Willis, Geoff (2011): Wealth, income, earnings and the statistical mechanics of flow systems.

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Abstract
This paper looks at empirical data from economics regarding wealth, earnings and income, alongside a flow model for an economy based on the general LotkaVolterra models of Levy & Solomon. The data and modelling suggest that a simple economic system might provide a tractable model for giving an exact statistical mechanical solution for an 'out of equilibrium' flow model. This might also include an exact mathematical definition of a 'dissipative structure' derived from maximum entropy considerations. This paper is primarily a qualitative discussion of how such a mathematical proof might be achieved.
Item Type:  MPRA Paper 

Original Title:  Wealth, income, earnings and the statistical mechanics of flow systems 
Language:  English 
Keywords:  wealth; earnings; income; entropy; lotka; volterra; dissipative 
Subjects:  D  Microeconomics > D3  Distribution > D31  Personal Income, Wealth, and Their Distributions D  Microeconomics > D5  General Equilibrium and Disequilibrium 
Item ID:  31139 
Depositing User:  Geoff Willis 
Date Deposited:  26. May 2011 19:00 
Last Modified:  04. Jan 2016 15:57 
References:  Ackland GJ, Gallagher ID, 2004. Stabilization of large generalized LotkaVolterra foodwebs by evolutionary feedback, Phys. Rev. Lett., 93, doi:10.1103/PhysRevLett.93.158701. Baek SK, Berhardsson S, Minnhagen P, 2011. Zipf’s law unzipped. New Journal of Physics 13 043004. Bouchaud JP, Mezard M, 2000. Wealth Condensation in a Simple Model of Economy. Physica A282:536545, condmat/0002374. Chatterjee A, Sinha S, Chakrabarti B, 2007. Economic inequality: Is it natural? Current Science 92 (10), 1383. Chatterjee A, Chakrabarti BK, 2007. Kinetic exchange models for income and wealth distributions. The European Physical Journal B 60, 135–149. Clementi F, Gallegati M, 2005. Income Inequality Dynamics: Evidence from a Pool of Major Industrialized Countries. Talk at the International Workshop on the Econophysics of Wealth Distributions, Kolkata. http://www.saha.ac.in/cmp/econophysics/abstracts.html Dewar RC, 2005. Maximum entropy production and nonequilibrium statistical mechanics. In NonEquilibrium Thermodynamics and the Production of Entropy: Life, Earth, and Beyond, edited by A. Kleidon and R. D. Lorenz, Springer Verlag, Heidelberg, Germany. Dragulescu A, Yakovenko VM, 2001. Evidence for the exponential distribution of income in the USA. Eur. Phys. J. B 20:585–89 Ferrero JC, 2010. The individual income distribution in Argentina in the period 20002009, A unique source of non stationary data. Arxiv preprint; http://arxiv.org/ftp/arxiv/papers/1006/1006.2057.pdf Gabaix X, 2009. Power Laws in Economics and Finance. Annual Reviews of Economics, 2009, 1, 25593. Gollin D, 2002. Getting Income Shares Right. Journal of Political Economy 110(2):458474. Kleidon A, Lorenz RD, (Eds), 2005. Nonequilibrium Thermodynamics and the Production of Entropy: Life, Earth, and Beyond. (Understanding Complex Systems) Springer, ISBN10: 3540224955. Levy M, Solomon S, 1996. Power Laws are Logarithmic Boltzmann Laws. International Journal of Modern Physics C, 7 (4), 595—600. Lotka AJ, 1925. Elements of physical biology. Baltimore: Williams & Wilkins Co Mitzenmacher M, 2004. A Brief History of Generative Models for Power Law and Lognormal Distributions. Internet Mathematics, 1(2):226–251. Newman MEJ, 2005. Power laws, Pareto distributions and Zipf’s law. Contemporary Physics, 46:323–351. Nirei M, Souma W, 2007. A two factor model of income distribution dynamics. Rev. Income Wealth 53:440–59 Office for National Statistics, 2003. New Earnings Survey. Stationary Office Books, http://www.statistics.gov.uk/statbase/Product.asp?vlnk=5749&More=Y Ozawa H, Ohmura A, Lorenz RD, Pujol T, 2003. The second law of thermodynamics and the global climate system – A review of the maximum entropy production principle, Rev Geophys 41: 1018. Pareto V, 1896. Cours d'economie politique. Reprinted as a volume of Oeuvres Completes (Droz. Geneva, 18961965) Reed WJ & Hughes BD, 2002. From gene families and genera to incomes and internet file sizes: Why power laws are so common in nature. Phys. Rev. E 66, 067103. Simkin MV, Roychowdhury VP, 2006. Reinventing Willis. preprint, http://arxiv.org/abs/physics/0601192 Sinha S, 2005. The Rich Are Different!: Pareto Law from asymmetric interactions in asset exchange models. In: Econophysics of Wealth Distributions, 177184 eds. A. Chatterjee, B. K. Chakrabarti and S. Yarlagadda, Springer Verlag, New York 2005. Slanina F, 2004. Inelastically scattering particles and wealth distribution in an open economy, Phys. Rev. E 69, n 4, 4610217. Solomon S, 2000. Generalized Lotka Volterra (GLV) models [of stock markets]. In G. Ballot and Weisbuch G., editors, Applications of Simulation to Social Sciences, pages 301–322. Hermes Science, Paris. http://arxiv.org/PS_cache/condmat/pdf/9901/9901250v1.pdf Souma W, 2001. Universal structure of the personal income distribution. Fractals, 9, 463–470. Pakko M, 2004. Labor’s Share, St Louis Fed, National Economic Trends, Aug 2004. http://research.stlouisfed.org/publications/net/20040801/cover.pdf Volterra V, 1926. Variazioni e fluttuazioni del numero d'individui in specie animali conviventi. Mem. R. Accad. Naz. dei Lincei. Ser. VI, vol. 2. Willis G, Mimkes J, 2005. Evidence for the Independence of Waged and Unwaged Income. Presented at the ‘Econophysics of Wealth Distributions’ International Workshop, Kolkata, India. March 2005. http://xxx.arxiv.cornell.edu/abs/condmat/0406694 Willis G, 2011. The Bowley Ratio. http://arxiv.org/abs/1105.2123 Willis G, 2011. Why Money Trickles Up. http://econodynamics.org Willis G, 2011. Why Money Trickles Up – Wealth and Income Distributions. http://arxiv.org/abs/1105.2122 Wright I, 2005. The social architecture of capitalism. Physica A 346, 589–620. Wright I, 2009. Implicit microfoundations for macroeconomics. Economics (ejournal) 3, 200919, Young AT, 2010. One of the things we know that ain't so: is US labor's share relatively stable? Journal of Macroeconomics (forthcoming). Vol 32, 1, March 2010, 90102. 
URI:  https://mpra.ub.unimuenchen.de/id/eprint/31139 