Classical Location
Theory
Based on: Alfred Weber, Über den
Standort der Industrien 1909
Minimum cost location
I vant to bite you on zee neck!
Source: The Lethbridge Herald January 27, 2003: A1
Weberian Location Theory
A deductive and normative theory to
explain industrial location
 Normative theory: to explain where
industrial activity should be located
 “The question of the best location is far
more dignified than determination of the
actual one” (August Losch, The
Economics of Location 1954)

Weberian Industrial Location
Theory

The best location of production is
determined by minimizing transportation
costs, assuming fixed locations for:
– Markets
– Raw materials
– Labour
Raw Materials and Weber’s
Material Index
Ubiquitous raw materials
 Localized raw materials

• Pure
• Gross
weight of localized raw material
Material index 
weight of finished product
If MI > 1, raw material orientation
 If MI < 1, market orientation

Weber’s Assumptions
Perfect competition: each producer
supplies a market of unlimited size with
no possibility of monopolistic
advantages arising from the chosen
location
 Fixed locations for raw materials, labour
and markets
 Isotropic surface




One localized pure raw material
Located at RM site
RM procurement cost increases away from raw
material site

But FP distribution cost decreases away from
raw material site and reaches a minimum at
the market itself.


With a pure raw material and a constant freight rate,
total transportation costs are constant.
Thus we should be indifferent about industrial
location, costs are same everywhere.

One localized pure raw material plus ubiquities
– Ubiquities add to the weight of the FP
– But they are as available at the market as everywhere else.

Market oriented industrial location
Soft drinks bottling plants: classic
examples of market orientation
Source: F.P. Stutz and A.R. de Souza The World Economy 3rd edition 1998 Prentice Hall

One localized gross raw material
– Location at RM site eliminates cost of transporting waste
materials

Processing of gross raw materials tends to be
oriented to raw material locations
Copper ore processing
Source: F.P. Stutz and A.R. de Souza The World Economy 3rd edition 1998 Prentice Hall
Orange grove, Florida Gulf Coast
Orange processing, Dade City FL
In the real world…
Freight rates for finished products are
higher than for raw materials.
 Terminal costs act as a fixed cost
discouraging industrial location at
intermediate locations.
 But intermodal transfers may require a
break-in-bulk which may favour an
intermediate location feasible.
 Freights are stepped by zones rather
than a smooth function of distance




So this kind of Weberian analysis is only the
beginning of a much more complex situation.
And it assumes only one raw material is required!
What if there is more than one input to an industrial
process?
Weber’s Varignon frame
A mechanical solution
 Imagine a board with holes located at
their relative locations. Tie strings
together and thread through the holes.
From each string we suspend weights
proportional to the quantity of localized
raw materials required for the product.
 Mathematical solutions are also
possible!

Varignon Frame
Source: F.P. Stutz and A.R. de Souza The World Economy 3rd edition 1998 Prentice Hall
Another Varignon Frame
Source: P. Dicken and P.E. Lloyd Location in Space 3rd edition 1990 Harper&Row
The Variable Cost Model

To expand on Weber’s model and avoid his
preoccupation with transportation costs, we
develop a new model focusing on total costs.

Based on David Smith’s Industrial Location
2nd ed. New York: John Wiley 1981
Imaginary data
Input
Cheapest
source
Basic cost Locational Locational
of
cost per $- pull
Quantity unit/mile ($/mile)
required
Distance
between
cost
isolines
Material
A
30.00
0.0333
1.00
5.00
Labor
B
30.00
0.0333
1.00
5.00
Power
C
30.00
0.0333
1.00
5.00
Land
None
5.00
Nil
Nil
--
Marketing None
5.00
Nil
Nil
--
Based on David Smith’s Industrial Location 2nd ed. New
York: John Wiley 1981
Understanding the data

Basic cost is for the required quantity to
produce one unit of output at its cheapest
source.
 It will cost an additional 3.33 cents per mile to
move each of the raw material, power and
labour inputs away from their minimum cost
locations.
 Land marketing are treated as ubiquities or
spatial constants.
 This may be shown graphically…
Imaginary surface

A locational triangle
 A, B, C represent
cheapest source for
inputs, material,
labour and power,
respectively-.
 Let’s add isocost
lines to point B
One supply funnel centred on B

Basic cost at point B is
$30.
 Beyond B, the
locational cost includes
transportation,
increasing at a fixed
rate away from B
creating a supply funnel
Three supply funnels



Add isocost lines to
points A and C
Note that locational pull
is the same for all three
inputs
These isocost lines are
known as isotims, they
rise away from points
A,B,and C (note that the
direction of slope is
indicated by the
orientation of isotim
labels)
Towards a total cost surface



We may plot the total
cost (basic cost +
locational cost) for any
point.
If we do this for every
point in space, we
create a total cost
surface.
We could then show the
shape of this three
dimensional surface
with a family of isocost
lines which are known
as….
Isodapanes I


A line joining equal total
cost locations drawn
around the minimum
total cost location
Note that as a specific
form of generic isolines,
these isodapane labels
are upside down!
Isodapanes II


To give a two dimensional
impression of this three
dimensional cost surface,
we may draw a profile along
line PQ
We may then project a line
downwards from each point
of intersection between an
isodapane and line PQ.
We may now
plot a “space
cost curve”
as a profile
of the total
cost surface
Price is spatially
fixed, hence
revenues are
represented as a
straight line.
Ma and Mb
indicate the
spatial margins
to profitability
Price is spatially
fixed, hence
revenues are
represented as a
straight line.
Ma and Mb
indicate the
spatial margins
to profitability
Point O
indicates the
minimum cost
location!
Adding Complexity to the Model

Allow basic costs
to vary
 Allow locational
costs to vary
 A new family of
isodapanes is
created which
yields,
 a new space-cost
curve!
Classical Location Theory
Data needs are huge
 Cost, revenue and profit surface for
each industry is complex and different
 Some industries have a flat “profit
topography,” others are more rugged,
and still more face mountain and
canyon-like features.
 But classical theory pays little heed to
strategic behaviour by multilocational
firms.
