# Exponential wealth distribution : a new approach from functional iteration theory*

ESAIM: Proceedings (2012)

• Volume: 36, page 189-196
• ISSN: 1270-900X

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## Abstract

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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${\mathit{f}}_{\mathit{n}\mathrm{+}\mathrm{1}}\mathrm{\left(}\mathit{x}\mathrm{\right)}\mathrm{=}\mathrm{\int }{\mathrm{\int }}_{\mathit{u}\mathrm{+}\mathit{v}\mathit{>}\mathit{x}} \frac{{\mathit{f}}_{\mathit{n}}\mathrm{\left(}\mathit{u}\mathrm{\right)}{\mathit{f}}_{\mathit{n}}\mathrm{\left(}\mathit{v}\mathrm{\right)}}{\mathit{u}\mathrm{+}\mathit{v}}\mathrm{d}\mathit{u}\mathrm{d}\mathit{v} \mathit{.}$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.

## How to cite

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López-Ruiz, Ricardo, López, José-Luis, and Calbet, Xavier. Fournier-Prunaret, D., Gardini, L., and Reich, L., eds. " Exponential wealth distribution : a new approach from functional iteration theory*." ESAIM: Proceedings 36 (2012): 189-196. <http://eudml.org/doc/251191>.

@article{López2012,
abstract = {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\begin\{equation\} f\_\{n+1\}(x) = \int\!\!\int\_\{u+v>x\}\,\{f\_n(u)f\_n(v)\over u+v\} \; \{\mathrm d\}u\{\mathrm d\}v \,. \nonumber \label\{syst1\} \end\{equation\}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.},
author = {López-Ruiz, Ricardo, López, José-Luis, Calbet, Xavier},
editor = {Fournier-Prunaret, D., Gardini, L., Reich, L.},
journal = {ESAIM: Proceedings},
keywords = {Econophysics; Wealth distributions; Random models; Statistical equilibrium; econophysics; wealth distributions; random models; statistical equilibrium},
language = {eng},
month = {8},
pages = {189-196},
publisher = {EDP Sciences},
title = { Exponential wealth distribution : a new approach from functional iteration theory*},
url = {http://eudml.org/doc/251191},
volume = {36},
year = {2012},
}

TY - JOUR
AU - López-Ruiz, Ricardo
AU - López, José-Luis
AU - Calbet, Xavier
AU - Fournier-Prunaret, D.
AU - Gardini, L.
AU - Reich, L.
TI - Exponential wealth distribution : a new approach from functional iteration theory*
JO - ESAIM: Proceedings
DA - 2012/8//
PB - EDP Sciences
VL - 36
SP - 189
EP - 196
AB - 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$$f_{n+1}(x) = \int\!\!\int_{u+v>x}\,{f_n(u)f_n(v)\over u+v} \; {\mathrm d}u{\mathrm d}v \,. \nonumber \label{syst1}$$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.
LA - eng
KW - Econophysics; Wealth distributions; Random models; Statistical equilibrium; econophysics; wealth distributions; random models; statistical equilibrium
UR - http://eudml.org/doc/251191
ER -

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