Proportionate vs disproportionate distribution of wealth of two individuals in a tempered Paretian ensemble

G. Oshanin, Yu. Holovatch and G. Schehr
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G. Oshanin: LPTMC - Laboratoire de Physique Théorique de la Matière Condensée - UPMC - Université Pierre et Marie Curie - Paris 6 - CNRS - Centre National de la Recherche Scientifique
Yu. Holovatch: ICMP - Institute for Condensed Matter Physics of NAS of Ukraine - NASU / НАН України - National Academy of Sciences of Ukraine = Національна академія наук України = Académie nationale des sciences d'Ukraine
G. Schehr: LPT - Laboratoire de Physique Théorique d'Orsay [Orsay] - UP11 - Université Paris-Sud - Paris 11 - CNRS - Centre National de la Recherche Scientifique

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Abstract: We study the distribution P(\omega) of the random variable \omega = x_1/(x_1 + x_2), where x_1 and x_2 are the wealths of two individuals selected at random from the same tempered Paretian ensemble characterized by the distribution \Psi(x) \sim \phi(x)/x^{1 + \alpha}, where \alpha > 0 is the Pareto index and $\phi(x)$ is the cut-off function. We consider two forms of \phi(x): a bounded function \phi(x) = 1 for L \leq x \leq H, and zero otherwise, and a smooth exponential function \phi(x) = \exp(-L/x - x/H). In both cases \Psi(x) has moments of arbitrary order. We show that, for \alpha > 1, P(\omega) always has a unimodal form and is peaked at \omega = 1/2, so that most probably x_1 \approx x_2. For 0

Date: 2011
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Published in Physica A: Statistical Mechanics and its Applications, 2011, 390 (23-24), pp.4340-4346. ⟨10.1016/j.physa.2011.06.067⟩

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Persistent link: https://EconPapers.repec.org/RePEc:hal:journl:hal-00611323

DOI: 10.1016/j.physa.2011.06.067

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