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One of the central theoretical structures of Economic Geography, used to explain where cities form and how big they will grow. Its simplest models are too idealized to have much actual predictive value, but they still illustrate basic ideas of urban center formation.

Central place theory and other location theories derive from the inherent spatial character of the two basic driving forces of economics: supply and demand. Distance contributes to inelasticity of supply, adding to a supplier's cost of providing goods and services, reducing his or her profit, and thus his or her willingness to supply those goods and services into a particular area. Distance also creates an inleasticity of demand, adding to a consumer's cost of accessing the same goods and services, and reducing their willingness to travel to a particular supplier to acquire them. For any particular good or service, a balancing act takes place between these two desires.

In the mid-19th Century, German landowner Johann Heinrich von Thünen (1780-1850) laid the foundations of economic geography, working out the principles of location rent while managing his estates. His principal work, Der isoleirte Staat in Beziehung auf Landwirthschaft und Nationalökonomie, oder Untersuchungen über den Einfluss, den die Getreidepreise, der Reichtum des Bodens und die Abgaben auf den Ackerbau ausüben, was published in several parts, in 1826, 1850, and 1863. Von Thünen built his model around a single market, and the assumption that farmers would seek to maximize the amount of money (or rent) they could extract from their land. Von Thünen derived rent formulas that could be applied to any crop, but for central place theory, the important notion is that the marginal rent for a particular crop is an inverse function of distance.

R = Y (p - c - fd)

R: Marginal Rent
Y: Crop Yield
p: crop price per unit yield
c: production cost per unit yield
f: freight rate (per unit yield, per unit distance)
d: distance

The rent function for different crops will be different, based upon price, production costs, and transportation costs. At a given distance from the market, the rent will be maximal for a given crop (Figure 1 below). This leads in turn to concentric zones around the market, within which the crop with the highest rent is grown. (Figure 2). It was not worth the effort of Appalachian corn farmers to ship their produce to Eastern cities, but when distilled into the much more valuable product whiskey, the same corn provided those farmers with a cash crop.

Von Thünen's model studied an isolated market with a limited reach, and was constructed at a time when most farm produce was brought to market by horse and cart. And so, his assumptions of linear rent functions for a limited area made sense. But of course, things were much more complicated.

In 1909, Alfred Weber devised an industrial location theory based upon an uneven distribution of raw materials, an inelasticity of labor transportation ability, and an assumption that factories are located at the point of least cost to acquire raw materials.

In 1933, German geographer Walter Christaller constructed an actual "central place theory"2. Von Thünen's location rent theory showed that there were distance thresholds for the distribution and consumption of goods and services. Each good or service has a maximum "range" that consumers will travel to get to it. Because of Economies of agglomeration (a spatial version of economies of scale), economic activities with similar ranges tend to cluster in the same markets. More expensive services cluster at fewer, more distant markets. In other words, larger towns provide more services than smaller towns.

Christaller, noting that that towns of a certain size rank (or "centrality") tended to be a certain distance apart, classified places into "higher-order" and "lower-order" centralities. He developed three models of arranging higher-order places among lower-order places, based upon some broad classifications of the centrality's function:

  • a market model where goods and services need to beas close as possible to their place of supply.
  • a traffic or transportation model where the ease of transportation between market centers causes the smaller-size markets to be located on transportation routes.
  • an administrative model where a hierarchy of administrative regions arises from a larger-order center serving as a government center for the places surrounding it.

If demand within a products range is sufficient, and spread evenly on throughout a region, suppliers will cover the region to absorb all of the demand. Consumers will minimize the cost and effort to acquire these services.

Because of this, on an ideal inhabited Euclidean Plane, the market areas of all the central places of a particular rank order tend to form a hexagonal tiling of the land. The three models assemble the hexagons, and divide market areas, in different ways. Each model identified by the size ratio K between a larger-order place's service area and a smaller-order place's service area.

  • In the marketing model (Figure 3), K=3.
  • In the transportation model (Figure 4), K=4.
  • In the administrative model (figure 5), K=7.

