Geodesic
Exponential wealth distribution : a new approach from functional iteration theory
Ricardo López-Ruiz1 ; José-Luis López2 ; Xavier Calbet3
1Dep. of Computer Science & BIFI, Faculty of Science, Universidad de Zaragoza, Zaragoza, Spain
2Dep. of Mathematical and Informatics Engineering, Universidad Pública de Navarra, Pamplona, Spain
3Eumetsat, Darmstadt, Germany
ESAIM. Proceedings, Tome 36 (2012), pp. 189-196
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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 \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} f n + 1 ( x ) = ∫ ∫ u + v > x   f n ( u ) f n ( v ) u + v d u d v   . 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.
DOI : 10.1051/proc/201236015

Ricardo López-Ruiz  1   ; José-Luis López  2   ; Xavier Calbet  3

1 Dep. of Computer Science & BIFI, Faculty of Science, Universidad de Zaragoza, Zaragoza, Spain
2 Dep. of Mathematical and Informatics Engineering, Universidad Pública de Navarra, Pamplona, Spain
3 Eumetsat, Darmstadt, Germany 
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     author = {Ricardo L\'opez-Ruiz and Jos\'e-Luis L\'opez and Xavier Calbet},
     title = {Exponential wealth distribution : a new approach from functional iteration theory},
     journal = {ESAIM. Proceedings},
     pages = {189--196},
     year = {2012},
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     doi = {10.1051/proc/201236015},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/proc/201236015/}
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Ricardo López-Ruiz; José-Luis López; Xavier Calbet. Exponential wealth distribution : a new approach from functional iteration theory. ESAIM. Proceedings, Tome 36 (2012), pp. 189-196. doi: 10.1051/proc/201236015

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