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Micro-macro relation of production: double scaling law for statistical physics of economy

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  • Hideaki Aoyama
  • Yoshi Fujiwara
  • Mauro Gallegati

Abstract

We show that an economic system populated by multiple agents generates an equilibrium distribution in the form of multiple scaling laws of conditional probability density functions, which are sufficient for characterizing the probability distribution. The existence of the double scaling law is demonstrated empirically for the sales and the labor of one million Japanese firms. Theoretical study of the scaling laws suggests lognormal joint distributions of sales and labor and a scaling law for labor productivity, both of which are confirmed empirically. This framework offers characterization of the equilibrium distribution with a small number of scaling indices, which determine macroscopic quantities, thus setting the stage for an equivalence with statistical physics, bridging micro- and macro-economics. Copyright Springer-Verlag Berlin Heidelberg 2015

Suggested Citation

  • Hideaki Aoyama & Yoshi Fujiwara & Mauro Gallegati, 2015. "Micro-macro relation of production: double scaling law for statistical physics of economy," Journal of Economic Interaction and Coordination, Springer;Society for Economic Science with Heterogeneous Interacting Agents, vol. 10(1), pages 67-78, April.
    • Handle: RePEc:spr:jeicoo:v:10:y:2015:i:1:p:67-78
    DOI: 10.1007/s11403-014-0124-6
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    1. Aoyama,Hideaki & Fujiwara,Yoshi & Ikeda,Yuichi & Iyetomi,Hiroshi & Souma,Wataru Preface by-Name:Yoshikawa,Hiroshi, 2010. "Econophysics and Companies," Cambridge Books, Cambridge University Press, number 9780521191494, January.
    2. Qi Li & Jeffrey Scott Racine, 2006. "Nonparametric Econometrics: Theory and Practice," Economics Books, Princeton University Press, edition 1, volume 1, number 8355.
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    1. Hosseiny, Ali & Gallegati, Mauro, 2017. "Role of intensive and extensive variables in a soup of firms in economy to address long run prices and aggregate data," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 470(C), pages 51-59.

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