Central Place Theory: Towards a
Geography of Urban Service Centres
• Questions?
• Review
• Developing threshold and range
into a spatial system of central
places
• Hierarchical ordering principles
1
2
Q Demanded
FLIP
Q Demanded
Spatial Demand Cone
Demand
Distance
Distance
Market location
Increasing
real price
RANGE:
The spatial extent of
demand before
demand drops to zero
Distance
3
Distance
Demand = zero
Threshold
Market
Threshold
Range
Range
4
Important definitions:
• Threshold:
• minimum DEMAND (volume of sales) needed
for a business to stay in operation
(and make a “normal” profit).
• Range:
• maximum distance over which a good can be
sold from point P
(i.e. where real price is low enough that people
will travel to market to buy it)
• Profit = R – T – really an excess profit
• Threshold and range is the spatial basis
for profit
5
Implications of the RANGE
Area of Extra Profit
Min area required to stay
in business (normal profits)
Isotropic surface
R
M
T
?
Unmet demand for
same good or
service
6
Implication of RANGE:
• room for more than one producer of
same good / service
• where would producer locate?
• > 2*R
• avoiding overlap
7
Implications of the RANGE
R
M
Homogeneous plain
2R distance
T
R
M
T
?
Unmet demand for
same good or
service
8
?
Unmet demand for
same good or
service
How can problem of interstitial areas of unmet
demand be solved?
9
Interstitial areas of unmet demand disappear if
R
markets are moved closer together
M
R
R
T
M
M
R
T
R
T
M
R
T
M
M
R
M
R
T
T
R
T
M
R
R
T
T
M
T
M
T
R
M
R
R
M
T
M
R
T
10
How will market area boundaries form given the
R
ellipses formed by overlapping
market areas?
M
R
R
T
M
M
R
T
R
T
M
R
R
T
M
M
R
T
Overlapping Trade
M
Areas
•Unfilled demand
T
now served
R
•Competition
T
M
R
R
T
T
M
T
M
T
R
M
R
R
M
T
M
R
T
11
A system of hexagonal market areas fills the plain so that
every consumer is served and no market areas overlap
Homogeneous plain
No Overlapping
Trade Areas
•Unfilled
demand
now served
•No competition
•Every producer
making “normal
profit”
12
13
Further economic / spatial
complications:
• T and R are good- or servicespecific
• Separate demand curves / cones for
each good or service
• Why?
• Different levels of demand
• Different sensitivity to distance etc.
14
Q Demanded
Good / service A
Good / service B
Good / service C
Distance
Distance
15
Q Demanded
Good / service A
Good / service B
Good / service C
Distance
Distance
Range A
Range B
Range C
Q Demanded
16
Good / service A
Good / service B
Good / service C
Distance
Distance
Range A
Range B
Range C
17
18
19
Orders of Goods / Services
• lower order goods
• small T & R
• (high frequency, low cost)
• higher order goods
• large T & R
• (low frequency,
high cost goods)
• i.e. different “geographies”
for different goods / services
Central Place Hierarchy: Cities,Towns,
Villages and Hamlets:
• Why cluster in Central Places?
• Agglomeration economies
• Urbanization economies
• Localization economies
• Clustering in Central Places
• Vertical arrangement of central Places
• (relative importance)
• Horizontal Arrangement of Central Places
• (situation of central places)
• Organization of central place hierarchy
• Ordering principles: k=3, 4 and 7
• Relationship between centres and market
areas
20
The Pain Will End Today:
Conclusion of Central Place Theory
Wednesday, November 3
 Chapters 5-8 of Wheeler et al.
 All lectures since October 8
 Format: same as Test 1

 M/C
– 40%
 FiB – 20%
 S/A – 40%
21
22
Central Place Theory: Recap
• Tertiary activities: the city as a
commercial centre…
• …within a hierarchical system
• Umlands
• Simplifying assumptions
• Spatial organization
23
Christaller’s k=3 (Marketing) Principle
• minimizes the market area size for any
order of centre, OR
• minimizes total consumer travel to
purchase central place goods
• Most efficient way of supplying
consumers
• Fixed relationship between each lower
order market area and the next higher
Christaller’s k=3
(Marketing) Principle
A
B
B
• Q. Where should
lower order B
centre locate?
• A. Midpoint
between 3 A
centres
B
B
A
B
B
A
B
B
B
A
B
A
B
B
B
24
Christaller’s k=3
(Marketing) Principle
A
B
B
• Q. Where should
lower order B
centre locate?
• A. Midpoint
between 3 A
centres
B
B
A
B
B
A
B
B
B
A
B
A
B
B
B
25
26
Christaller’s K=3 (Marketing) Principle
Order
High 1
Number of
Centres of
Various Orders
1
2
3
3
9
4
27
Low 5
81
Christaller’s k=3 (Marketing) Principle
and distance
27
• Centres of given order are equally spaced
• Centres of next higher order are 3½ (=1.73)
times distance between next lower order
centres.
d AA  d BB k
• e.g.
• If lower order B centres were 1km apart, grade A (next
higher order) centres would be:
• dAA=1*√3 = 1.73 km apart
• If grade B centres were 3 km apart, grade A centres would
be:
• dAA= 3*√3 = 3*1.73 = 5.19 km apart
Recap: “Rule of threes” in Christaller’s
k=3 hierarchy of central places
1. There are the equivalent of 3 lower order
market areas in each higher order market
area OR
• Each higher order market area is 3 times larger
than the next lower order market area
2. The number of successively lower order
centres increases as the sequence 3n for
n=0,1,2…
3. The distance between two higher order
centres is 3½ (=1.72) times distance
between next lower order centres.
