Unified Zipf-Gibrat Framework for City Formation and Growth: A Theory and Empirics behind the Core-Periphery Tiebout-Weibull Model
Anna KaźmierczakDepartment of Mathematics and Computer Science, University of Lodz, Banacha 22, Lodz, 90-238, PolandAlexander ShapovalDepartment of Mathematics and Computer Science, University of Lodz, Banacha 22, Lodz, 90-238, PolandShlomo WeberFaculty of Humanities, Natural and Social Sciences, New Uzbekistan University, Tashkent, Uzbekistan
ABI
Abstract
This paper examines the patterns of city formation driven by two seemingly different empirical regularities: the rank distribution of cities (Zipf’s Law) and the patterns of city growth (Gibrat’s Law). We combine the core-periphery approach of economic geography (Prebish 1950 and Friedmann 1966) with the local public goods model (Tiebout 1956) to construct an equilibrium distribution of cities. Then, by endowing the equilibrium with the Weibull distribution of individual locations, we provide a unified economic foundation for Zipf’s and Gibrat’s Laws. We also show that our core-periphery Tiebout-Weibull equilibrium distribution is in almost total compliance with the U.S. Census data.
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