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Entropy and equilibrium state of free market models

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  • J. R. Iglesias
  • R. M. C. de Almeida
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    Abstract

    Many recent models of trade dynamics use the simple idea of wealth exchanges among economic agents in order to obtain a stable or equilibrium distribution of wealth among the agents. In particular, a plain analogy compares the wealth in a society with the energy in a physical system, and the trade between agents to the energy exchange between molecules during collisions. In physical systems, the energy exchange among molecules leads to a state of equipartition of the energy and to an equilibrium situation where the entropy is a maximum. On the other hand, in the majority of exchange models, the system converges to a very unequal condensed state, where one or a few agents concentrate all the wealth of the society while the wide majority of agents shares zero or almost zero fraction of the wealth. So, in those economic systems a minimum entropy state is attained. We propose here an analytical model where we investigate the effects of a particular class of economic exchanges that minimize the entropy. By solving the model we discuss the conditions that can drive the system to a state of minimum entropy, as well as the mechanisms to recover a kind of equipartition of wealth.

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    File URL: http://arxiv.org/pdf/1108.5725
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    Paper provided by arXiv.org in its series Papers with number 1108.5725.

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    Date of creation: Aug 2011
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    Handle: RePEc:arx:papers:1108.5725

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    1. F. Clementi & M. Gallegati, 2004. "Power Law Tails in the Italian Personal Income Distribution," Papers cond-mat/0408067, arXiv.org.
    2. Gallegati, Mauro & Keen, Steve & Lux, Thomas & Ormerod, Paul, 2006. "Worrying trends in econophysics," Physica A: Statistical Mechanics and its Applications, Elsevier, Elsevier, vol. 370(1), pages 1-6.
    3. Sinha, Sitabhra, 2006. "Evidence for power-law tail of the wealth distribution in India," Physica A: Statistical Mechanics and its Applications, Elsevier, Elsevier, vol. 359(C), pages 555-562.
    4. Arnab Chatterjee & Bikas K. Chakrabarti & S. S. Manna, 2003. "Pareto Law in a Kinetic Model of Market with Random Saving Propensity," Papers cond-mat/0301289, arXiv.org, revised Jan 2004.
    5. Iglesias, J.R. & Gonçalves, S. & Pianegonda, S. & Vega, J.L. & Abramson, G., 2003. "Wealth redistribution in our small world," Physica A: Statistical Mechanics and its Applications, Elsevier, Elsevier, vol. 327(1), pages 12-17.
    6. Victor M. Yakovenko & J. Barkley Rosser, 2009. "Colloquium: Statistical mechanics of money, wealth, and income," Papers 0905.1518, arXiv.org, revised Dec 2009.
    7. Adrian Dragulescu & Victor M. Yakovenko, 2001. "Exponential and power-law probability distributions of wealth and income in the United Kingdom and the United States," Papers cond-mat/0103544, arXiv.org, revised Mar 2001.
    8. Pianegonda, S. & Iglesias, J.R., 2004. "Inequalities of wealth distribution in a conservative economy," Physica A: Statistical Mechanics and its Applications, Elsevier, Elsevier, vol. 342(1), pages 193-199.
    9. Adrian Dragulescu & Victor M. Yakovenko, 2000. "Statistical mechanics of money," Papers cond-mat/0001432, arXiv.org, revised Aug 2000.
    10. Sitabhra Sinha, 2003. "Stochastic Maps, Wealth Distribution in Random Asset Exchange Models and the Marginal Utility of Relative Wealth," Papers cond-mat/0304324, arXiv.org.
    11. Drăgulescu, Adrian & Yakovenko, Victor M., 2001. "Exponential and power-law probability distributions of wealth and income in the United Kingdom and the United States," Physica A: Statistical Mechanics and its Applications, Elsevier, Elsevier, vol. 299(1), pages 213-221.
    12. Ausloos, Marcel & Pe¸kalski, Andrzej, 2007. "Model of wealth and goods dynamics in a closed market," Physica A: Statistical Mechanics and its Applications, Elsevier, Elsevier, vol. 373(C), pages 560-568.
    13. Chatterjee, Arnab & K. Chakrabarti, Bikas & Manna, S.S, 2004. "Pareto law in a kinetic model of market with random saving propensity," Physica A: Statistical Mechanics and its Applications, Elsevier, Elsevier, vol. 335(1), pages 155-163.
    14. Makoto Nirei & Wataru Souma, 2007. "A Two Factor Model Of Income Distribution Dynamics," Review of Income and Wealth, International Association for Research in Income and Wealth, vol. 53(3), pages 440-459, 09.
    15. Iglesias, J.R. & Gonçalves, S. & Abramson, G. & Vega, J.L., 2004. "Correlation between risk aversion and wealth distribution," Physica A: Statistical Mechanics and its Applications, Elsevier, Elsevier, vol. 342(1), pages 186-192.
    16. Pianegonda, S & Iglesias, J.R & Abramson, G & Vega, J.L, 2003. "Wealth redistribution with conservative exchanges," Physica A: Statistical Mechanics and its Applications, Elsevier, Elsevier, vol. 322(C), pages 667-675.
    17. Jean-Philippe Bouchaud & Marc Mezard, 2000. "Wealth condensation in a simple model of economy," Science & Finance (CFM) working paper archive 500026, Science & Finance, Capital Fund Management.
    18. J. R. Iglesias, 2010. "How simple regulations can greatly reduce inequality," Papers 1007.0461, arXiv.org, revised Jul 2010.
    19. Bouchaud, Jean-Philippe & Mézard, Marc, 2000. "Wealth condensation in a simple model of economy," Physica A: Statistical Mechanics and its Applications, Elsevier, Elsevier, vol. 282(3), pages 536-545.
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    1. > Schools of Economic Thought, Epistemology of Economics > Heterodox Approaches > Thermoeconomics > The economy system and entropy minimization

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