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: The spatial extent of demand before demand drops to zero

Demand = zero

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

Implications of the RANGE Homogeneous plain 2R distance R T M ? Unmet demand for same good or service

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

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

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? 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

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”

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.

Q Demanded Good / service A Good / service B Good / service C Distance Distance

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

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

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

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 Tertiary activities: the city as a commercial centre… …within a hierarchical system Umlands Simplifying assumptions Spatial organization

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

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

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

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) Principle 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 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 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

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

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

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

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

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

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…

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 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 B A 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 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) Principle Trade Barrier Normal Trade

Christaller’s k=7 (Administration) Principle 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/

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

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 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

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