Geoscience Reference
In-Depth Information
Fig. 14.1
Hotelling's duopoly on a linear market
order to follow the argument, first consider a graphical representation of Hotelling's
scenario as shown in Fig. 14.1 . Here, the linear market extends from 0 to 1, and the
locations of the two competitors are shown as A and B , respectively. They charge
mill prices p A and p B , respectively, and transportation costs are linear, resulting
in full prices to the customers shown in the two “V” shaped functions. The two
functions intersect at some point X , which is usually referred to as the marginal
customer , i.e., the customer who pays the same full price (i.e., the mill price plus
transportation costs) purchasing from firm A as he does purchasing from firm B .As
a matter of fact, the function that describes the full price for all customers on the
line segment is the lower envelope of the two “V”-shaped functions. Furthermore,
the market can now be subdivided into the following parts: The first piece of length
a is firm A 's hinterland ,which A captures in its entirety. Similarly, the stretch b on
the right is firm B 's hinterland, which is captured by B . The remaining area is the
competitive region between firms A and B . (The terms “hinterland” and “competitive
region” appear to have been introduced by Smithies 1941 .) This is subdivided into
parts x and y , such that x is the part in which customers can purchase more cheaply
from firm A , while in y , customers can purchase the good more cheaply from
firm B .
This allows us to determine the market shares of the two firms simply as
M ( A ) D a C x for firm A and M ( B ) D b C y for firm B . This depiction of the scenario
also permits us to examine the two forces that govern the process. The market share
force pushes the two facilities towards each other. The reason is that—given that
his opponent does not react, at least temporarily—a facility can move towards its
competitor and, in doing so, not lose market in its own hinterland, while gaining in
the competitive region. This force applies, as long as customers do not have finite
(and reasonably low) reservation prices , i.e., an upper bound on the full price they
are able or willing to pay for the good. On the other hand, there is the competitive
pricing force that pushes the two facilities apart. The reason is that if the two firms
locate very close to each other, whatever price one of them sets, his competitor can
Search WWH ::




Custom Search