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	Urban Scaling Laws	Urban Density Gradient Model
Field	Urban Studies	Human Geography
Family	Regression model	Regression model
Year of origin	2007	1951
Originator	Luís Bettencourt & Geoffrey West	Colin Clark; Edwin Mills & Richard Muth (theory); Bruce Newling (quadratic form)
Type	Power-law regression of urban indicators against population size	Family of functional models of urban population density as a function of distance from the centre
Seminal source	Bettencourt, L. M. A., Lobo, J., Helbing, D., Kühnert, C., & West, G. B. (2007). Growth, innovation, scaling, and the pace of life in cities. Proceedings of the National Academy of Sciences, 104(17), 7301–7306.	Clark, C. (1951). Urban population densities. Journal of the Royal Statistical Society. Series A (General), 114(4), 490–496.
Aliases	Urban Scaling, Settlement Scaling Theory, Power-Law Urban Scaling, Superlinear and Sublinear Urban Scaling	Urban Density Function, Population Density Gradient, Density-Distance Function, Monocentric Density Model
Related	4	4
Summary	Urban scaling laws describe how the aggregate properties of cities — wealth, innovation, infrastructure, crime — change systematically with population size, following power laws rather than growing in simple proportion. Building on the 2007 work of Luís Bettencourt, Geoffrey West and colleagues, the framework shows that socioeconomic outputs typically scale superlinearly (a doubling of population more than doubles GDP and patents) while infrastructure scales sublinearly (larger cities need proportionally fewer roads and cables per person), with a single exponent β capturing the regularity across an entire urban system.	The urban density gradient model is the broad family of functional relationships that describe how population density varies with distance from a city's centre. Its canonical member is Colin Clark's 1951 negative-exponential form, but the family also includes Bruce Newling's quadratic-exponential function that permits a density crater at the core, simpler linear and Smeed forms, and the economic micro-foundation supplied by the Muth-Mills monocentric city model. Together these give planners and economists a compact, comparable language for urban spatial structure.