Starting in the 1930s, German geographer August Lösch began to build upon and modify Christaller’s model. He did this, in part, because he noticed that the variation in K is very important in shaping the organizations of centers and the numbers of centers at each level in a hierarchy. Because Christaller arbitrarily choose the K=3, K=4, and K-7 values, Lösch argued that, in such a model, no particular K value could be considered sacrosanct. From the point of view of Lösch, Christaller’s three locational principles were simply interesting special cases. Lösch suggests that, in fact, a large number of K values can be used. The only restriction, according to Lösch, is that a hexagonal pattern must be maintained in the model. In contrast to Christaller K=7 hierarchy of 1,6,42,294, Lösch put forth that a K=7 hierarchy would be more efficient if it were arranged 7, 13, and 19 because, in these cases, places are not divided among several different centers.

This modification of Christaller’s original model is important because many market areas of sizes K=3, 4, . . ., n are situated so that they all have at least one common center, and with the rotation of these hexagons we are able to achieve six sectors with central places that include many types of businesses. Additionally, this process creates a maximization of agglomeration relative to production locations, maximized local purchases, and minimizes the total distance between production points. The resultant pattern results in city-rich and city-poor sectors. This arrangement of linear clusters of central places conforms to the principle of least effort (that people will generally attempt to minimize the effort needed to do business, i.e., all else equal, they will trade at the nearest retail establishment). The graphic above provides a visual demonstration of this concept. The basic properties of the city-rich part of the model are that the greatest numbers of locations coincide, local purchases are maximized, distances between central places are minimized, and the volume of shipments and the total length of transportation routes are minimized. The city-poor parts of the model account for an uneven distribution of population, cities, and businesses.

Löschian Model.
Credit: Lösch (1954, cited in Gore 1984)

In order to arrive at these modifications, Lösch identified the three smallest market areas. Lösch worked on the assumption that a farmer at a given location (A1) produces a commodity in excess of the need in his market area and therefore sells the excess to customers in adjacent market areas (A2 and 3). This results in a triangular market area. If A1 increases output, it may become a central place (B1) and the farmer will then sell his output in a hexagon consisting of six triangles. The market area of B1 would then be increased by encroaching on the market areas of neighboring central places (B2 and 3), by either rotating the hexagon around B1 or by rotating and enlarging the hexagon so that it expands into open space without touching any other settlement (see graphic above).  Lösch indicated that the smallest market areas are only the smallest in an infinite series. The multiple rotations and enlargements of hexagons created market areas with K values of 9, 12, 13, 16, 19, 21, and 25. The landscape, according to Lösch, is made up of a discontinuous series of central place possibilities, because there are variations in the efficiencies of the various possible arrangements.

Therefore, the models developed by Christaller and Lösch are very different because they result in markedly different systems. The permanent K constraint in Christaller’s model means that all places at the same level in a hierarchy have the same business types, and all higher-order places must contain all the business types contained in lower-order places. Lösch noted that this does not accurately reflect the spatial organization of central places in the “real world.” Thus, the model developed by Lösch presents a less definite hierarchical arrangement than does Christaller’s. In the Löschian system, settlements of the same size are not required to have the same arrangement of business types, and higher-order central places do not need to have all the functions available in lower-order places (although they will probably tend to have most of them).

Whereas central-place theory provides great insights into the hierarchy of urban places, it has shortcomings. For one thing, these models are simply descriptive in nature. Additionally, they do not take into account non-optimal human decisions and fail to consider the historical process through which capitalism developed as the framework in which places come to positions of dominance. Moreover, central-place theory deals only with relationships between consumers and producers in a region. It does not consider settlement patterns that are the result of long-distance trade between regions. Furthermore, central-place theory rests on the assumption of uniformity of space.

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