title: A model of urban scaling laws based on distance dependent interactions.
abstract: Socio-economic related properties of a city grow faster than a linear relationship with the population, in a log-log plot, the so-calledsuperlinear scaling. Conversely, the larger a city, the more efficient it is in the use of its infrastructure, leading to asublinear scalingon these variables. In this work, we addressed a simple explanation for those scaling laws in cities based on the interaction range between the citizens and on the fractal properties of the cities. To this purpose, we introduced a measure of social potential which captured the influence of social interaction on the economic performance and the benefits of amenities in the case of infrastructure offered by the city. We assumed that the population density depends on the fractal dimension and on the distance-dependent interactions between individuals. The model suggests that when the city interacts as a whole, and not just as a set of isolated parts, there is improvement of the socio-economic indicators. Moreover, the bigger the interaction range between citizens and amenities, the bigger the improvement of the socio-economic indicators and the lower the infrastructure costs of the city. We addressed how public policies could take advantage of these properties to improve cities development, minimizing negative effects. Furthermore, the model predicts that the sum of the scaling exponents of social-economic and infrastructure variables are 2, as observed in the literature. Simulations with an agent-based model are confronted with the theoretical approach and they are compatible with the empirical evidences.
authors.affiliation: Departamento de Física (DFI) , Universidade Federal de Lavras (UFLA) , Caixa Postal 3037, 37200-000 Lavras, Minas Gerais, Brazil.
authors.forename: Fabiano L
authors.initials: FL
authors.lastname: Ribeiro
authors.affiliation: Laboratory on Human-Environment Relations in Urban Systems-HERUS , École polytechnique fédérale de Lausanne (EPFL) Station 2 , 1015 Lausanne, Switzerland.
authors.forename: Joao
authors.initials: J
authors.lastname: Meirelles
authors.affiliation: EACH-Universidade de São Paulo (USP) , Av. Arlindo Bettio, 1000 (Vila Guaraciaba), 03828-000 São Paulo, SP, Brazil.
authors.forename: Fernando F
authors.initials: FF
authors.lastname: Ferreira
authors.affiliation: EACH-Universidade de São Paulo (USP) , Av. Arlindo Bettio, 1000 (Vila Guaraciaba), 03828-000 São Paulo, SP, Brazil.
authors.forename: Camilo Rodrigues
authors.identifier: 0000-0001-6783-6695
authors.initials: CR
authors.lastname: Neto
keywords: agglomeration effects; complex systems; power laws; public policies; scaling laws; urban indicators