1. Chapter 8 The Location of Tertiary Activities Introduction Classical Central-Place Theory Applications of Central Place Theory Modifications of Classical Theory Summary

2. The Production System in Space Where are production system elements located? Why are they located there? How are they connected together? What are the spatial impacts of production processes? How are these changing over time? What are the impacts of economic processes on other social processes? Alternative production systems: neoclassical, behavioral-organizational, and structural (Marxist)

3. Simplifying Assumptions: The Isotropic Plain The concept: equal properties in all directions: Flat, no movement barriers Transport costs proportional to distance Equal Quality Environment Population evenly spaced Identical Income Levels, Tastes, Demands Perfect Knowledge: consumers & producers Producers seek to maximize profit Scale economies exist in production

4. Demand and Supply Principles S S D D $ QQ(t) P A model of expectations!

5. A Simple Market Model of Demand for Sausages Price: $2/ pound Transport cost: 10 cents/mile each way ($.20 round trip) Budget: $8 each week for Sausage Therefore, at the market where TC = 0, 4# each week can be purchased given this budget for sausages. At 10 miles: $2 Transport cost (.1 /mile x 10 miles each way) this leaves $6 for Sausages, or 3# per week. If travel rises to 40 miles, then travel costs are $8, then there is no income to use to purchase sausages. This is the RANGE of the good for this market price and demand quantity.

7. Basic Model, Continued Now, let us assume that the costs of production are $140, and for the moment NOT variable with scale (size of production (Q). This means that the threshold for the example here is 20 miles of market extent: Distance:# customersQ*PRevTotal Up to 114 x 288 up to 1063 x 23644 up to 20242 x 296140 up to 30261 x 252192

8. Demand Cone Principles Quantity Demanded Distance Zero Distance Range

9. Threshold and Range Relationship Threshold Range Threshold Situation: Demand > Costs Situation: Demand < Costs

10. Competition for Customers Unserved customers Possibly maximum profit Market area Figure 8.4: suggests that sellers press towards each other, creating hexagonal market areas and possibly eliminating excess profits ? How would producers like to set their price? At the level that maximizes profit, which is at a scale of output where marginal revenues and marginal costs are equal.

11. Lösch’s Market Area Development Sequence

12. Alternative Spatial Market Areas

13. Spatial Competition If producers behave as spatial monopolists, then circular market areas arise, with the range equal to the market area maximizing profit. If producers behave competitively, they will pack together (as in Fig. 8.4) shrinking market area size until excess profit disappears.

14. Christaller’s Central Place Models Marketing Principle Transportation Principle Administration Principle Figure 8.3 Implications of each for transportation routes

15. Marketing Principle

16. Marketing Principle - Order of Goods

17. Lösch’s Ten Smallest Market Areas

18. Lösch’s Model

19. Lösch’s System Of Transport Lines and Centers With Activity-rich And Activity-poor sectors

20. Fox & Kumar’s Square Market Areas

21. Central Place Systems: Evidence Hierarchies? Are they out there? – Groups of functions vs. continuous spread by size? – Rank Size models as surrogates – Rank Stability over time Do Consumers Travel as Expected? – Desire Line Analyses Are Centers Spaced as we Expect? – Nearest-Neighbor Statistical Tests – Impact of Density of Settlements

22. Ideal Patterns of Functions Rank Size of PlaceLargest Smallest # of functions Discrete breaks

23. Ideal Patterns of Functions versus continuous pattern of functions Rank Size of PlaceLargest Smallest # of functions Discrete breaks Figure 1.18 show a pattern in between these alternatives

24. Lösch’s Test of Spacing of Central Places in Iowa Region Theoretical # Actual# Theoretical Actual Size of of Spacing Spacing (Order) Settlements Settlements 1 615 5.6 2 154 153 11.2 10.3 3 39 39 22.4 23.6 4 10 9 44.8 49.6 5 2 or 3 3 89.6 94.0 6 0 or 1 0 179.2 ?

25. Two Examples of Central Place Hierarchies from Table 1.4 S.W. Ontario # Centers# Functions Population 10 1-12 25-1702 2 19-22 408-486 2 28-32 673-676 1 78 3507 1 99 22,224 1 150 77,190 Southwest Iowa # Centers# Functions Population 29 less than 10 less than 150 32 10-25 150-400 15 28-50 500-1500 9 over 55 2000-7000

26. Isard’s Model With Varying Density

27. Seyfried’s Urban Heirarchy

28. Impact of Density on Trade Area Size

29. Rank-Size Relationships In many urban systems where population and rank exhibit a relatively continuous distribution, the rank-size model predicts well: P r = P 1 / r q where q tends towards 1. Example: If P 1 = 100,000, q = 1, and rank = 25, Then P 25 = 100,000/25 = 4,000 Figure 1.20 Overhead: U.S. 1790-1950 U.S. Cities - 1960 - 1998 Exception: Primate City conditions

30. Rank Relations Over Time

31. Rank Position Top 20 U.S. Metro Areas

32. Movement of Consumers to Central Places Desire lines : Fig. 1.21, 1.22 Beyers hardware lawnmower data Overlapping trade areas – Pacific Northwest data for high order services - Eastern Montana - Southern Idaho - Southwest Oregon

34. Spacing of Urban Centers Tests using “nearest neighbor” statistic: Index = observed average distance expected average distance Expected distance is for a random distribution Index = 1 for a random distribution Index = 0 if all places are clustered Index = 2.15 for a perfect hexagonal pattern Table 1.6: Mixed results! Figure 1.23: Impact of settlement density

35. Spatial Pattern of Settlements

36. Uniform Hexagonal R = 2.15Uniform Square R = 2.0 Clustered R=0.0 Random R=1.0

37. Central Place Theory & Evidence: Additional Issues PSRC Vision 2020 Periodic Markets Movement up and down the hierarchy Changes in the scope of retailers: Walmart, Nordstrom; 7-Eleven Minimarts = gas station + food The Internet: Homegrocer.com; Amazon.com

38. Periodic Market Concept AC Q $ AR(1) Individual Markets AR(2) AR(1) is revenue from a single market AR(2) is revenue combined by traveling to all three markets

39. 5 Day Periodic Market System

40. Skinner’s Model of Periodic Markets In China