chapter 3: classical location theory of the firm
TRANSCRIPT
Space and Economics
Chapter 3: Classical Location Theory of the Firm
Author
Wim Heijman (Wageningen, the Netherlands)
July 21, 2009
3. Classical location theory of the firm
� 3.1 Minimization of transportation costs: one final product
� 3.2 Minimization of transportation costs: one resource, one final product
� 3.3 Trans�shipment costs � 3.4 Other location factors � 3.5 Alfred Weber’s theory on location of the firm � 3.6 The Theory of the market areas� 3.7 Spatial elasticity of demand � 3.8 Market forms: spatial duopoly � 3.9 Application
3.1 Minimization of transportation costs: one final product
� Location of one ice cream vendor on the beach
� Customers equally distributed over the beach
� Customers have equal preferences for ice cream
� The lower the average distance between ice cream vendor and customers the more ice cream will be sold
3.1 Minimization of transportation costs: one final product
A B C D E
100m 100m 100m 100m
Figure 3.1: Beach with five visitors.
3.1 Minimization of transportation costs: one final product
m, 2005
m 400 m 300 m 200 m 100 m 0:A =++++
m, 1405
m 300 m 200 m 100 m 0 m 100:B =++++
m, 1205
m 200 m 100 m 0 m 100 m 002:C =++++
m, 1405
m 100 m 0 m 100 m 200 m 003:D =++++
m. 2005
m 0 m 100 m 200 m 300 m 400:E =++++
3.1 Minimization of transportation costs: one final product
A B C D E
210
200
190
180
170
160
150
140
130
120
110
Location
Averagedistance
3.1 Minimization of transportation costs: one final product
A B C1
2
3
a
b
Figure 3.3:
Optimum location in a two/dimensional space.
3.2 Minimization of transportation costs: one resource, one final product
A BS
ta
100 km
tb
Figure 3.4: Location of a firm that produces only one product with the help of one
raw material
3.2 Minimization of transportation costs: one resource, one final product
bbaa fbtfatK +=
10.0 ;100 : 1000; : == ba ffba
,100 ab tt −=
( ) .90100010.0100100100010.0 aaa tttK +=⋅−⋅+⋅=
Figure 3.5: Minimization of transportation costs with one input and one product.
3.2 Minimization of transportation costs: one resource, one final product
0 10 20 30 40 50 60 70 80 90 100
11
10
9
8
7
6
5
4
3
2
1
km
ta
x €1000
K
K = 1000 + 90 x
A B
ta
3.3 Trans�shipment costs
* Trans/shipment costs are costs that are made when the transportation mode changes.
* For example, in a sea port, the cargo may be transported further to the hinterland by truck, rail or inland waterways.
* Trans/shipment costs are normally expressed in money units per weight unit (e.g. euro’s per ton)
3.3 Trans�shipment costs
Figure 3.6: Location S of a business with transshipment location O
G MS O
t g
T
t m
3.3 Trans/shipment costs
,gmmmgg gomofmtfgtK +++=
,gm tTt −=
.)( mgmgmg gomoTmftmfgfK +++−=
3.3 Trans�shipment costs
� In the case of trans/shipment costs the optimum location is found with:
.)(
,
,
TmftmfgfK
goTgfK
moTmfK
mgmgo
ggm
mmg
+−=
+=
+=
3.3 Trans�shipment costs
� If
� Then the firm is footloose
.omg KKK ==
3.4 Other location factors
� Apart from transportation costs there are two other important location factors:
� labour costs;
� agglomeration benefits or external economies of scale.
3.4 Other location factors
Agglomeration: a spatial clustering of interacting firms that is mutually beneficial because it generates a decrease in production costs
Deglomeration: spatial deconcentration of firms because of external diseconomies of scale
3.5 Alfred Weber’s theory on locationy
xA B
C
S
tc
tb
ys
xsxc
xb
yc
at
Figure 3.8: Location triangle.
Alfred Weber (1886�1958)
Pierre Varignon (1654�1722)
3.5 Alfred Weber’s theory on location
A B
C
S
tc
tbta
Figure 3.9: The Varignon frame.
