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