摘要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.
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.
ZHANG Jiang**;WANG You-Gui
. Size Dependency of Income Distribution and Its Implications[J]. 中国物理快报, 2011, 28(3): 38901-038901.
ZHANG Jiang**, WANG You-Gui
. Size Dependency of Income Distribution and Its Implications. Chin. Phys. Lett., 2011, 28(3): 38901-038901.
[1] Pareto V 1964 Cours Dconomie Politique: Nouvelle ed Bousquet G H and Busino G (Paris: Librairie Droz, Geneva)
[2] Yakovenko V M et al 2009 Rev. Mod. Phys. 81 1703
[3] Clementi F and Gallegati M 2005 Physica A 350 427
[4] Ding N and Wang Y G 2007 Chin. Phys. Lett. 24 2434
[5] Silva A C and Yakovenko V M 2005 Europhys. Lett. 69 304
[6] Zipf G K 1932 Selected Studies of the Principle of Relative Frequency in Language 1st edn (Cambridge: Harvard University Press)
[7] Albert R and Barabasi A L 2002 Rev. Mod. Phys. 74 47
[8] Souma W 2000 cond-mat/0011373
[9] Richmond P, Hutzler S, Coelho R and Repetowicz P 2006 Econophys. and Sociophys. (Berlin: Wiley-VCH)
[10] Chatterjee A et al 2004 Physica A 335 155
[11] Dragulescu A and Yakovenko V 2001 Physica A 299 213
[12] Xu Y et al 2010 Chin. Phys. Lett. 27 078901
[13] Miyazima S, Lee Y, Nagamine T and Miyajima H 2000 Physica A 278 282 DOI:10.1016/S0378-4371(99)00546-4
[14] Kim B J and Park S M 2005 Physica A 347 683
[15] Anh H et al 2007 J. Korean. Phys. Soc. 51 1812
[16] Bernhardsson S et al 2009 New J. Phys. 11 123015
[17] Nordbeck S 1971 Geor. Ann. B 53 54
[18] Kleiber M 1932 Hilgardia 6 315
[19] Brown J H and West G B 2000 Scaling in Biology (New York: Oxford University)
[20] West G B and Brown J H 2005 J. Exp. Biol. 208 1575
[21] Isalgue A et al 2007 Physica A 382 643
[22] Bettencourt L M 2007 Res. Policy 36 107
[23] Bettencourt L M et al 2007 P. Natl. Acad. of Sci. USA 104 7301
[24] Roehner B 1984 Int. J. Syst. Sci. 15 917
[25] Zhang J and Yu T K 2010 Physica A 389 4887
[26] Lu L Y, Zhang Z K and Zhou T 2010 PloS ONE 5 e14139
[27] van Leijenhorst D C et al 2005 Inform. Sciences 170 263
[28] Baldovin F and Stella A L 2007 Phys. Rev. E 75 020101
[29] Stella A L and Baldovin F 2010 J. Stat. Mech-theory E 2010 P02018
[30] http://www.irs.gov/taxstats/indtaxstats/article/0, id=134951,00.html
[31] Malcai O et al 2002 Phys. Rev. E 66 031102
[32] Blanchard O 2000 Macroeconomics (New York: Prentice Hall)
[33] Wu L F and Zhang J 2011 Allometric Scaling and Size-Dependent Distributions of Massive Human Online Behaviors (in preparation)
2011, Vol. 28 
