Lecture Notes in Economics and Mathematical Systems

Theory of Zipf's Law and Beyond

Authors: Saichev, Alexander I., Malevergne, Yannick, Sornette, Didier

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About this book

Zipf's law is one of the few quantitative reproducible regularities found in economics. It states that, for most countries, the size distributions of city sizes and of firms are power laws with a specific exponent: the number of cities and of firms with sizes greater than S is inversely proportional to S. Zipf's law also holds in many other scientific fields. Most explanations start with Gibrat's law of proportional growth (also known as "preferential attachment'' in the application to network growth) but need to incorporate additional constraints and ingredients introducing deviations from it. This book presents a general theoretical derivation of Zipf's law, providing a synthesis and extension of previous approaches. The general theory is presented in the language of firm dynamics for the sake of convenience but applies to many other systems. It takes into account (i) time-varying firm creation, (ii) firm's exit resulting from both a lack of sufficient capital and sudden external shocks, (iii) the coupling between firm's birth rate and the growth of the value of the population of firms. The robustness of Zipf's law is understood from the approximate validity of a general balance condition. A classification of the mechanisms responsible for deviations from Zipf's law is also offered.

Table of contents (10 chapters)

  • Introduction

    Saichev, Alexander (et al.)

    Pages 1-7

  • Continuous Gibrat’s Law and Gabaix’s Derivation of Zipf’s Law

    Saichev, Alexander (et al.)

    Pages 9-18

  • Flow of Firm Creation

    Saichev, Alexander (et al.)

    Pages 19-40

  • Useful Properties of Realizations of the Geometric Brownian Motion

    Saichev, Alexander (et al.)

    Pages 41-57

  • Exit or “Death” of Firms

    Saichev, Alexander (et al.)

    Pages 59-72

Buy this book

eBook $109.00
price for Mexico (gross)
  • ISBN 978-3-642-02946-2
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $139.00
price for Mexico
  • ISBN 978-3-642-02945-5
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Theory of Zipf's Law and Beyond
Authors
Series Title
Lecture Notes in Economics and Mathematical Systems
Series Volume
632
Copyright
2010
Publisher
Springer-Verlag Berlin Heidelberg
Copyright Holder
Springer-Verlag Berlin Heidelberg
eBook ISBN
978-3-642-02946-2
DOI
10.1007/978-3-642-02946-2
Softcover ISBN
978-3-642-02945-5
Series ISSN
0075-8442
Edition Number
1
Number of Pages
XII, 171
Number of Illustrations and Tables
44 b/w illustrations
Topics