Abstract
A one-parametric version of the Pareto distribution can be obtained as unique solution of a differential equation for Lorenz curves. This distribution, also, is unique among self-similar Lorenz curves as well as among all so-called Gini self-similar Lorenz curves. Median self-similarity leads to a wider solution manifold but every function of this manifold is interpolated by a Pareto distribution. The Pareto distribution is also obtainable from an iterative process that considers every Lorenz curve as a distribution function.
Parameters of best fit Pareto distributions are given for empirical income data. These show a great imbalance for the world as a whole and indicate that the most prosperous nations lie in a “productive inequality range”. Some remarks to changes in social balance over the last decade are given. Also, there is a reference to Thomas Piketty’s important work “Capital in the 21st century”,
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Bundesregierung (2008) Lebenslagen in Deutschland, Der dritte Armuts- und Reichtumsbericht der Bundesregierung. Report, Berlin
Cowell FA (2009) Measuring inequality. LSE handbooks in economics series. Prentice Hall, London. http://darp.lse.ac.uk/papersDB/Cowell$_$measuringinequality3.pdf with additional data at http://darp.lse.ac.uk/Frankweb/MI3.htm
Easton B (2002) Beware the median. Soc Policy Res Cent Newslett 82:6–7 (University of New South Wales, Sydney). www.eastonbh.ac.nz/?p=28
Eichhorn W, Gleissner W (1985) On a functional differential equation arising in the theory of wealth. Aequationes Math 28:190–198
G20 (2013) Tax annex to the St. Petersburg G20 leaders declaration. Conference document, St. Petersburg. www.mofa.go.jp/files/000013928.pdf
Heinaman R (1998) Social justice in Plato’s Republic. Polis 15:23–43
Herlyn E (2012) Einkommensverteilungsbasierte Präferenz- und Koalitionsanalysen auf der Basis selbstähnlicher Equity-Lorenzkurven. Springer Gabler, Wiesbaden
Iritani J, Kuga K (1983) Duality between the Lorenz curves and the income distribution functions. Econ Stud Q 34:9–21
Jantzen RT, Volpert K (2012) On the mathematics of income inequality: splitting the Gini index in two. Am Math Mon 119:824–837
Kämpke T (2010) The use of mean values vs. medians in inequality analysis. J Econ Soc Meas 35:43–62
Kämpke T (2011) Ordinary differential equations with inverted functions. World Acad Sci Eng Technol 60:1490–1500
Kämpke T, Pestel R, Radermacher FJ (2003) A computational concept for normative equity. Eur J Law Econ 15:129–163
Kämpke T, Radermacher FJ (2005) Equity analysis by functional approach. In: Data analysis and decision support. Springer, Heidelberg, pp 241–248
Kämpke T, Stark M (2002) The world income distribution and its equity. FAW working paper, Ulm
Kleiber C (2008) The Lorenz curve in economics and econometrics. In: Betti G, Lemmi A (eds) Advances on income inequality and concentration measures. Collected papers in memory of Corrado Gini and Max O. Lorenz. Routledge, London, pp 225–242
Krämer H (2014) Verteilungsgerechtigkeit in einer sozialen Marktwirtschaft. WISO direkt. Friedrich Ebert Stiftung, Bonn, pp 1–4
Piketty T (2014) Capital in the twenty-first century. Harvard University Press, Cambridge
Piketty T, Saez E (2014) Inequality in the long run. Science 344:838–843
Piketty T, Saez E (2014) Inequality in the long run. Supplementary material. Science 344. www.sciencemag.org/344/6186/636/suppl/DCI
Radermacher FJ (2004) Balance or destruction: ecosocial market economy as a key to global sustainable development. Ökosoziales Forum Europa, Vienna
Radermacher FJ, Beyers B (2007) Welt mit Zukunft – Überleben im 21. Jahrhundert. Murmann Verlag, Hamburg [new printing 2011]
Sharma JK (2010) Fundamentals of business statistics. Pearson Education India, Delhi
Thistle PD (1989) Duality between generalized Lorenz curves and distribution functions. Econ Stud Q 40:183–187
Wilkinson R, Pickett K (2010) The spirit level: why more equal societies almost always do better. Penguin, London
Worldbank (2001) World Development Report 2000/2001. Report, Washington
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2015 Springer International Publishing Switzerland
About this chapter
Cite this chapter
Kämpke, T., Radermacher, F.J. (2015). Pareto Distribution, Self-similarity and Empirics. In: Income Modeling and Balancing. Lecture Notes in Economics and Mathematical Systems, vol 679. Springer, Cham. https://doi.org/10.1007/978-3-319-13224-2_7
Download citation
DOI: https://doi.org/10.1007/978-3-319-13224-2_7
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-13223-5
Online ISBN: 978-3-319-13224-2
eBook Packages: Business and EconomicsEconomics and Finance (R0)