28
Christaller’s k=3
(Marketing) Principle
A
B
B
• Problem: lower
order centres, B, are
not on the straight
line route between
higher order
centres, A
B
B
A
B
B
A
B
B
B
A
B
A
B
B
B
29
30
Introducing:
Christaller’s k=4 (Traffic) Principle
• alternate arrangement that maximizes
travel efficiency / connectivity between
highest order places.
• if transportation lines (roads etc) linked
highest order places, grade B
goods/centres would locate half-way
between 2 A order places on road
network -- results in k=4 system
• k=4 is does not minimize total consumer
travel but does minimize route-miles on
main arterials
• Text calls it transportation principle
Christaller’s k=4
(Traffic) Principle
A
B
A
• Q. Where should lower
order B centre locate?
• A. Midpoint between 2
A centres connected
by road
B
B
B
A
B
A
B
B
A
Transportation linkage (connectivity)
e.g. road
31
Christaller’s k=4
(Traffic) Principle
A
B
A
B
B
B
A
B
A
B
B
A
Transportation linkage (connectivity)
e.g. road
32
Christaller’s k=4
(Traffic) Principle
A
•
•
B
A
Q. Where should lower
order C centre locate?
A. Midpoint between 2 B
centres connected by
road
B
B
B
A
B
A
B
B
A
Transportation linkage (connectivity)
e.g. road
33
Christaller’s k=4
(Traffic) Principle
A
B
A
B
B
B
A
B
A
B
B
A
Transportation linkage (connectivity)
e.g. road
34
Christaller’s k=4
(Traffic) Principle
A
B
A
B
B
B
A
B
A
B
B
A
Transportation linkage (connectivity)
e.g. road
35
Christaller’s k=4
(Traffic) Principle
A
1/2 of area
1
B
A
B
B
4
B
B
A
B
B
Each higher order
centre has the
A
equivalent
of 4 trade
areas of the next
lower order
K = 1 + 1/2
A
Transportation linkage (connectivity)
e.g. road
(6) =4
36
37
Christaller’s k=4 (Traffic) Principle
Order
High 1
Number of
Centres of
Various Orders
1
2
4
3
16
4
64
Low 5
256
Series: 40,41,42,43,44…
Christaller’s k=4 (Traffic) Principle and
Distance between Centres
38
• Centres of given order are equally spaced
• Centres of next higher order are 4½ (=2)
times distance between next lower order
centres.
d AA  d BB k
• e.g.
• If lower order B centres are 1km apart, grade A
(next higher order) centres are:
• dAA=1*√4 = 2 km apart
• If grade B centres 3 km apart, grade A centres are:
• dAA= 3*√4 = 3*2 = 6 km apart
The “rule of fours” in Christaller’s k=4
hierarchy of central places
1. There are the equivalent of 4 lower order
market areas in each higher order market
area OR
• Each higher order market area is 4 times larger
than the next lower order market area
2. The number of successively lower order
centres increases as the sequence 4n for
n=0,1,2…
3. The distance between two higher order
centres is 4½ (=2) times distance between
next lower order centres.
39
Christaller’s k=3
Principle - Reprise
A
B
B
• Problem: lower
order centres, B,
and their market
areas are divided
among higher order
market centres, A
B
B
40
A
B
B
A
B
B
B
A
B
A
B
B
B
Introducing: Christaller’s K=7
(Administrative) Principle
• Each lower level in hierarchy should be
contained within trade area boundary of
higher level
• Administrative boundaries might prohibit
discourage trade across borders etc.
• Perverse effects of political borders
• Bar closing hours
• Community standards vs. cross border
drinking
• Sunday shopping issues
• Community standards vs. cross border
shopping
• Fireworks, Post Falls ID and sales tax
41
Christaller’s k=7
(Administration) Principle
42
A
A
A
A
A
Normal Trade
Trade Barrier
Christaller’s k=7
(Administration) Principle
43
A
A
A
A
A
Trade areas restricted
to same region
Christaller’s k=7
(Administrative Principle)
Each green
hexagon
contains the
equivalent
of 7 blue
hexagons
Source: Sandra Lach Arlinghaus:http://www-personal.umich.edu/~sarhaus/image/solstice/sum04/sampler/
44
45
Christaller’s k=7
(Administration) Principle
Equiv Trade
Order Areas Contained
in Highest Order
High 1
1
2
7
3
49
4
343
Low 5
2401
The “rule of sevens” in Christaller’s k=7
hierarchy of central places
1. There are the equivalent of 7 lower order
market areas in each higher order market
area OR
• Each higher order market area is 7 times larger
than the next lower order market area
2. The number of successively lower order
centres increases as the sequence 7n for
n=0,1,2…
3. The distance between two higher order
centres is 7½ (=2.65) times distance
between next lower order centres.
46
47
Common Elements of k=3, k=4, k=7
• k value specifies regular hierarchical
ordering of places/markets
• Model of order: regular, discrete, rigid,
hierarchy
• Equilibrium or “steady state” in a space
economy.
Central Place Theory
• A normative spatial model...
• “...more honoured in the breach than in
the observance” (Hamlet)
A professor’s necktie
48
49
Central Place Theory
• A way of thinking about hierarchies
• Urban centres
• Urban functions
• Market areas
• A starting point for theorizing about
space and spatial dynamics
• The basis for retail and trade area
studies for planning urban
commercial functions and macromarketing