Christaller's ideal hexagons, like von Thünen's location rent fomulae, consider only the price of goods and services, and the cost of transporting them. They assume that buying power is evenly distributed across the landscape. They assume perfectly rational economic decisions. They completely ignore all physical factors (morphology, soils and climate) and cultural factors. A river, a mountain range, a relatively drier or colder area, all distort the pattern. However, Christaller central place theory does show the tendency of cities to form in hierarchies based upon the services they provide.



                     |\
                    ^| \
                    ||  \
                    M|   \
                    a|.   \   <- Crop #1 predominates
                    r| `.  \
                    g|   `. \
                    i|     `.\
                    n|       `\
                    a|         \.
                    l|          \`.
                     |`-._     | \ `.
                    R|    `-._    \  `.   <- Crop #2 predominates
                    e|        `-._ \   `.
                    n|            `-\_   `.
                    t|         |     \`-._ `.
                     |                \   `-._.   
                     |                 \      ``._
                     |                  \        `:-._
                     |         |         \      |  `. `-._   <- Crop #3 predominates
                     |                    \          `.   `-._
                     |                     \           `.     `-._
                     |                      \            `.       `-._
                     +---------|----------------|---------------------|----------
                                         Distance from market -->              

                             Figure 1. Rent curves for three hypothetical crops

                    
                                           `.                       \
                                             `.                      \
                 _.-----._     |               \                      \
              .-'         `-.                   \                     |
            .'               `.                 |                     |
           /            Crop   \     Crop       |       Crop          |
           |             1     |       2        |        3            |
           |         o  zone   |     zone       |       zone          |
           |         ^         |                |                     |
           \         Market    /                |                     |
            `.               .'                 |                     |
              `-._       _.-'                   /                     |
                  `-----'                      /                      /
                                             .'                      /
                                           .'                       /

                           Figure 2. Concentric crop-growing zones based on Figure 1

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  |   /         \   |   /         \   |   /         \   |   /         \   |   /         \   |   /         \   |
--+--<     @     >--+--<     @     >--+--<     @     >--+--<     @     >--+--<     @     >--+--<     @     >--+
  |   \         /   |   \         /   |   \         /   |   \         /   |   \         /   |   \         /   |
  |    \       /    |    \       /    |    \       /    |    \       /    |    \       /    |    \       /    |
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       \   |   /         \   |   /         \   |   /         \   |   /         \   |   /         \   |   /
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       /   |   \         /   |   \         /   |   \         /   |   \         /   |   \         /   |   \
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-----<     o     >-----<     o     >-----<     o     >-----<     o     >-----<     o     >-----<     o     >--
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  o     >-----<     o     >-----<     o     >-----<     o     >-----<     o     >-----<     o     >-----<     o
  |    /       \    |    /       \    |    /       \    |    /       \    |    /       \    |    /       \    |   
  |   /         \   |   /         \   |   /         \   |   /         \   |   /         \   |   /         \   |
--+--<     @     >--+--<     @     >--+--<     @     >--+--<     @     >--+--<     @     >--+--<     @     >--+

Marketing model (k=3)


  @     >-----<=====o=====>-----<    (@)    >-----<=====o=====>-----<     @     >-----<===
       /     / \         / \     \         /     / \         / \     \         /     / \
      /     /   \       /   \     \       /     /   \       /   \     \       /     /   \
-----<     o     >-----<     o     >-----<     o     >-----<     o     >-----<     o     >
      \   /     /       \     \   /       \   /     /       \     \   /       \   /     /
       \ /     /         \     \ /         \ /     /         \     \ /         \ /     /
==o=====>-----<     @     >-----<=====o=====>-----<     @     >-----<=====o=====>-----<
       / \     \         /     / \         / \     \         /     / \         / \     \
      /   \     \       /     /   \       /   \     \       /     /   \       /   \     \
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      \     \   /       \   /     /       \     \   /       \   /     /       \     \   /
       \     \ /         \ /     /         \     \ /         \ /     /         \     \ /
  @     >-----<=====o=====>-----<     @     >-----<=====o=====>-----<     @     >-----<===
       /     / \         / \     \         /     / \         / \     \         /     / \
      /     /   \       /   \     \       /     /   \       /   \     \       /     /   \
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      \   /     /       \     \   /       \   /     /       \     \   /       \   /     /
       \ /     /         \     \ /         \ /     /         \     \ /         \ /     /
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  @     >-----<=====o=====>-----<    (@)    >-----<=====o=====>-----<     @     >-----<===
       /     / \         / \     \         /     / \         / \     \         /     / \
      /     /   \       /   \     \       /     /   \       /   \     \       /     /   \
-----<     o     >-----<     o     >-----<     o     >-----<     o     >-----<     o     >
      \   /     /       \     \   /       \   /     /       \     \   /       \   /     /
       \ /     /         \     \ /         \ /     /         \     \ /         \ /     /
==o=====>-----<     @     >-----<=====o=====>-----<     @     >-----<=====o=====>-----<
       / \     \         /     / \         / \     \         /     / \         / \     \
      /   \     \       /     /   \       /   \     \       /     /   \       /   \     \
-----<     o     >-----<     o     >-----<     o     >-----<     o     >-----<     o     >
      \     \   /       \   /     /       \     \   /       \   /     /       \     \   /
       \     \ /         \ /     /         \     \ /         \ /     /         \     \ /
  @     >-----<=====o=====>-----<     @     >-----<=====o=====>-----<     @     >-----<===

