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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. Spatial Demand Cone. Increasing real price. Market location. RANGE:

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central place theory towards a geography of urban service centres
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
slide2

Spatial Demand Cone

Increasing real price

Market location

RANGE:

The spatial extent of demand before demand drops to zero

important definitions
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
implications of the range
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

implication of range
Implication of RANGE:
  • room for more than one producer of same good / service
    • where would producer locate?
    • > 2*R
    • avoiding overlap
implications of the range7

R

R

M

M

T

T

Implications of the RANGE

Homogeneous plain

2R distance

?

Unmet demand for same good or service

slide8

R

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?

Unmet demand for same good or service

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

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Interstitial areas of unmet demand disappear if markets are moved closer together
how will market area boundaries form given the ellipses formed by overlapping market areas

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How will market area boundaries form given the ellipses formed by overlapping market areas?
  • Overlapping Trade Areas
  • Unfilled demand now served
  • Competition
slide12

R

M

T

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”
further economic spatial complications
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.
slide14

Q Demanded

Good / service A

Good / service B

Good / service C

Distance

Distance

slide15

Q Demanded

Good / service A

Good / service B

Good / service C

Distance

Distance

Range A

Range B

Range C

slide16

Q Demanded

Good / service A

Good / service B

Good / service C

Distance

Distance

Range A

Range B

Range C

orders of goods services
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
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
the pain will end today conclusion of central place theory
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%
central place theory recap
Central Place Theory: Recap
  • Tertiary activities: the city as a commercial centre…
  • …within a hierarchical system
  • Umlands
  • Simplifying assumptions
  • Spatial organization
christaller s k 3 marketing principle
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 principle24

A

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Christaller’s k=3 (Marketing) Principle
  • Q. Where should lower order B centre locate?
  • A. Midpoint between 3 A centres
christaller s k 3 marketing principle25

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Christaller’s k=3 (Marketing) Principle
  • Q. Where should lower order B centre locate?
  • A. Midpoint between 3 A centres
christaller s k 3 marketing principle and distance
Christaller’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
recap rule of threes in christaller s k 3 hierarchy of central places
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.
christaller s k 3 marketing principle29

A

B

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B

A

Christaller’s k=3 (Marketing) Principle
  • Problem: lower order centres, B, are not on the straight line route between higher order centres, A
introducing christaller s k 4 traffic principle
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

B

B

B

B

B

B

B

Transportation linkage (connectivity)

e.g. road

Christaller’s k=4 (Traffic) Principle

A

  • Q. Where should lower order B centre locate?
  • A. Midpoint between 2 A centres connected by road

A

A

A

A

christaller s k 4 traffic principle32

B

B

B

B

B

B

B

Transportation linkage (connectivity)

e.g. road

Christaller’s k=4 (Traffic) Principle

A

A

A

A

A

christaller s k 4 traffic principle33

B

B

B

B

B

B

B

Transportation linkage (connectivity)

e.g. road

Christaller’s k=4 (Traffic) Principle

A

  • Q. Where should lower order C centre locate?
  • A. Midpoint between 2 B centres connected by road

A

A

A

A

christaller s k 4 traffic principle34

A

A

A

A

A

B

B

B

B

B

B

B

Transportation linkage (connectivity)

e.g. road

Christaller’s k=4 (Traffic) Principle
christaller s k 4 traffic principle35

A

A

A

A

A

B

B

B

B

B

B

B

Transportation linkage (connectivity)

e.g. road

Christaller’s k=4 (Traffic) Principle
christaller s k 4 traffic principle36

1/2 of area

4

6

1

5

3

2

B

B

B

B

B

B

B

Transportation linkage (connectivity)

e.g. road

Christaller’s k=4 (Traffic) Principle

A

A

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

A

A

1/2

1 +

K =

(6)

=4

A

christaller s k 4 traffic principle and distance between centres
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
the rule of fours in christaller s k 4 hierarchy of central places
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.
christaller s k 3 principle reprise

A

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B

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Christaller’s k=3 Principle - Reprise
  • Problem: lower order centres, B, and their market areas are divided among higher order market centres, A
introducing christaller s k 7 administrative principle
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
christaller s k 7 administration principle43
Christaller’s k=7 (Administration) Principle

A

A

A

A

A

Trade areas restricted to same region

christaller s k 7 administrative principle
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/

the rule of sevens in christaller s k 7 hierarchy of central places
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.
common elements of k 3 k 4 k 7
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)
central place theory
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