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central place theory

  A theoretical account of the size and distribution of settlements within an urban system in which marketing is the predominant urban function. The theory assumes that both buyers (customers) and sellers (shopowners) make utility-maximizing decisions: the theory is normative, showing what might appear in certain idealized circumstances.

The two main approaches to central place theory were developed by German economic geographers — Walter Christaller and August Lösch. Christaller dealt only with retailing functions, and based his theory on two concepts: the range of a good (the maximum distance a consumer will travel to purchase that good alone); and the threshold for a good (the minimum volume of business necessary for an establishment selling that good alone to be commercially viable). He assumed constant utilities across all consumers and all shopowners and also that different goods would have different ranges and thresholds, which would determine both the number and distribution of establishments — providing a good in an area with a given population.

Christaller (1966) grouped retail establishments into seven orders, with similar thresholds and ranges within each. To derive the geography of the location of the different orders, he argued that shopowners locate their establishments as close to customers as possible, to minimize travelling costs and so maximize both shop turnover and consumer satisfaction: shops are located centrally within their hinterlands.

If population is uniformly distributed across an area where movement in all directions is unimpeded, then meeting this centrality requirement produces a hexagonal network of shop locations in central places. (Hexagons are the most efficient geometrical figures for the exhaustion of a territory without overlap.) Central places with the lowest order functions (having the smallest thresholds and ranges) have the densest network, those in the next order have a less dense hexagonal network, and so forth. All central places of a particular order also contain all of the characteristic functions of the lower order centres (so that if first order central places are characterized by grocers\' shops, second order places by butchers\' shops, and third order places by hardware stores, then every third order central place will contain grocers\' and butchers\' shops as well as one or more hardware stores). This produces a hierarchy of central places — with seven levels according to the original theory (whose details were influenced by Christaller\'s empirical observations in southern Germany).

Christaller suggested three ways in which that hierarchical spatial structure could be organized. The first (a in the figure) minimizes the number of settlements serving an area by having each at the meeting point of three hexagons. This is his k = 3 (or marketing principle) model, in which the number of settlements at each level of the hierarchy below the second is three times the number at the next highest. (Thus, with one at the highest, seventh, order, the numbers are 1, 2, 6, 18, 54, 162, 486.) The figure (a) illustrates this arrangement with a three-level hierarchy only.

In Christaller\'s k = 4 (or transport principle) model the goal is to minimize the length of roads needed to join all adjacent pairs of central places. As shown in (b), each settlement is centrally located on each side of a hexagon, at the boundary of two rather than three hinterlands. The number of settlements is thus greater than in the k = 3 model (in the ratio 1, 2, 8, 32, 128, 512, 2048). Finally, he suggested a k = 7 (or administrative principle) model (c in the figure) in which each lower order hinterland nested exclusively within that of a single higher-order central place only — producing a sequence of 1, 6, 42, 294, 2058, 14,406, and 100,842 settlements.

Lösch\'s (1954) model was less restrictive than Christaller\'s because rather than bundle functions into orders he treated each as having a separate range, threshold and hexagonal hinterland. Wherever feasible, establishments in these functions were clustered in the same settlements but in his system all central places with a function having a particular threshold need not contain examples of all functions with smaller thresholds. The result is a more complicated pattern of central places than in Christaller\'s presentation, and Lösch also incorporated other urban functions (such as manufacturing). Whereas Christaller\'s theory predicted a stepped hierarchical form to the city-size distribution (i.e. all places in an order had the same population), Losch\'s was consistent with a continuous distribution of population sizes.

These two theories were central to much of the early work on spatial structures undertaken during geography\'s quantitative revolution in the 1960s. Christaller\'s, in particular, was used many times as the basis for searches for hierarchically structured, hexagonal arrangements of central places, both in rural areas and within cities (see also retailing, geography of), and for distance-minimizing patterns of consumer shopping choice. Christaller\'s was used also as the basis for planning settlement patterns, in a variety of contexts. The \'marketing principle\' was used in the newly-settled polders of the Netherlands, for example, whereas the \'adminisrative principle\' was employed under the Nazis in the \'resolution\' of the \'Eastern Question\': Christaller was an expert adviser in the \'Reich Commissariat for the Strengthening of Germany\' (Freeman, 1987). (RJJ)

{img src=show_image.php?name=bkhumgeofig7a.gif }

{img src=show_image.php?name=bkhumgeofig7b.gif }

{img src=show_image.php?name=bkhumgeofig7c.gif }

central place theory The size and spacing of central places, plus their hinterlands (left) and routes (right), according to three variants of Christaller\'s model: (a) the market principle, which minimum of the number of centres: (b) the transport principle, which minimizes the road length: and (c) the administrative principle, in which hinterlands are nested hierarchically

References Christaller, W. 1966: Central places in Southern Germany, trans. C. W. Baskin. Englewood Cliffs, NJ and London: Prentice-Hall (first German edition, 1933). Freeman, M.J. 1987: Atlas of Nazi Germany. London: Croom Helm. Lösch, A. 1954: The economics of location. New Haven, CT: Yale University Press; Oxford: Oxford University Press (first German edition, 1940);

Suggested Reading Beavon, K.S.O. 1977: Central place theory: a reinterpretation. London and New York: Longman. Berry, B.J.L. 1967: Geography of market centers and retail distribution. Englewood Cliffs, NJ and London: Prentice-Hall. Berry, B.J.L and Parr, J.B. 1988: Geography of market centers and retail distribution, 2nd edn. Englewood Cliffs, NJ: Prentice-Hall. Preston, R.E. 1985: Christaller\'s neglected contribution to the study of the evolution of central places. Progress in Human Geography 9: 177-93.



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