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	Clark Density Model	Bid-Rent Analysis
分野	Human Geography	Human Geography
系統	Regression model	Regression model
提唱年	1951	1964
提唱者	Colin Clark	William Alonso
種類	Empirical regression model of urban population density decline with distance	Theory of urban land rent and land-use allocation by distance to the centre
原典	Clark, C. (1951). Urban population densities. Journal of the Royal Statistical Society. Series A (General), 114(4), 490–496.	Alonso, W. (1964). Location and Land Use: Toward a General Theory of Land Rent. Harvard University Press, Cambridge, MA. ISBN: 9780674537019
別名	Clark's Law, Negative-Exponential Density Model, Exponential Population Density Gradient, Clark Density Gradient	Bid-Rent Theory, Alonso Bid-Rent Model, Urban Land-Rent Model, Bid-Rent Curve Analysis
関連	4	4
概要	The Clark density model is the classic empirical description of how urban population density falls with distance from the city centre, formulated by the economist Colin Clark in 1951. It states that density declines exponentially outward from a central peak, so that plotting the logarithm of density against distance yields a straight line whose slope is the density gradient. This negative-exponential 'law' became the standard model of urban spatial structure and the empirical foundation for later monocentric-city theory.	Bid-rent analysis is the urban-economics theory that explains how land rent and land use are organized by distance to the city centre. Developed by William Alonso in 1964, it represents each land use — commerce, industry, housing — by a bid-rent curve giving the maximum rent that use is willing to pay at each distance from the central business district. Because uses with steeper curves outbid others for central land, the observed rent is the upper envelope of all the curves, and the city sorts into concentric zones with the highest bidder winning each ring.