Geography Reference
In-Depth Information
Price/Cost
O
Z
L
Market of A in time period
1
Market of B in time period
1
Market of A in time period
2
with a price cut by Firm A
Figure 3.15
The effect of price competition on the Hotelling result
models this is known as the Bertrand problem and it is a problem which is
faced by all oligopoly industries and firms.
The Bertrand problem can be depicted in price space as in Figure 3.16,
in which the best price response of each firm is plotted against the price
offered by the other competitor firm. The price
p
a
charged by firm
A
which
is its best response
r
a
(
p
b
) to the price offered
p
b
by firm
B
, is to just offer a
price which just undercuts the price
p
b
. Similarly, the best price
p
b
offered
by firm
B
is to offer a price response
r
b
(
p
a
) which just undercuts the price
p
a
offered by firm
A
.
If price competition is engaged in when the firms are located at the
centre of the market
Z
the Bertrand problem of an unending downwards
price spiral becomes unavoidable. However, the objective of the firms
in the Hotelling model is to acquire, preserve or gain monopoly power.
Therefore, in order to generate localized monopoly power, as prices spiral
downwards due to the Bertrand problem, each firm has an incentive
to move away from its competitor in order to generate positive profits
by maintaining a degree of localized monopoly power over some of the
market area. Unfortunately, neither firm has an incentive to move away
