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AKSOE: Physik sozio-ökonomischer Systeme

AKSOE 10: Poster Session (posters are expected to be displayed the full day 8:30-18:00)

AKSOE 10.27: Poster

Mittwoch, 29. März 2006, 16:00–18:00, P2

Random fragmentation with inequality constraint: A model of income distribution — •Aparna Basu — Institute of Genomics and Integrative Biology, (at TCGA) 254 Okhla Industrial Estate-Phase 3, New Delhi 110020, INDIA

The unequal distribution of wealth in society is a universal feature that has been noted and quantified fairly early. In 1897 Wilfredo Pareto observed a power law distribution of income relating the fraction f(x) of the population earning income x, to x. Another curve frequently used to represent income inequality is the Lorenz curve connecting the proportion p of total income earned by individuals earning less than or equal to x to the proportion q of persons in this income group. The qualitative features of economic inequality typified by these relationships appear to be universal, holding across a wide variety of social, economic and political structures. Moreover, similar distributions are seen in other areas such as language, species diversity, etc. This suggests that the observed regularity may be statistical in character. In this paper, we have used the fragmentation of the unit line as a statistical model of the distribution of wealth in society, with an added constraint that forces the fragments to be unequal, thereby incorporating the observed inequality of incomes as a property of the model. The most probable distribution obtained is a variant of the Lorenz curve, and is represented by the equation P=(Q-QlnQ)^b (where Q and P are 1-q and 1-p respectively, and b is a free parameter.) We compare model results with observed data on income distribution.