle Scholar
  11. J.R. Iglesias, S. Goncalves, G. Abramson, J.L. Vega, Physica A 342, 186 (2004) CrossRefADSMathSciNetGoogle Scholar
  12. A. Das, S. Yarlagadda, Physica A 353, 529 (2005) CrossRefADSGoogle Scholar
  13. A. Das, S. Yarlagadda, Phys. Scr. T 106, 39 (2003) CrossRefADSGoogle Scholar
  14. M. Rodriguez-Achach, R. Huerta-Quintanilla, Physica A 361, 309 (2006) CrossRefADSGoogle Scholar
  15. B. Hayes, Am. Scient. 90, 400 (2002) CrossRefGoogle Scholar
  16. A. Chakraborti, B.K. Chakrabarti, Eur. Phys. J. B 17, 167 (2000) CrossRefADSGoogle Scholar
  17. J.P. Bouchaud, M. Mezard, Physica A 282, 536 (2000) CrossRefADSGoogle Scholar
  18. S. REDNER, Am. J. Phys. 58, 267 (1990) CrossRefADSGoogle Scholar
  19. S. Ispolatov, P.L. Krapivsky, S. Redner, Eur. Phys. J. B 2, 267 (1998) CrossRefADSGoogle Scholar

Copyright information

© EDP Sciences/Società Italiana di Fisica/Springer-Verlag 2007

Authors and Affiliations

  • C. F. Moukarzel
    • 1
  • S. Gonçalves
    • 2
  • J. R. Iglesias
    • 2
  • M. Rodríguez-Achach
    • 1
  • R. Huerta-Quintanilla
    • 1
  1. 1.Depto. de Física Aplicada, CINVESTAV del IPN, Av. Tecnológico Km 6, 97310 MéridaYucatánMexico
  2. 2.Instituto de Física, Universidade Federal do Rio Grande do SulPorto AlegreBrazil

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