Modeling the origin of urban output scaling laws

Abstract

Urban outputs often scale superlinearly with city population. A difficulty in understanding the mechanism of this phenomenon is that different outputs differ considerably in their scaling behaviors. Here, we formulate a physics-based model for the origin of superlinear scaling in urban outputs by treating human interaction as a random process. Our model suggests that the increased likelihood of finding required collaborations in a larger population can explain this superlinear scaling, which our model predicts to be non-power-law. Moreover, the extent of superlinearity should be greater for activities that require more collaborators. We test this model using a novel dataset for seven crime types and find strong support.

8 pages, 5 figures

References in corpus (6)

• Power-law distributions in empirical data
• Dynamics of person-to-person interactions from distributed RFID sensor networks
• Universal power law governing pedestrian interactions
• Superlinear Scaling for Innovation in Cities
• From global scaling to the dynamics of individual cities
• Empirical analysis on the connection between power-law distributions and allometries for urban indicators

Cited by in corpus (5)

• More crime in cities? On the scaling laws of crime and the inadequacy of per capita rankings -- a cross-country study
• Dynamics of Cities
• Scaling Laws for Function Diversity and Specialization Across Socioeconomic and Biological Complex Systems
• Scaling of Urban Income Inequality in the United States
• Mathematical models to explain the origin of urban scaling laws: a synthetic review