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

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Central Place Theory: Towards a Geography of Urban Service Centres

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

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

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

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

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

  12. 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”

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

  17. 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

  18. 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

  19. 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%

  20. Central Place Theory: Recap • Tertiary activities: the city as a commercial centre… • …within a hierarchical system • Umlands • Simplifying assumptions • Spatial organization

  21. 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

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

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

  24. Christaller’s K=3 (Marketing) Principle

  25. 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

  26. 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.

  27. A B B B B A B A B B A B B B B B 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

  28. 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

  29. 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

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

  31. 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

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

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

  34. 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

  35. Christaller’s k=4 (Traffic) Principle Series: 40,41,42,43,44…

  36. 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

  37. 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.

  38. A B B B B A B A B B A B B B B B 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

  39. 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

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

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

  42. 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/

  43. Christaller’s k=7 (Administration) Principle

  44. 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.

  45. 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)

  46. A professor’s necktie

  47. 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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