Description 
1 online resource (xii, 171 pages) : illustrations 
Series 
Lecture notes in economics and mathematical systems, 00758442 ; 632 

Lecture notes in economics and mathematical systems ; 632.

Contents 
Introduction  Continuous Gibrat's Law and Gabaix's Derivation of Zipf's Law  Flow of Firm Creation  Useful Properties of Realizations of the Geometric Brownian Motion  Exit or "Death" of Firms  Deviations from Gibrat's Law and Implications for Generalized Zipf's Laws  Firm's Sudden Deaths  NonStationary Mean Birth Rate  Properties of the Realization Dependent Distribution of Firm Sizes  Future Directions and Conclusions  List of the Main Notations 
Summary 
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) timevarying 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 
Bibliography 
Includes bibliographical references (pages 167170) and index 
Notes 
Print version record 
Subject 
Urban economics  Mathematical models


Economic geography  Mathematical models.


Zipf's law.


Cities and towns  Growth  Mathematical models


Economics.


Distribution (Probability theory)


Economics


distribution (statisticsrelated concept)


economics.


Affaires.


Science économique.


Economie de l'entreprise.


Cities and towns  Growth  Mathematical models


Economic geography  Mathematical models


Urban economics  Mathematical models


Zipf's law

Form 
Electronic book

Author 
Malevergne, Yannick


Sornette, Didier, 1957

ISBN 
9783642029462 

3642029469 
