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Chapter 8 The Location of Tertiary Activities
• Introduction
• Classical Central-Place Theory
• Applications of Central Place Theory
• Modifications of Classical Theory
• Summary
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)
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
Demand and Supply Principles
S
SD
D
$
QQ(t)
P
A model of expectations!
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.
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 ofmarket extent:
Distance: # customers Q*P Rev TotalUp to 1 1 4 x 2 8 8up to 10 6 3 x 2 36 44up to 20 24 2 x 2 96 140up to 30 26 1 x 2 52 192
Demand Cone Principles
Quantity Demanded
DistanceZeroDistance
Range
Threshold and Range Relationship
Threshold
Range
Range
Threshold
Situation: Demand > Costs
Situation:Demand < Costs
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 levelthat maximizes profit, which is at a scale of output where marginal revenues and marginal costs are equal.
Lösch’s Market Area Development Sequence
Alternative Spatial Market Areas
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.
Christaller’s Central Place Models
• Marketing Principle
• Transportation Principle
• Administration Principle
• Figure 8.3
• Implications of each for transportation routes
Marketing Principle
Marketing Principle - Order of Goods
Lösch’s Ten Smallest Market Areas
Lösch’s Model
Lösch’sSystemOf TransportLines andCentersWithActivity-richAndActivity-poorsectors
Fox & Kumar’s Square Market Areas
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
Ideal Patterns of Functions
Rank Size of PlaceLargest Smallest
# of
fu
nct
ion
s
•
• • •
• • • • • • • • •
• • • • • • • • • • • • • • • • • • • • • • • • • • •
Discrete breaks
Ideal Patterns of Functionsversus continuous pattern of functions
Rank Size of PlaceLargest Smallest
# of
fu
nct
ion
s
•
• • •
• • • • • • • • •
• • • • • • • • • • • • • • • • • • • • • • • • • • •
Discrete breaks
Figure 1.18 show a patternin between these alternatives
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 ?
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
Isard’s Model With Varying Density
Seyfried’s Urban Heirarchy
Impact of Density on Trade Area Size
Rank-Size RelationshipsIn many urban systems where population and rank exhibit a relatively continuous distribution, the rank-size model predicts well:
Pr = P1 / rq where q tends towards 1.
Example: If P1 = 100,000, q = 1, and rank = 25,
Then P25 = 100,000/25 = 4,000
• Figure 1.20
• Overhead: U.S. 1790-1950
• U.S. Cities - 1960 - 1998
• Exception: Primate City conditions
Rank Relations Over Time
Rank Position Top 20 U.S. Metro AreasRank 1998 1980 19601 NYC NYC NYC2 L.A. L.A. L.A.3 Chicago Chicago Chicago4 Washington D.C. Philadelphia Philadelphia5 San Francisco San Francisco Detroit6 Philadelphia Detroit San Francisco7 Boston Boston Boston8 Detroit Washington D.C. Cleveland9 Dallas-Ft. Worth Houston Pittsburgh10 Houston Dallas-Ft. Worth St. Louis11 Atlanta Cleveland Washington, D.C.12 Miami-Ft. L. Miami Baltimore13 Seattle Pittsburgh Dallas14 Phoenix St. Louis Minneapolis15 Cleveland Baltimore Houston16 Minneapolis Atlanta Seattle17 San Diego Minneapolis Miami18 St. Louis Seattle Buffalo19 Denver San Diego Cincinnati20 Pittsburgh Cincinnati Atlanta
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
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
Spatial Pattern of Settlements
Uniform Hexagonal R = 2.15 Uniform Square R = 2.0
Clustered R=0.0Random R=1.0
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
Periodic Market Concept
AC
Q
$
AR(1)
Individual Markets
AR(2)
AR(1) is revenue from a single marketAR(2) is revenue combined by traveling to all three markets
5 Day Periodic Market System
Skinner’sModel ofPeriodicMarketsIn China