The External Structure of Cities
Here we look at the external structure of cities - that is the land use and distributions of smaller settlements
around cities. You would be forgive for thinking that all cities arecarefully planned, but this is not so. With
few exceptions, cities and their surrounding settlements grow organically and geographers and
sociologists have attempted to uncover the underlying scientific principles that shape settlement growth,
distribution and structure.

Bid-rent theory (von Thünen, 1826)

Bid-rent theory models how the demand and hence price for land changes with distance from the central
business district (CBD)
. It assumes the following:

1. That different land users will compete with one another for land near the city centre, principally because
it is traditionally the most accessible part of the city for the largest population – historically good transport
routes often radiate toward the city centre as people travel there to do business. All land users are
‘economic men’ – motivated only by maximising their profits.
2. The city is assumed to be the only market for surplus agricultural produce and commodities – there is
no external trade (the city is isolated).
3. The city is built on an
isotropic plain. An isotropic plain is one in which all the physical parameters are
the same at any point and in any direction, so the terrain is perfectly flat everywhere and equally well
drained, so that any area of the land is equally suitable for any purpose, other than differences due to
proximity to the CBD. Soil, climate and topography are the same everywhere.
4. All farmers and traders receive a similar price for their produce at any one time.
5. One form of transport is available and transport costs increase in proportion to distance travelled.
Locational rent is the money a farmer gains for growing his crops on any particular piece of land (the
farmer’s profit).

    Locational rent = revenue from selling crop – (costs of production + transport costs).

Von Thunen’s first model predicts that the intensity of production of a particular crop declines with distance
from the market (the CBD) and thus the rent of land declines with distance from the CBD. Intensive farming
which requires costly inputs is therefore located nearest the market as transport costs will be minimal (as
needed to offset the higher production costs).
Von Thunen’s second model takes more consideration of specific land-use patterns. Product X has a high
market value and which is perishable (and so expensive to transport) is located near to the city. For
example, milk is perishable and requires refrigeration for transport over large distances and so is
expensive to transport and so is located near the market. Product Y sells for less, but also has lower
production costs will become more profitable than X when produced at a certain greater distance from the
market. Eventually, product Z with still lower transport costs becomes more profitable even further from the
market. As a second example, von Thunen’s model applies well to the hill farms around cities in southern
Italy, where there is poor transport and villages are fairly isolated.

Wheat is sold at $100 per tonne and its production cost is $20 per tonne and its transport cost is $2 per
tonne per mile.
Farm A is 0 miles from the market,
    Locational rent = revenue from selling crop – (costs of production + transport costs)            
             = $100 – ($20 + 0)
             = $80 per tonne.
Farm B is 15 miles from the market:
    Locational rent = $100 – ($20 + $30) = $50 per tonne.
Farm C is 30 miles from the market:
    Locational rent = $100 – ($20 + $60) = $20 per tonne.

Potatoes have a market price of $110 per tonne, a production cost of $25 per tonne and transportation
costs of $3 per tonne per mile.
    For farm A: locational rent = $120 – ($25 + 0) = $95 per tonne.
    For farm B: locational rent = $120 – ($25 + $45) = $50 per tonne.
    For farm C: locational rent = $120 – ($25 + $90) = $5 per tonne.

Therefore, to maximise their profits given these two choices of crop, farm A will produce potatoes, farm B
would produce either or both and farm C will produce wheat.

Various factors will of course modify these patterns in the real world. One of which is the presence of
special transport routes, such as a navigable river passing through the CBD – those crops located near
the market due to their higher transport costs may now extend some distance from the market along the
river. The presence of other nearby markets, such as a satellite city within the central cities hinterland will
also disrupt the pattern as the second city may be a focus for intensive, expensive to transport crops.
In this day and age of improved transport, von Thunen’s model still applies but to whole regions rather
than to individual cities. For example, in western Europe there is an inner ring of intensive farming and
dairying centred on England, northern France, northern Germany, Holland, Belgium and Denmark.
Forestry extends around this, and includes Scotland, Wales, southern France, southern Germany, western
Poland and the western Czech Republic. Increasingly extensive field crops occupy a ring still further out
and ranching covers eastern Europe, Spain, Portugal and Italy.
Central Place Theory (Christaller, 1933)

Christaller’s theory predicts how settlements are spaced out and how they evolve over time. The model is
based on the following assumptions:
1. An isotropic plain.
2. The plain has an even and uniform spread of purchasing power (the market is uniform and the same
3. Travel costs are the same everywhere and in every direction and increase in proportion to the distance
4. Every part of the plain is served by a
central place and the circles of influence of these central places fills the
plain. A central place is a place offering a variety of goods in the centre of the market area, such as a village,
town or city.

