Geography Reference
In-Depth Information
In the initial Hotelling game, we will also assume that the firms do not
compete in terms of output pricing, such that their only strategic decisions
are with regard to their location. The reason is that changes in location
can be used in order to change the overall spatial market area of the firm.
In terms of the firm's strategy we assume that each firm makes a strategic
decision regarding location on the basis of the assumption that its com-
petitor will not change its existing location choice. As such, each firm is
rather passive in as much as it takes the existing competitive environment
as given and reacts accordingly. In the game theory literature this par-
ticular set of rules describing the nature of the competitive environment
are known as 'Cournot conjectures'. If the firms react to each other over
sequential time periods it is quite straightforward to determine the loca-
tional outcome.
In order to motivate our Hotelling game of spatial competition we once
again assume a market space OL containing two firms A and B , with A
located to the left of B . The distance from O to A is here denoted as a , and
the distance from L to B is here denoted as b . The distance from each firm
to the market boundary is x . The distance from O to the market boundary
Z is denoted as z , and the total distance OL is denoted as l. In order for
this duopoly of two competing firms to exist there must be three condi-
tions satisfied. The first condition is that a consumer located at point O
must always buy from firm A . In other words, the delivered price of the
output of A at O must always be less than the delivered price of the output
of B at O . Following Richardson (1978) and McCann (2001) this can be
written as:
p A
1 t A a , p B
1 t B ( l 2 b )
(3.5)
Similarly, a consumer located at point L must always buy from firm B .
This can be written as:
p B
1 t B b , p A
1 t A ( l 2 a )
(3.6)
Thirdly, at the same time there must also be an indifferent consumer at a
distance z somewhere between A and B . For this indifferent consumer the
delivered prices must be the same. In other words:
p A
1 t A ( z 2 a ) 5 p B
1 t B ( l 2 b 2 z )
(3.7)
If we set t A 5 t B , then rearranging equation (3.7) gives:
p A
2 p B
1 2 tz 2 ta 2 t l 1 tb 5 0
(3.8)
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