eprintid: 646
rev_number: 16
eprint_status: archive
userid: 2
dir: disk0/00/00/06/46
datestamp: 2011-06-30 14:26:16
lastmod: 2013-11-21 13:03:15
status_changed: 2011-06-30 14:26:16
type: article
metadata_visibility: show
item_issues_count: 0
creators_name: Pammolli, Fabio
creators_name: Buldyrev, Sergey V.
creators_name: Riccaboni, Massimo
creators_name: Yamasaki, Kazuko
creators_name: Fu, Dongfeng
creators_name: Matia, Kaushik
creators_name: Stanley, H. Eugene
creators_id: f.pammolli@imtlucca.it
creators_id: 
creators_id: massimo.riccaboni@imtlucca.it
creators_id: 
creators_id: 
creators_id: 
creators_id: 
title: A generalized preferential attachment model for business firms growth rates: II. Mathematical treatment
ispublished: pub
subjects: HB
subjects: HG
subjects: QC
divisions: EIC
full_text_status: none
note: PACS.  89.75.Fb Structures and organization in complex systems - 89.65.Gh Economics; econophysics, financial markets, business and management 
abstract: We present a preferential attachment growth model to obtain the distribution P(K) of number of units K in the classes which may represent business firms or other socio-economic entities. We found that P(K) is described in its central part by a power law with an exponent ϕ = 2+b/(1-b) which depends on the probability of entry of new classes, b. In a particular problem of city population this distribution is equivalent to the well known Zipf law. In the absence of the new classes entry, the distribution P(K) is exponential. Using analytical form of P(K) and assuming proportional growth for units, we derive P(g), the distribution of business firm growth rates. The model predicts that P(g) has a Laplacian cusp in the central part and asymptotic power-law tails with an exponent ζ = 3. We test the analytical expressions derived using heuristic arguments by simulations. The model might also explain the size-variance relationship of the firm growth rates. 
date: 2007
date_type: published
publication: The European Physical Journal B
volume: 57
number: 2
publisher: Springer
pagerange: 131-138
id_number: 10.1140/epjb/e2007-00165-8
refereed: TRUE
issn: 1434-6028
official_url: http://dx.doi.org/10.1140/epjb/e2007-00165-8
citation:   Pammolli, Fabio and Buldyrev, Sergey V. and Riccaboni, Massimo and Yamasaki, Kazuko and Fu, Dongfeng and Matia, Kaushik and Stanley, H. Eugene  A generalized preferential attachment model for business firms growth rates: II. Mathematical treatment.  The European Physical Journal B, 57 (2).  pp. 131-138.  ISSN 1434-6028      (2007)