The optimum market area shape is a circle as the circle minimises the maximum distance anyone needs to
travel to reach the store. However, there are regions between adjacent circles filling a plain which fall outside
the market areas:
What is needed is a series of overlapping circular market areas, but this slightly reduces the market area of
each central place:
The end result is that the market areas become hexagons, since hexagons can cover the whole surface of a
plain most efficiently:
Note that the settlements are equally spaced and each has an hexagonal area of influence or hinterland (or
service area). The question now is how would we expect central places of differing hierarchy (e.g. towns and
cities) to be located relative to one another?

K = 3 system: the market principle

Christaller made a number of predictions based upon different systems. In the K = 3 system or market principle
optimises the markets of each central place. For each six lowest order settlements (hamlets) there is a larger
settlement (village) which is also equally spaced from other settlements of the same order and has its own
larger hexagonal hinterland. The shoppers in smaller settlements divide into three equal groups when shopping
in the three nearest larger settlements. As each village is surrounded by six hamlets, each donating one third of
its market to each of the three villages nearest to it, each village serves (6 x 1/3 = 2) 2 hamlets worth plus its
own immediate area, giving 2+1 = 3 hamlets worth. The pattern repeats in a similar manner for towns (each
town being served by 6 villages and each city by 6 towns). The number of settlements at progressively lower
orders follows the geometric series: 1, 3, 9, 27, … . In other words, supposing a region has three cities, then it
wall have 9 towns and 27 villages, or if it has 27 cities then it will have 9 larger metropolises into which people
from the 27 smaller cities may commute. The k = 3 system ensures that lower order settlements are as near as
possible to larger settlements. This is best visualised with the help of a diagram:
K = 4 system: the transport (traffic) principle

In this system each settlement serves three settlements of the next lowest order plus its own central area (e.g. a
town is served by ½ of 6 villages + its own central area = 3 + 1 = 4). This optimises transport as the shoppers in
smaller settlements divide into two equal groups when shopping in the two nearest larger settlements and this
maximises the number of central places on straight-line routes (which optimises transport even if each
settlement is not as close as possible to a larger settlement). This is important when transport is especially
important or expensive. The numbers of progressively lower order settlements follows the series: 1, 4, 16, 64,
… .
K = 7 system: the administrative principle

In a region with strongly developed central administration. The k = 7 system eliminates shared allegiance, such
that each settlement falls entirely within the hinterland of a larger settlement, e.g. a town is served by all of the
6 nearest villages plus its own central place (6 + 1 = 7). The number of settlements of progressively lower order
follows the series: 1, 7, 49, 343, … .
How realistic is central place theory?

Of course, the model is an idealisation, in the real world regions are not homogeneous and plains are not
isotropic and human beings are not always rational. Also market areas are never exactly hexagonal, due to
intervening geography and transport networks. However, models that rest upon assumptions are easier to
construct than models that relax these assumptions. However, it is best to begin with a simple model that seems
approximately plausible, test its predictions and then relax an assumption if necessary and repeat the process
with a more complicated model. This is the process of mathematical and scientific modelling. The aim is to
derive the simplest model that explains the main features of the reality. In this way we end up with the best
model for making predictions and we also gain an understanding of which factors are more important. In reality,
settlement patterns ought to be a blend of the K = 3, 4 and 7 systems (and others) as each factor is more or
less important in a different geographical region.

The picture below shows Christaller’s actual results as he applied his central place theory to southern
Germany. Clearly, the actual pattern does not exactly match the model with its perfect continuum of hexagonal
hinterlands, but the basis of the model appears to have passed the test, so the factors Christaller considered –
optimising markets, transport and administration, are certainly important factors that help determine the location
of settlements. Other geographers have applied the theory with some success in regions with flat terrain, such
as the American mid-West, the Argentinian pampas, the Chinese lowlands, England and East Anglia.
Lösch’ Theory, 1954

Lösch  modified Christaller’s model to make it more realistic in a wider range of geographical settings. He
retained the hexagonal hinterlands but did not assume an even spread of population. Lösch  also assumed that
different goods required market areas of different sizes and so different K values. He used K values of 3, 4, 7,
9, 12, 13, 19 and more for up to 150 different goods and superimposed a different sized hinterland around
each settlement for each good. He arranged these hinterlands such that the greatest number of lowest order
settlements existed in the minimum of space. From this pattern emerged six settlement-rich sectors around a
major central place and six settlement-poor sectors between them, where services were sparse. This
arrangement is called the
Löschian economic landscape. Rather than a rigid hierarchy of settlement size, this
produces a continuum of settlement sizes. This is illustrated in the figure below:
Like Chrsitaller’s model, the Löschian model has been successfully applied around Exeter, Norwich, some
Japanese towns and the central former USSR and London (where physical factors may provide an alternative
explanation, such as clustering of settlements around the River Thames?). Reality may be more complicated
than these models, but that does not invalidate their usefulness.
Bid Rent Theory
Bid Rent Theory
Central Place Theory
Central Place Theory
Central Place Theory
Central Place Theory K3
Central Place Theory K4
Central Place Theory K7
Christaller's results
Losch Settlement Theory
Losch model for London
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