Figure 4. Transportation model (K=4)


-----<     o     >>====<<    o     >>----<     o     >-----<<    o     >-----<     o     >>
      \         //      \         /       \\        /       \         //      \         /
       \       //        \       /         \\      /         \       //        \       /
  o     >>====<<    o     >-----<     o     >>----<     @     >-----<<    o     >-----<
       //      \\        /       \         //      \         /       \\        /       \
      //        \\      /         \       //        \       /         \\      /         \
<====<<    o     >>====<     o     >>====<<    o     >-----<     o     >-----<     @     >-
      \         /       \\        //      \\        /       \         //      \         /
       \       /         \\      //        \\      /         \       //        \       /
  o     >-----<     o     >>====<<    o     >>====<<    o     >>====<<    o     >-----<
       /       \         //      \         /       \\        //      \\        /       \
      /         \       //        \       /         \\      //        \\      /         \
-----<     @     >-----<<    o     >-----<     o     >>====<<    o     >>====<<    o     >>
      \         /       \\        /       \         //      \         /       \\        //
       \       /         \\      /         \       //        \       /         \\      //
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>====<<    o     >>====<<    o     >-----<     o     >>----<     @     >-----<<    o     >-
      \\        //      \\        /       \         //      \         /       \\        /
       \\      //        \\      /         \       //        \       /         \\      /      
  o     >>====<<    o     >>====<<    o     >>====<<    o     >-----<     o     >>----<
       //      \         /       \\        //      \\        /       \         //      \
      //        \       /         \\      //        \\      /         \       //        \
-----<<    o     >-----<     o     >>====<<    o     >>====<<    o     >>====<<    o     >-
      \\        /       \         //      \         /       \\        //      \\        /
       \\      /         \       //        \       /         \\      //        \\      /
  o     >>----<     @     >-----<<    o     >-----<     o     >>====<<    o     >>====<<
       //      \         /       \\        /       \         //      \         /       \\
      //        \       /         \\      /         \       //        \       /         \\
>====<<    o     >-----<     o     >>----<     @     >-----<<    o     >-----<     o     >>
      \\        /       \         //      \         /       \\        /       \         //
       \\      /         \       //        \       /         \\      /         \       //
  o     >>====<<    o     >>====<<    o     >-----<     o     >>----<     @     >-----<<
       /       \\        //      \\        /       \         //      \         /       \\
      /         \\      //        \\      /         \       //        \       /         \\
-----<     o     >>====<<    o     >>----<     o     >-----<<    o     >-----<     o     >>

Figure 5. Administrative model (K=7)


1"The isolated state in reference to farming and national economics, or, investigations into the effects of the price of grain and land rent on the practice of agriculture." (something's not right)

2Die zentralen Orte in Süddeutschland. Jena: Gustav Fischer, 1933. Oh, and yes, the timing creeps me out, too.

Sources:

Vague recollections of economic geography courses, long ago, shaken loose by

Audrey N. Clark, Penguin Dictionary of Geography, 1990, ISBN 0-14-051253-0

Günter Krumme, University of Washington online Location Theories course syllabus at http://faculty.washington.edu/krumme/450/

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