3.5 Alfred Weber’s theory on location
Original Varignon Frame
3.5 Alfred Weber’s theory on location
.)()( ,)( , 222222sccscsbsbssa yyxxtxxytyxt −+−=−+=+=
,ccbbaa fctfbtfatK ++=
.)()( )( 222222sccscsbsbssa yyxxcfxxybfyxafK −+−+−+++=
.0=∂∂=
∂∂
ss y
K
x
K
3.5 Alfred Weber’s theory on location
S+20
+40+60
-10
V
W
-70
Figure 3.10: Transportation cost optimum with isodapanes.
3.5 Alfred Weber’s theory on location
S+20
+40
+60
S
+20
+40
+60
1 2S
-60
Figure 3.11: Agglomeration benefits.
3.5 Alfred Weber’s theory on location
0 20
+20
+40
+60
10
10
10
10
20
20
20
30
30
30
30
0 20101020 3030
y
y
x
100
20
40
60
80
100
20
40
60
80
=0
y =0
Production costs
Spatial marginto profitability
SpatialCost curve
Total Revenue
Figure 3.12: Spatial margins to profitability.Figure 3.12: Spatial margins to profitability.
3.5 Alfred Weber’s theory on location
Figure 3.13: Sections in the location triangle.
y
xA B
C
S
tc
ys
40
20 60
y =0
y = 5
y =10
y =15
y =20
y =25
y =30
y =35
y =40yc
xsxc
xb
tbbta
3.5 Alfred Weber’s theory on location
05
1015
2025
3035
4045
5055
60
110
105
100
95
90
85
80
75
70
y =0y =5y =10
y =15
y =20
y =25
y =30
y =35
y =40
76,44
K
x
Figure 3.14: Transportation cost curves of a classical location problem.
3.5 Alfred Weber’s theory on location
K
Figure 3.15: 3�D presentation of the transportation cost function.
.)40()20()60(5.0 222222ssssss yxxyyxK −+−+−+++=
3.5 Alfred Weber’s theory on location
www.corusgroup.com/file_source/staticfiles/corus_locations.pdf
3.6 The theory of market areas
Three important authors:
� Walter Christaller (1934),
� Tord Palander (1935),
� August Lösch (1939).
3.6 The theory of market areas
3.6 The theory of market areas
A B
Market area A Market area B
Pa Pb
Fa Fb
O G ZDistance
Prices and costs
Figure 3.17: Palander’s market areas
3.6 The theory of market areas
quantity
distancedistance OAB
distance
distance
Figure 3.18: Quantity consumed as a function of the distance to the location of the
producer (O); the spatial demand function.
3.6 The theory of market areas
Figure 3.19: Seven firms with their market areas.
3.6 The theory of market areas
Figure 3.20: Hexagonal structure and hierarchy of central places.
3.7 Spatial elasticity of demand
.distancein change %
demandin change %
q
x
dx
dq
q
x
x
q
x
xq
q
E ds ≈
∆∆=
∆
∆
==
.α−= Kxq
.1
ααα
α
−=−= −
−−
Kx
xKxE d
s
3.7 Spatial elasticity of demand
Figure 3.21: Spatial demand curve with fixed spatial demand elasticity of �1.
0
2
4
6
8
10
12
1 3 5 7 9 11 13 15 17 19
x
q
3.8 Market forms: spatial duopoly
A B
AB
A B
AB
BA
1
2
3
4
5
Figure 3.22: Spatial duopoly: Hotelling’s Law.
3.8 Market forms: spatial duopoly
Hotelling’s Law:
� spatial competition leads to clustering of competitors in the centre
� Hotelling’s Law is based on a zero spatial demand elasticity:
� In terms of game theory Hotelling’s Law describes a Nash Equilibrium
� Hotelling’s Law is also used by political scientists to explain the positioning of candidates running for a political position:
http://www.rawstory.com/exclusives/steinberg/ice_cream_082005.htm
.0=α
Harold Hotelling (1895/1973)
3.9 Application www.sugartech.co.za/factories/index.php
Sugar factory
Figure 3.23: Location of sugar factories in the Netherlands in 1992
