Modeling the origin of urban output scaling laws

TL;DR

This paper presents a physics-inspired model explaining superlinear urban output scaling as a result of increased collaboration likelihood in larger populations, supported by empirical data on crime types.

Contribution

It introduces a novel, non-power-law model linking human interactions to superlinear scaling in urban outputs, validated with real-world crime data.

Findings

Superlinear scaling arises from increased collaboration opportunities in larger cities.

The model predicts a non-power-law form of scaling, differing from traditional models.

Empirical data on seven crime types supports the model's predictions.

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.