1. 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

2. Spatial Demand Cone Increasing real price Market location RANGE:
The spatial extent of demand before demand drops to zero

3. Demand = zero

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 ?
Unmet demand for same good or service T

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
Homogeneous plain
2R distance R T M ?
Unmet demand for same good or service

8. Unmet demand for same good or service?
Unmet demand for same good or service R T M R T M R T M

9. How can problem of interstitial areas of unmet demand be solved?

10. Interstitial areas of unmet demand disappear if markets are moved closer together

11. How will market area boundaries form given the ellipses formed by overlapping market areas?
Overlapping Trade Areas
Unfilled demand now served
Competition R T M R T M R T M R T M R T M R T M

12. A system of hexagonal market areas fills the plain so that every consumer is served and no market areas overlap
Homogeneous plain R T M
No Overlapping Trade Areas
Unfilled demand now served
No competition
Every producer making “normal profit”

13. Further economic / spatial complications:
T and R are good- or service-specific
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. Distance
Q Demanded
Good / service A
Good / service B
Good / service C
Range A
Range B
Range C

16. Q Demanded
Good / service A
Good / service B
Good / service C
Distance
Distance
Range A
Range B
Range C

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

20. 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

21. 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%

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

24. Christaller’s k=3 (Marketing) PrincipleB A
Christaller’s k=3 (Marketing) Principle
Q. Where should lower order B centre locate?
A. Midpoint between 3 A centres

25. Christaller’s k=3 (Marketing) PrincipleB A
Christaller’s k=3 (Marketing) Principle
Q. Where should lower order B centre locate?
A. Midpoint between 3 A centres

26. Number of Centres of Various Orders
Christaller’s K=3 (Marketing) Principle
Order
Number of Centres of Various Orders
High 1 1 2 3 9 4 27
Low 5 81

27. Christaller’s k=3 (Marketing) Principle and distance
Centres of given order are equally spaced
Centres of next higher order are 3½ (=1.73) times distance between next lower order centres.
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

28. Recap: “Rule of threes” in Christaller’s k=3 hierarchy of central places
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
The number of successively lower order centres increases as the sequence 3n for n=0,1,2…
The distance between two higher order centres is 3½ (=1.72) times distance between next lower order centres.

29. Christaller’s k=3 (Marketing) PrincipleB A
Christaller’s k=3 (Marketing) Principle
Problem: lower order centres, B, are not on the straight line route between higher order centres, A

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

31. Christaller’s k=4 (Traffic) Principle
Q. Where should lower order B centre locate?
A. Midpoint between 2 A centres connected by road B A B B B A B A
Transportation linkage (connectivity)
e.g. road B B A

32. Christaller’s k=4 (Traffic) PrincipleB A B B B A B A
Transportation linkage (connectivity)
e.g. road B B A

33. Christaller’s k=4 (Traffic) Principle
Q. Where should lower order C centre locate?
A. Midpoint between 2 B centres connected by road B A B B B A B A
Transportation linkage (connectivity)
e.g. road B B A

34. Christaller’s k=4 (Traffic) PrincipleB
Transportation linkage (connectivity)
e.g. road
Christaller’s k=4 (Traffic) Principle

35. Christaller’s k=4 (Traffic) PrincipleB
Transportation linkage (connectivity)
e.g. road
Christaller’s k=4 (Traffic) Principle

36. Christaller’s k=4 (Traffic) Principle
1/2 of area 1 6 B 2 A B 5 3 B B
Each higher order centre has the equivalent of 4 trade areas of the next lower order 4 A B A
Transportation linkage (connectivity)
e.g. road B B
K =
1 +
1/2
(6) =4 A

37. Number of Centres of Various Orders
Christaller’s k=4 (Traffic) Principle
Order
Number of Centres of Various Orders
High 1 1 2 4 3 16 64
Low 5
256
Series: 40,41,42,43,44…

38. Christaller’s k=4 (Traffic) Principle and Distance between Centres
Centres of given order are equally spaced
Centres of next higher order are 4½ (=2) times distance between next lower order centres.
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

39. The “rule of fours” in Christaller’s k=4 hierarchy of central places
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
The number of successively lower order centres increases as the sequence 4n for n=0,1,2…
The distance between two higher order centres is 4½ (=2) times distance between next lower order centres.

40. Christaller’s k=3 Principle - RepriseB A
Christaller’s k=3 Principle - Reprise
Problem: lower order centres, B, and their market areas are divided among higher order market centres, A

41. 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

42. Christaller’s k=7 (Administration) Principle
Trade Barrier
Normal Trade

43. Christaller’s k=7 (Administration) Principle
Trade areas restricted to same region

44. Christaller’s k=7 (Administrative Principle)
Each green hexagon contains the equivalent of 7 blue hexagons
Source: Sandra Lach Arlinghaus:

45. Equiv Trade Areas Contained in Highest Order
Christaller’s k=7 (Administration) Principle
Order
Equiv Trade Areas Contained in Highest Order
High 1 1 2 7 3 49 4
343
Low 5
2401

46. The “rule of sevens” in Christaller’s k=7 hierarchy of central places
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
The number of successively lower order centres increases as the sequence 7n for n=0,1,2…
The distance between two higher order centres is 7½ (=2.65) times distance between next lower order centres.

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)

48. A professor’s necktie

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 macro-marketing