Association between population distribution and urban GDP scaling

Area of Science:

• Urban studies
• Economic geography
• Complexity science

Background:

• Urban scaling and Zipf's law are key theories in urban science, often studied in isolation.
• Previous research has not fully explored the relationship between these two fundamental urban paradigms.

Purpose of the Study:

• To investigate the empirical connection between urban scaling laws and Zipf's law across numerous global cities.
• To derive a mathematical expression linking the exponents of urban scaling and Zipf's law.
• To analyze how population distribution affects urban Gross Domestic Product (GDP) scaling.

Main Methods:

• Analysis of population and GDP data for nearly 5,000 cities in 96 countries.
• Empirical validation of the relationship between urban scaling and Zipf's law exponents.
• Development of a model to simulate the observed relationships and account for random variations.

Main Results:

• A significant empirical link was demonstrated between urban scaling and Zipf's law.
• An expression relating the urban scaling and Zipf exponents was derived and validated through simulations.
• Increasing returns to scale in urban GDP were observed globally, but less pronounced in countries with more metropolises (smaller Zipf exponent).

Conclusions:

• Urban scaling and Zipf's law are interconnected, challenging the view of them as independent phenomena.
• The distribution of city sizes (Zipf's law) influences the scaling of urban GDP.
• Intra-city dynamics alone do not fully explain urban scaling; population distribution plays a crucial role.