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Universal patterns of inequality

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2010-NJP-v12-n7-p0750321. Introduction2. Statistical mechanics and thermodynamics of money2.1. Entropy maximization for division of a limited resource2.2. Flow of money and people between two countries with different temperatures2.3. Thermodynamics of money and wealth2.4. The circuit of money and the circuit of goods3. Two-class structure of income distribution3.1. Introduction3.2. Income dynamics as a combination of additive and multiplicative stochastic processes3.3. Comparison with the personal income data from the Internal Revenue Service (IRS)3.4. The fraction of income in the upper tail and speculative bubbles3.5. The power-law exponent of the upper tail3.6. The Lorenz plot and Gini coefficient for income inequality4. Probability distribution of the global energy consumption4.1. Introduction4.2. Energy consumption distribution as division of a limited resource4.3. Empirical data analysis4.4. The effect of globalization on the inequality of energy consumption5. ConclusionsAcknowledgmentsReferencesThe open–access journal for physicsNew Journal of PhysicsUniversal patterns of inequalityAnand Banerjee and Victor M Yakovenko1Department of Physics, University of Maryland, College Park,Maryland 20742-4111, USAhttp://www.physics.umd.edu/∼yakovenk/New Journal of Physics 12 (2010) 075032 (25pp)Received 2 December 2009Published 30 July 2010Online at http://www.njp.org/doi:10.1088/1367-2630/12/7/075032Abstract. Probability distributions of money, income and energy consumptionper capita are studied for ensembles of economic agents. The principle ofentropy maximization for partitioning of a limited resource gives exponentialdistributions for the investigated variables. A non-equilibrium difference ofmoney temperatures between different systems generates net fluxes of moneyand population. To describe income distribution, a stochastic process withadditive and multiplicative components is introduced. The resultant distributioninterpolates between exponential at the low end and power law at the high end,in agreement with the empirical data for the USA. We show that the increasein income inequality in the USA originates primarily from the increase inthe income fraction going to the upper tail, which now exceeds 20% of thetotal income. Analyzing the data from the World Resources Institute, we findthat the distribution of energy consumption per capita around the world can beapproximately described by the exponential function. Comparing the data for1990, 2000 and 2005, we discuss the effect of globalization on the inequality ofenergy consumption.1Author to whom any correspondence should be addressed.New Journal of Physics 12 (2010) 0750321367-2630/10/075032+25$30.00 © IOP Publishing Ltd and Deutsche Physikalische Gesellschaft2Contents1. Introduction 22. Statistical mechanics and thermodynamics of money 32.1. Entropy maximization for division of a limited resource . . . . . . . . . . . . . 32.2. Flow of money and people between two countries with different temperatures . 52.3. Thermodynamics of money and wealth . . . . . . . . . . . . . . . . . . . . . . 62.4. The circuit of money and the circuit of goods . . . . . . . . . . . . . . . . . . 83. Two-class structure of income distribution 93.1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93.2. Income dynamics as a combination of additive and multiplicative stochasticprocesses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103.3. Comparison with the personal income data from the Internal Revenue Service(IRS) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113.4. The fraction of income in the upper tail and speculative bubbles . . . . . . . . 123.5. The power-law exponent of the upper tail . . . . . . . . . . . . . . . . . . . . 153.6. The Lorenz plot and Gini coefficient for income inequality . . . . . . . . . . . 164. Probability distribution of the global energy consumption 174.1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 174.2. Energy consumption distribution as division of a limited resource . . . . . . . . 184.3. Empirical data analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 184.4. The effect of globalization on the inequality of energy consumption . . . . . . 225. Conclusions 23Acknowledgments 24References 241. IntroductionTwo types of approaches are utilized in science to describe the natural world around us. Oneapproach is suitable for systems with a small number of degrees of freedom, such as a harmonicoscillator, a pair of gravitating bodies and a hydrogen atom. In this case, the goal is to formulateand solve dynamical equations of motion of the system, be it within Newtonian, relativistic orquantum mechanics. This approach is widely used beyond physics to study dynamical systemsin chemistry, biology, economics, etc. In the opposite limiting case, we deal with systemsconsisting of a very large number of degrees of freedom. In this case, statistical description isemployed, and the systems are characterized by probability distributions. In principle, it shouldbe possible to derive a statistical description from microscopic dynamics, but it is rarely feasiblein practice. Thus, it is common to use general principles of the theory of probabilities to describestatistical systems, rather than to derive their properties from microscopic equations of motion.Statistical systems are common in physics, chemistry, biology, economics, etc.Any probability distribution can be thought of as representing some sort of ‘inequality’among the constituent objects of the system, in the sense that the objects have different valuesof a given variable. Thus, a study of probability distributions is also a study of inequalitydeveloping in a system for statistical reasons. To be specific, let us consider an economic systemwith a large number of interacting agents. In the unrealistic case where all agents have exactlyNew Journal of Physics 12 (2010) 075032 (http://www.njp.org/)3the same values of economic variables, the system can be treated as a single agent called the‘representative agent’. This approach is common in traditional economics, but by constructionit precludes a study of inequality among the agents. However, social and economic inequalityis ubiquitous in the real world, and its characterization and understanding are a very importantissue.In this paper, we apply the well-developed


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