Abstract
In this chapter, some basic concepts useful in studying income distribution are analyzed, such as income distribution, income inequality, and polarization. In addition, a great body of this chapter is also devoted to discussing some indexes and formulas, Gini Coefficient, and several distribution functions in particular, which are mainly employed to measure income inequality and polarization.
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Notes
- 1.
One of the authors of this book introduced some indexes in his former book (Chen Zongsheng and Zhou Yunbo 2002), and some new indexes are supplemented in this book.
- 2.
The four natures are also indexes to assess the eligibility of Lorentz Curve’s estimation equation.
- 3.
This part of analysis is partly borrowed from Hong Xingjiang and Li Jinchang (2007).
- 4.
In fact, the Income Worsening Index mentioned before may also serve as an index to judge polarization.
- 5.
The two axioms are increased spread and increased bipolarization. For any \( n \) dimensional income vectors \( x \) and \( y \), given the same median, suppose \( {x_{ - }} \) and \( {y_{ - }} \) indicate income vectors below the median, and \( {x_{ + }} \) and \( {y_{ + }} \) indicate income vectors above the median. If \( {y_{ - }} \le {x_{ - }} \) and \( {x_{ + }} \le {y_{ + }} \), we will have a more increased spread of \( y \) relative to \( x \); this is called increased spread axiom. If \( {y_{ - }} \) and \( {y_{ + }} \) depend on progressive income transfer of \( {x_{ - }} \) and \( {x_{ + }} \), respectively, we will have a more polarized \( y \) than \( x \); this is called increased bi-polarization axiom.
- 6.
For index function \( y = {a^{\gamma }} \), since \( {\rm d} y/{\rm d} \gamma = {a^{\gamma }}\ln a \), so when \( a > 1 \), \( {\rm d} y/{\rm d} \gamma > 0 \); when \( a < 1 \), \( {\rm d} y/{\rm d} \gamma < 0 \). In the case of the book, when \( a > 1 \), \( x(i) > 2m \), and when \( a < 1 \), \( x(i) < 2m \).
- 7.
For these technical issues, one of the authors discussed these issues in his former book (Chen Zongsheng and Zhou Yunbo 2002). In this book, we will discuss them in more detail.
References
Chen Zongsheng, Zhou Yunbo (2002) More remarks on income distribution during China’s reform and development—is there polarization in China? Economy and Science Press, Beijing
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Esteban JM, Ray D (1994) On the measurement of polarization. Econometrica 62(4):819–851
Hong Xingjian, Li Jinchang (2007) Review of methods for measuring polarization and polarized Chinese residents’ income. Econ Res 11
Morgan J (1962) The anatomy of income distribution. Rev Econ Stat 44(3):270–283
Zhao Renwei, Li Shi, Riskin K (eds) (1999) Income distribution in economic reform and growth: a second study on China’s income distribution. Chinese Fiscal and Economic Press, Beijing
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© 2012 Springer-Verlag Berlin Heidelberg
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Zhou, Y., Qin, Y. (2012). Concept of Income Distribution and Indexes and Methods for Measuring Income Inequality. In: Empirical Analysis on Income Inequality of Chinese Residents. Gu Shutang Academic Fund of Economics, vol 1. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-24952-5_2
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DOI: https://doi.org/10.1007/978-3-642-24952-5_2
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