One-Dimensional Urban Scaling

TL;DR

This paper explores how a simple one-dimensional model of a city can reveal fundamental urban scaling behaviors, demonstrating increasing returns to scale through simulations and theory.

Contribution

It introduces a one-dimensional urban model to intuitively analyze scaling effects, providing insights into agglomeration and economies of scale in simplified city structures.

Findings

Decreasing accessibility with distance can lead to agglomeration effects.

The model shows increasing returns to scale in one-dimensional cities.

Numerical and theoretical analysis support the findings.

Abstract

In this paper, we apply recent findings from urban scaling theory to evaluate how it could be applied to a one-dimensional archetypal city. Our focus is on how the simplicity of a one-dimensional model can provide intuitive insights that might be obscured in more complex, multidimensional models. With this instructive model, it is possible to visualize that if the population's accessibility decreases more slowly than the increase in distance, an agglomeration effect occurs. This leads to increasing returns to scale when considering interactions between people or economies of scale in the case of amenities that serve the city. These findings highlight a key characteristic of complex systems: interacting parts that together exhibit properties that are not evident when considered individually. The results presented here are derived from both numerical simulations and theoretical analysis. Although one-dimensionality is used here as a simplification, many natural (e.g., Su{\l}oszowa in Poland) and artificial cities (e.g., The Line in Saudi Arabia) worldwide are shaped this way.