| CROSS-DISCIPLINARY PHYSICS AND RELATED AREAS OF SCIENCE AND TECHNOLOGY |
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Size Dependency of Income Distribution and Its Implications |
| ZHANG Jiang**, WANG You-Gui
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Department of Systems Science, School of Management, Beijing Normal University, Beijing 100875
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| Cite this article: |
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ZHANG Jiang, WANG You-Gui 2011 Chin. Phys. Lett. 28 038901 |
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Abstract We systematically study the size dependency of income distributions, i.e. income distribution versus the population of a country. Using the generalized Lotka–Volterra model to fit the empirical income data for 1996–2007 in the U.S.A., we find an important parameter λ that can scale with a β power of the size (population) of the U.S.A. in that year. We point out that the size dependency of income distributions, which is a very important property but seldom addressed in previous studies, has two non-trivial implications: (1) the allometric growth pattern, i.e. the power-law relationship between population and GDP in different years, can be mathematically derived from the size-dependent income distributions and also supported by the empirical data; (2) the connection with the anomalous scaling for the probability density function in critical phenomena, since the re-scaled form of the income distributions has asymptotically exactly the same mathematical expression for the limit distribution of the sum of many correlated random variables.
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| Keywords:
89.65.Gh
89.75.Da
89.75.Kd
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Received: 02 December 2010
Published: 28 February 2011
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| PACS: |
89.65.Gh
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(Economics; econophysics, financial markets, business and management)
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89.75.Da
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(Systems obeying scaling laws)
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89.75.Kd
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(Patterns)
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