Geography Reference
In-Depth Information
If the transport rates
t
A
and
t
B
for the two firms are the same, and the
source prices,
p
A
and
p
B
, of the two firms are also the same, we have:
a
1 l 2
b
2
z
5
(3.9)
The value of
z
given in equation (3.9) represents the size of the market
captured by firm
A
, and the size of the market captured by firm
B
can thus
be represented as:
l 2
z
5 l 2
a
a
1 l 2
b
2
b
1 l 2
a
2
b
5
(3.10)
Recalling from Figure 3.12 that
c
5 (l−
b
), we can rewrite (3.10) as:
a
1 l 2
(
l 2
c
)
2
a
1
c
2
z
5
5
(3.11)
In other words, if the transport rates are the same and also the product
source prices are the same, the market area boundary between the two
firms is exactly half way between the two firms, and is independent of the
transport rates. Therefore, for a given source production price
p
A
, known
as a 'mill' price, the market revenue of firm
A
depends on maximizing the
value of
z
. From Figure 3.12 we see that this is achieved by increasing
the distance
a
and reducing the distance
b
as much as possible, while still
ensuring that firm
A
is to the left of firm
B
. This is the 'one-shot' locational
optimum strategy. However, the Hotelling model allows for the fact that
the competition game can be played as a sequential location game under
Cournot conjectures, and the location behaviour implied by equation
(3.11) then triggers locational leapfrogging behaviour.
In Figure 3.13 we illustrate the outcome of this sequential Hotelling
spatial competition game by examining the case where the firms
A
and
B
are initially located at one quarter and three quarters of the way along the
market
OL
, respectively. As such, at the start of the game firm
A
will have
monopoly power over
OZ
and firm
B
will have monopoly power over
ZL
,
both of which are obviously identical market shares. In time period one,
following the behaviour implied by equation (3.11), firm
A
will therefore
move from its original location to a location at
C
, just to the left of
B
. In
this way firm
A
will increase its market share from
OZ
to a new maximum
value of
OC
. In contrast, although firm
B
will still retain market share over
BL
, its market share is now a minimum following the strategic location
behaviour of firm
A
.
