02980nmm a2200349 u 4500001001200000003002700012005001700039007002400056008004100080020001800121100002600139245012300165250001700288260006300305300004200368505047900410653002300889653004200912653002700954653001900981653001701000653001801017700003401035700003101069041001901100989003601119490005601155028003001211856007201241082000801313520130901321EB000382670EBX0100000000000000023572200000000000000.0cr|||||||||||||||||||||130626 ||| eng a97836420294621 aSaichev, Alexander I.00aTheory of Zipf's Law and BeyondhElektronische Ressourcecby Alexander I. Saichev, Yannick Malevergne, Didier Sornette a1st ed. 2010 aBerlin, HeidelbergbSpringer Berlin Heidelbergc2010, 2010 aXII, 171 p. 44 illusbonline resource0 aContinuous Gibrat#x2019;s Law and Gabaix#x2019;s Derivation of Zipf#x2019;s Law -- Flow of Firm Creation -- Useful Properties of Realizations of the Geometric Brownian Motion -- Exit or #x201C;Death#x201D; of Firms -- Deviations from Gibrat#x2019;s Law and Implications for Generalized Zipf#x2019;s Laws -- Firm#x2019;s Sudden Deaths -- Non-stationary Mean Birth Rate -- Properties of the Realization Dependent Distribution of Firm Sizes -- Future Directions and Conclusions aProbability Theory aMacroeconomics and Monetary Economics aQuantitative Economics aMacroeconomics aEconometrics aProbabilities1 aMalevergne, Yannicke[author]1 aSornette, Didiere[author]07aeng2ISO 639-2 bSpringeraSpringer eBooks 2005-0 aLecture Notes in Economics and Mathematical Systems50a10.1007/978-3-642-02946-240uhttps://doi.org/10.1007/978-3-642-02946-2?nosfx=yxVerlag3Volltext0 a339 aZipf'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