Geoscience Reference
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uniformly distributed. (The often-mentioned “ice cream vendors on the beach” were
actually introduced by Lösch
1954
.) Each customer has a fixed and inelastic demand
for a given homogeneous good. Duopolists are now attempting to independently
enter the market, offering identical products. The competitors are profit maximizers,
and they attempt to achieve their objective by determining their respective locations
and prices; first both competitors choose their respective locations, followed by
the simultaneous choice of prices. It is assumed that both competitors employ
mill (or f.o.b.) pricing (a pricing policy in which customers pay a price set by the
facility and take care of the transportation themselves) and that transportation costs
between customers and facilities are linear. Customers will patronize the facility
that offers the good for the lowest full price, i.e., the smallest sum of mill price and
transportation costs. For simplicity, it is commonly assumed that the costs of the
firms have been normalized to zero.
Already in his original paper, Hotelling did not restrict himself to the aforemen-
tioned “main street” with customers in search for inexpensive physical goods from
brick-and-mortar retailers. One of the nonphysical applications he mentioned was
what we today refer to as brand positioning, viz., the location of a brand in some
feature space. More specifically, Hotelling used the example of ciders offered by
two firms, whose single distinguishing characteristic is their respective sweetness.
Given that a brand is sweeter (more sour) if it is located more to the right (left) side
of the market segment, the two firms will determine optimal locations and prices so
as to maximize their respective profits.
Similar, albeit with a marked difference, is the political positioning model that
was also mentioned in Hotelling's original paper. The idea was very simply for
each of two political parties to each locate their own candidate, so as to maximize
the number of votes (i.e., the number of customers, or the market share) that the
candidate would obtain. The line segment was used to mimic the traditional left-
right scale in politics, voters (i.e., their “ideal points,” which symbolize their most
favored position on the line) were again assumed to be uniformly distributed on the
line segment, and the candidates would not have any inherent stand on the issues,
they would simply position themselves at a point, where it would win them the
largest number of votes. However, in contrast to all other previously mentioned
applications, there are no prices in this model.
The main focus of Hotelling's original paper is the existence (or the lack) of a
stable solution, i.e., an equilibrium. Hotelling asserts that an equilibrium would exist
with both firms locating next to each other at the center of the market. This result
is often dubbed the “principle of minimum differentiation,” in reference to products
or political candidates being very similar to each other. Even though in a footnote,
Hotelling cautions that his result would not hold in highly competitive situation
(which is precisely what occurs when the two firms locate very close to each other),
he presented his agglomeration result as his major finding. Other authors, such as
Lerner and Singer (
1937
) and Eaton and Lipsey (
1975
) obtained different results, but
their contributions were based on Hotelling-style models albeit with fixed and equal
prices. Hotelling's original result was not disputed until d'Aspremont et al. (
1979
)
demonstrated 50 years later that no equilibrium exists in Hotelling's model. In
