Issue |
ESAIM: Proc.
Volume 36, April 2012
European Conference on Iteration Theory 2010
|
|
---|---|---|
Page(s) | 189 - 196 | |
DOI | https://doi.org/10.1051/proc/201236015 | |
Published online | 28 August 2012 |
Exponential wealth distribution : a new approach from functional iteration theory*
1
Dep. of Computer Science & BIFI, Faculty of Science,
Universidad de Zaragoza, Zaragoza, Spain
e-mail: rilopez@unizar.es
2
Dep. of Mathematical and Informatics Engineering, Universidad
Pública de Navarra, Pamplona, Spain
e-mail: jl.lopez@unavarra.es
3
Eumetsat, Darmstadt, Germany
e-mail: xcalbet@googlemail.com
Different approaches are possible in order to derive the exponential regime in statistical systems. Here, a new functional equation is proposed in an economic context to explain the wealth exponential distribution. Concretely, the new iteration [1] given by
It is found that the exponential distribution is a stable fixed point of this functional iteration equation. From this point of view, it is easily understood why the exponential wealth distribution (or by extension, other kind of distributions) is asymptotically obtained in different multi-agent economic models.
Résumé
Différentes approches pour dériver le régime asymptotique exponentiel dans les systèmes statistiques sont possibles. Ici une nouvelle équation fonctionnelle est proposée, dans le cadre des systèmes économiques, pour expliquer la distribution exponentielle. Nous montrons que cette distribution est le seul point fixe vers lequel la dynamique de cette équation fonctionnelle évolue quand l’itération va vers l’infini. De ce point de vue, il est facile de comprendre l’ubiquité de cette distribution (ou d’autres) en différents problèmes statistiques réels.
Mathematics Subject Classification: 91B64 / 91B50 / 62P20
Key words: Econophysics / Wealth distributions / Random models / Statistical equilibrium
Mots clés : Econophysique / Distribution des richesses / Modèle aleatoire / Equilibre statistique
R.L-R. acknowledges financial support from the Spanish research project DGICYT-FIS2009-13364-C02-01.
e-mail: rilopez@unizar.es
© EDP Sciences, SMAI 2012
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