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	Urban Density Gradient Model	Von Thünen Land-Use Model
Field	Human Geography	Human Geography
Family	Regression model	Regression model
Year of origin	1951	1826
Originator	Colin Clark; Edwin Mills & Richard Muth (theory); Bruce Newling (quadratic form)	Johann Heinrich von Thünen
Type	Family of functional models of urban population density as a function of distance from the centre	Theory of agricultural land use and land rent around a market
Seminal source	Clark, C. (1951). Urban population densities. Journal of the Royal Statistical Society. Series A (General), 114(4), 490–496.	von Thünen, J. H. (1966). Von Thünen's Isolated State (P. Hall, Ed.; C. M. Wartenberg, Trans.). Pergamon Press, Oxford. (Original work published 1826).
Aliases	Urban Density Function, Population Density Gradient, Density-Distance Function, Monocentric Density Model	Von Thunen Model, Isolated State Model, Agricultural Location Theory, Von Thünen Rings
Related	4	4
Summary	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.	The von Thünen model is the founding theory of agricultural land use, explaining how the pattern of farming around a market emerges from transport costs and land rent. Set out by Johann Heinrich von Thünen in his 1826 work Der isolierte Staat, it imagines an isolated city on a uniform plain and shows that the rent a farmer can pay for land falls with distance to the market, so different crops and farming intensities sort themselves into concentric rings around the city. It is the earliest formal model in economic geography and the ancestor of bid-rent and urban land-use theory.