Researchers have established that there is a power-law relationship between various urban indicators — such as revenue and wealth — and city population size, meaning that these socio-economic quantities increase more than proportionally as the city population expands. Interpretations of this relationship include high levels of social interconnectivity, social exchange, and industrial complexity in dense urban systems, which drive further developments in these cities. Yet, existing models of the scaling phenomenon assume that all of the residents of a city have equal levels of productivity and numbers of network contacts — and that they equally contribute to the city’s total outputs — when, in fact, cities exhibit heavy-tail distributions, in which small fractions of the population contribute to large proportions of the urban indicators. In a recent work, Martin Arvidsson and colleagues acknowledge the skewness of urban indicators and offer a comprehensive study on how the heavy tails contribute to the urban scaling relationship.
Using micro-level data from Sweden, Russia and the United States, the authors show that on average — and across different indicators of interconnectivity, productivity, and innovation — the top 10% of the population is responsible for 50% of the city’s output; as a matter of fact, removing the top 10% from the data substantially reduces the scaling exponent. In addition, the authors demonstrate that deviations in city tails account for deviations from scaling laws, which might explain why some cities outperform or underperform on a given urban indicator. Notably, the authors develop an agent-based model that describes how within-city distributions and scaling exponents are positively linked, which reproduces many of the empirical features observed in the study. Such a model can be used by policymakers to derive a more detailed picture of urban growth. Perhaps more importantly, both the study and the model shed a light on how urban inequality is associated with the socio-economic growth of cities.
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