Reilly's challenge: new laws of retail gravitation which define systems of central places
This paper attempts a reformulation and generalisation of Reilly's (1931) law of retail gravitation. Reilly himself challenged workers in the field to produce new evidence which would refute or strength his law, and developments in spatial-interaction theory during the last decade are used here in taking up this challenge. A critique of Reilly's law sets the scene: by adopting a gravity model more general than the Newtonian model used by Reilly, it is shown how the limitations of the law with respect to hierarchy, spatial competition, locational size, and the symmetry of trade flows, are overcome. In particular the notion of Reilly's law as a special case of the market-area analysis originating from Fetter (1924) and Hotelling (1929) is demonstrated in terms of a theory of the breakpoint implying spatial price - cost indifference. Another approach, through entropy-maximisation and its dual problem, leads to similar conclusions with regard to prices, and it also serves to introduce multicentred spatial competition. These ideas are then generalised in several ways: through notions about the influence of prior spatial information, through concepts of consumer as well as producer market areas or fields, and through the implications of the analysis for the family of spatial-interaction models. A speculation on the relationship of price differentials to Tobler's (1975) interaction winds is made, and the paper is concluded with an application of these models to the definition of an urban hierarchy in the Reading subregion.
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