1 Central Place Theory: Towards a Geography of Urban Service Centres Questions? Review Developing...

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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

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DistanceQ

D

em

ande

d

Demand

Distance

FLIP

Dis

tanc

e

Q Demanded

Demand

Rea

l Pric

e p

er U

nit

Market

Threshold

Range

Threshold

Range

Market location

Spatial Demand Cone

RANGE:The spatial extent of demand before demand drops to zero

Increasing real price

3Distance

Q

De

man

ded

Demand

Distance

FLIP

Dis

tanc

e

Q Demanded

Demand

Rea

l Pric

e p

er U

nit

Market

Threshold

Range

Threshold

Range

Demand = zero

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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

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Implications of the RANGE

R

T

M

Isotropic surface

Area of Extra Profit Min area required to stay in business (normal profits)

?Unmet demand for

same good or service

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Implication of RANGE:

• room for more than one producer of same good / service• where would producer locate?• > 2*R• avoiding overlap

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Implications of the RANGE

R

T

M

Homogeneous plain

?Unmet demand for


R

T

M

2R distance

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R

T

M

R

T

M

R

T

M

R

T

M

R

T

M

T

M

R

T

M

R

T

M

T

M

R

T

M

R

T

M

R

T

M

T

M

T

M

T

M

R

M

R

M

?Unmet demand for


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

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R

T

MR

T

MR

T

M R

T

M

R

T

MR

T

MR

T

M R

M

R

T

M

R

T

MR

T

M R

T

MR

T

M

R

R

T

M

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

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R

T

MR

T

MR

T

M R

T

M

R

T

MR

T

MR

T

M R

M

R

T

M

R

T

MR

T

M R

T

MR

T

M

R

R

T

M

How will market area boundaries form given the ellipses formed by overlapping market areas?

Overlapping Trade Areas•Unfilled demand now served•Competition

12A system of hexagonal market areas fills the plain so that every consumer is served and no market areas overlap

No Overlapping Trade Areas•Unfilled demand now served•No competition•Every producer making “normal profit”

Homogeneous plain

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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.

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Distance

Q Demanded

Distance

Good / service A

Good / service B

Good / service C

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Distance

Q Demanded

Distance

Good / service A

Good / service B

Good / service C

Range A

Range B

Range C

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Distance

Q Demanded

Distance

Good / service A

Good / service B

Good / service C

Range A

Range B

Range C

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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

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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

2121

The Pain Will End Today:The Pain Will End Today:Conclusion of Central Place Conclusion of Central Place

TheoryTheoryWednesday, November 3Wednesday, November 3Chapters 5-8 of Wheeler Chapters 5-8 of Wheeler et al.et al. All lectures since October 8All lectures since October 8 Format: same as Test 1Format: same as Test 1

M/C – 40%M/C – 40% FiB – 20%FiB – 20% S/A – 40%S/A – 40%

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Central Place Theory: Recap

• Tertiary activities: the city as a commercial centre…

• …within a hierarchical system• Umlands• Simplifying assumptions• Spatial organization

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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

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A

A

A

A

A

Christaller’s k=3 (Marketing) Principle

• Q. Where should lower order B centre locate?

• A. Midpoint between 3 A centresB

BB

B B B

BB

B

B

B

B

B

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A

A

A

A

A



• A. Midpoint between 3 A centresB

BB

B B B

BB

B

B

B

B

B

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Christaller’s K=3 (Marketing) Principle

OrderNumber of Centres of

Various Orders

High 1

1

2 3

3 9

4 27

Low 5 81

27Christaller’s k=3 (Marketing) Principleand 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

kdd BBAA

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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.

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A

A

A

A

A


• Problem: lower order centres, B, are not on the straight line route between higher order centres, A

B

BB

B B B

BB

B

B

B

B

B

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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

31Christaller’s k=4 (Traffic) Principle


• A. Midpoint between 2 A centres connected by road

A

A

A

A

AB

B

B B

B

B B

Transportation linkage (connectivity)e.g. road


A

A

A

A

AB

B

B B

B

B B



• Q. Where should lower order C centre locate?

• A. Midpoint between 2 B centres connected by road

A

A

A

A

AB

B

B B

B

B B



A

A

A

A

AB

B

B B

B

B B



A

A

A

A

AB

B

B B

B

B B


1/2 of area

Each higher order centre has the equivalent of 4 trade areas of the next lower order

1

23

45

6

K = 1 + 1/2 (6) =4

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Christaller’s k=4 (Traffic) Principle

OrderNumber of Centres of

Various Orders

High 1

1

2 4

3 16

4 64

Low 5 256

Series: 40,41,42,43,44…

38Christaller’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

kdd BBAA

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The “rule of fours” in Christaller’s k=4 hierarchy of central places




3. The distance between two higher order centres is 4½ (=2) times distance between next lower order centres.

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A

A

A

A

A

Christaller’s k=3 Principle - Reprise

• Problem: lower order centres, B, and their market areas are divided among higher order market centres, A

B

BB

B B B

BB

B

B

B

B

B

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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

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A

A

A

A

A

Christaller’s k=7 (Administration) Principle

Normal Trade

Trade Barrier

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A

A

A

A

A


Trade areas restricted to same region

44Christaller’s k=7 (Administrative Principle)

Source: Sandra Lach Arlinghaus:http://www-personal.umich.edu/~sarhaus/image/solstice/sum04/sampler/

Each green hexagon contains the equivalent of 7 blue hexagons

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Order

Equiv Trade Areas Contained

in Highest Order

High 1

1

2 7

3 49

4 343

Low 5 2401

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The “rule of sevens” in Christaller’s k=7 hierarchy of central places




3. The distance between two higher order centres is 7½ (=2.65) times distance between next lower order centres.

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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)

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A professor’s necktie

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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

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