Geography Reference
In-Depth Information
Price/Cost
O
A
Z
C
B
L
Market of A in time period
1
Market of B in time period
1
Market of A in time period
2
Market of B in
time period
2
Figure 3.13
The Hotelling spatial framework
According to our assumptions or conjectures, firm
B
will now assume that
firm
A
will maintain its location at
C
. Therefore, in time period two, in
order to maximize its market, firm
B
will now move just to the left of
C
.
Similarly, in the following time period, firm
A
will respond by moving to
the left of firm
B
, and so on. This process will continue until both firms are
located at
Z
, in the middle of the market. Once both firms are located at
Z
, neither firm has any incentive to change its location behaviour, because
any location change will involve a reduction in market share of the firm
that moves relative to the 50 per cent market share it gained when loca-
tion is at
Z
. In game theory, any situation in which neither firm has any
incentive to change their behaviour is known as a 'Nash equilibrium', and
where the competition has been purely in output quantities determined by
the market size rather than competition according to prices, then we have
what is know as a Nash-in-quantities (Carlton and Perloff 2005). The loca-
tional result in which both firms are located at the centre of the market is
therefore the Nash-in-quantities equilibrium for this particular locational
game. Consequently, once the firms reach this point they no longer con-
tinue to move: this is the Hotelling result. From equation (3.11) we also
see that this result holds irrespective of the initial distribution of the firms,
so the case examined here in which both firms were originally located at
