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Wealth condensation in a simple model of economy

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Author Info
Jean-Philippe Bouchaud (Science & Finance, Capital Fund Management, CEA Saclay;)
Marc Mezard (Universite Paris Sud (Orsay))
Abstract

We introduce a simple model of economy, where the time evolution is described by an equation capturing both exchange between individuals and random speculative trading, in such a way that the fundamental symmetry of the economy under an arbitrary change of monetary units is insured. We investigate a mean-field limit of this equation and show that the distribution of wealth is of the Pareto (power-law) type. The Pareto behaviour of the tails of this distribution appears to be robust for finite range models, as shown using both a mapping to the random `directed polymer' problem, as well as numerical simulations. In this context, a transition between an economy dominated by a few individuals from a situation where the wealth is more evenly spread out, is found. An interesting outcome is that the distribution of wealth tends to be very broadly distributed when exchanges are limited, either in amplitude or topologically. Favoring exchanges (and, less surprisingly, increasing taxes) seems to be an efficient way to reduce inequalities.

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Paper provided by Science & Finance, Capital Fund Management in its series Science & Finance (CFM) working paper archive with number 500026.

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Date of creation: Feb 2000
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Handle: RePEc:sfi:sfiwpa:500026

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G10 - Financial Economics - - General Financial Markets - - - General (includes Measurement and Data)

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  1. Carmen Pellicer-Lostao & Ricardo Lopez-Ruiz, 2009. "Economic Models with Chaotic Money Exchange," Quantitative Finance Papers 0901.1038, arXiv.org. [Downloadable!]
  2. Zoltan Kuscsik & Denis Horvath, 2007. "Statistical properties of agent-based market area model," Quantitative Finance Papers 0710.0459, arXiv.org. [Downloadable!]
  3. G. Willis & J. Mimkes, 2004. "Evidence for the Independence of Waged and Unwaged Income, Evidence for Boltzmann Distributions in Waged Income, and the Outlines of a Coherent Theory of Income Distribution," Quantitative Finance Papers cond-mat/0406694, arXiv.org. [Downloadable!]
  4. Bertram Düring & Daniel Matthes & Giuseppe Toscani, 2008. "A Boltzmann-type Approach to the Formation of Wealth Distribution Curves," CoFE Discussion Paper 08-05, Center of Finance and Econometrics, University of Konstanz. [Downloadable!]
  5. Tatsuo Yanagita & Tamotsu Onozaki, 2008. "Dynamics of a market with heterogeneous learning agents," Journal of Economic Interaction and Coordination, Springer, vol. 3(1), pages 107-118, June. [Downloadable!] (restricted)
  6. Yougui Wang & Ning Ding, 2005. "Dynamic Process of Money Transfer Models," Quantitative Finance Papers physics/0507162, arXiv.org. [Downloadable!]
  7. Geoff Willis & Juergen Mimkes, 2004. "Evidence for the Independence of Waged and Unwaged Income, Evidence for Boltzmann Distributions in Waged Income, and the Outlines of a Coherent Theory of Income Distribution," Microeconomics 0408001, EconWPA. [Downloadable!]
  8. T. Kämpke & R. Pestel & F.J. Radermacher, 2003. "A Computational Concept for Normative Equity," European Journal of Law and Economics, Springer, vol. 15(2), pages 129-163, March. [Downloadable!] (restricted)
  9. Marco Raberto & Silvano Cincotti & Sergio Focardi & Michele Marchesi, 2003. "Traders' Long-Run Wealth in an Artificial Financial Market," Computational Economics, Springer, vol. 22(2), pages 255-272, October. [Downloadable!] (restricted)
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  10. Wataru Souma, 2002. "Physics of Personal Income," Quantitative Finance Papers cond-mat/0202388, arXiv.org. [Downloadable!]
  11. Yoshi Fujiwara & Wataru Souma & Hideaki Aoyama & Taisei Kaizoji & Masanao Aoki, 2002. "Growth and Fluctuations of Personal Income," Quantitative Finance Papers cond-mat/0208398, arXiv.org. [Downloadable!]
  12. B. Düring & G. Toscani, 2007. "Hydrodynamics from kinetic models of conservative economies," CoFE Discussion Paper 07-06, Center of Finance and Econometrics, University of Konstanz. [Downloadable!]
  13. Geoff Willis, 2004. "Laser Welfare: First Steps in Econodynamic Engineering," Microeconomics 0408003, EconWPA. [Downloadable!]
  14. Victor M. Yakovenko & J. Barkley Rosser, 2009. "Colloquium: Statistical Mechanics of Money, Wealth, and Income," Quantitative Finance Papers 0905.1518, arXiv.org. [Downloadable!]
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