Geography Reference
In-Depth Information
fes
for firm
A
, and
rmn
for firm
B
. At the end of the location game in
the case of both firms the delivered prices are traced by the lines that go
through the points
gko
. Now we can compare these delivered price curves
in Figure 3.14 at the respective locations at the start and the end of the
Hotelling location game. The consumers who are located in the centre of
the market benefit by generally reduced delivered prices, represented by
jhkl
, whereas those located at the edges of the market lose by generally
higher delivered prices, represented by (
efgh
)1(
lmno
). The gain in lower
prices for the centrally-located consumers is outweighed by the increase
in prices for the more peripheral consumers. The net effect is therefore a
social welfare loss.
The Hotelling location conclusions discussed here also broadly hold in
situations where firms charge the same delivered price for a given product
at all locations. In such situations, the marginal profitability of each deliv-
ery will be different according to the distance between the firm and the
location of the customer. This is because the transport costs of outputs
must be absorbed by the firm. As such, the profits associated with deliver-
ies to nearby customers will be much higher than those for deliveries to
distant customers. The firm will therefore wish to locate so as to minimize
the transport costs. In most cases, this will still also imply an equilibrium
location at the centre of the market.
3.5.1
Price Competition, the Bertrand Problem and Non-price
Competition
These stable Hotelling model's location conclusions start to break down
if we also now allow for price competition. The problem can be explained
with the help of Figure 3.15.
In Figure 3.15, we can consider what would happen if price competition
is now allowed in the situation where both firms
A
and
B
are located at
Z
in the centre of the market, after having played the Hotelling location
game. If firm
A
now lowers its sales price marginally in time period 1 when
both firms are located at
Z
, in time period 2 firm
A
will gain all of the
market. From our assumption about Cournot conjectures in which a firm
assumes that its competitor keeps the same strategy it has already adopted,
we know that firm
B
therefore now assumes that firm
A
will maintain both
its new lower price and also its location at
Z
. Therefore in time period 3,
firm
B
also lowers its market price just below that of firm
A
, in order to
gain all of the market. This process will continue and the long-run Nash
equilibrium of this price war is that both firms will end up selling at zero
profit while still being located at point
Z
, because the market sale price will
be driven down to the marginal costs of production. Within oligopolistic
