Christaller’s Central Place Model

Introduction:

Walther Christaller, a German geographer, proposed his theory of central places in his book “Central Place in Southern Germany” in 1933. Central Place Theory (CPT) is an attempt to explain the spatial arrangement, size, and number of settlements. In the flat landscape of southern Germany Christaller noticed that towns of a certain size were roughly equidistant. By examining and defining the functions of the settlement structure and the size of the hinterland he found it possible to model the pattern of settlement locations using geometric shapes. 

Assumptions:

Christaller made a number of assumptions such as: 

1. There is an isotropic plane (flat surface) on which natural resources are evenly Distributed.
2. Population is evenly distributed on plane.
3. All consumers have similar purchasing power and same taste or demand for the goods and services.
4. There is no excess profit (perfect competition).
5. There is a single means of transport and transport costs rises proportionately with distance.
6. Consumers visit the nearest central place as this minimizes the distance travelled.
7. The entrepreneurs are economic men with aim on profit maximization. As people will prefer to visit the nearest center, suppliers will locate themselves as far away from each other as possible to maximize their market areas.
8. The central place hierarchy acts as a closed system.

Towns act as central places for the country side. They come into being to carry out at a central, accessible place. Christaller acknowledges that this basic assumption is derived from former work of Gradman (1916), who contended that the distinctive role of the town was to be the centre of its rural surroundings and a facilitator of local commerce with the neighbouring areas, collecting and exporting the local products, importing and distributing the necessary goods and services which the countryside demands. Though the population of town may be important by virtue of its size but it cannot be a measure of centrality.

Explanation of some terms: Central Place, low order, high 
order, sphere of influence

• A Central Place is a settlement which provides one or more services for the population living around it. 
• Simple basic services (e.g. grocery stores) are said to be of low order while specialized services (e.g. universities) are said to be of high order. 
• Having a high order service implies there are low order services around it, but not vice versa.
• Settlements which provide low order services are said to be low order settlements. Settlements that provide high order services are said to be high order settlements.
• The sphere of influence is the area under influence of the Central Place.

Details of the theory

Centrality

It refers to central location of the town in an area to which it serves. 

Town provides goods and services to its surroundings area. However, this town may or may not be geographically centrally located.

Complementary Area

Complementary area is the area for which central place is the focal point. This area would be larger for bigger and more important central places and smaller for the less important ones.

Threshold

The minimum population that is required to bring about the provision of certain good or services 

Range of goods or services

The average maximum distance people will travel to purchase goods and services.

From these two concepts the lower and upper limits of goods or services can be found. With the upper and the lower limits, it is possible to see how the central places are arranged in an imaginary area.

Arrangement of the Central places/ settlements: 

As transport is equally easy in all direction, each central place will have a circular market area as shown in C in the following diagram:

However, circular shape of the market areas results in either un-served areas or over-served areas. To solve this problem, Christaller suggested the hexagonal shape of the markets as shown in D in the above diagram. Within a given area there will be fewer high order cities and towns in relation to the lower order villages and hamlets. For any given order, theoretically the settlements will be equidistance from each other. The higher order settlements will be further apart than the lower order ones.

The three principles in the arrangement of the central places:

Christaller noted three different arrangements of central places according to the following principles:

1. The marketing principle (K=3 system)

Under the marketing principle, an urban settlement reveals consumer demand. Each consumer would try to be as close as possible to every level of the hierarchy so as to minimize the amount of travelling for the consumer. Thus, a settlement of every order would be surrounded by six other settlements of the next order. The low order centres position themselves on the boundaries of market areas of middle order centres. People at lower order center will have a choice between three higher order centers since all three are equidistant. Each higher order centerthen receives one third of the customer of six immediately lower order centers which are located on the boundary of its market area. It serves a population equivalent to two lower order centers (6*1/3), besides its own population. Therefore, overall it serves a total of three central places (6*1/3=2+1=3). For each one of the largest settlements there would be three of the second grades, nine of the third grade, twenty-seven of the fourth grades and so on. Thus, there is only one center of the highest order and number of centers at every level below it increases by a factor of three.

The marketing principle (K=3 system)

2. The transportation principle (K=4 system)

The transport principle states that the distribution of central places is most favourable when as many places of concern or importance lie on one traffic route between two important towns, the route being established as straight and as cheap as possible. The more unimportant places may not be taken into cognizance. The central places would thus be lined up on straight traffic routes which radiate out from central point. Central places are so located that lower order centers lie along the straight line paths between higher order centers. In the transport principle, a lower order centre is equidistant from two lower order centers (6*1/2) plus its own (1) making a total of four. When central places are arranged according to transport principle, the lower order centers are located at the midpoint of each side 

of the hexagon rather than at the corner. Thus, the transport principle produces a hierarchy organized in a k=4 arrangement in which a central place are nested according to the rule of four. This is termed as K=4 network principle. The number of settlement serving as central places at each decreasing in the hierarchy would be 1, 4, 16, 64,256...and so on.

The transportation principle (K=4 system)

3. The administrative principle (K=7 system)

The market areas of each of the higher order centers include the higher market area of each of the six neighboring lower order centers. This is because law and administration in theory do not experience exponential decay with distance but remain fully enforced up to the boundaries of the administrative units in which they are applied. This is the most efficient if each higher order place clearly controls the territories of those places beneath it in the system. For the administrative principle the numerical progression would be as 1, 7, 49, 343… and so on.

The administrative principle (K=7 system)