Geography Reference
In-Depth Information
and the products are differentiated here along a circular (non finite) a
product space. The location of each firm
F
, 1. . .
n
, implies a particular
set of product characteristics as reflected in a particular brand. In terms
of strategic behaviour we once again assume that the firms compete in
an environment of Cournot conjectures, whereby each firm assumes that
its competitor firm will maintain the same strategic behaviour as it has
already adopted. In our case, this implies that the firm will maintain its
same location behaviour along the product space, and the same principle
can also be adopted if we were to treat the Salop model primarily in terms
of geographical space.
As with the Hotelling model, in the Salop model each consumer is
assumed to be rational. Yet, there is a subtle shift between the explicitly
geographical space version of the Hotelling model described above and
the product space Salop model described here. In this latter case, each
location reflects a slightly different set of product characteristics, or put in
another way, a different brand. As such, in this model a rational consumer
therefore aims to relate the utility derived from consuming a particular
set of product characteristics to the cost of purchasing that particular
set of characteristics, in order to gain the 'best buy'. Once again, we can
reinterpret this as saying that a rational consumer aims to relate the utility
derived from consuming a particular brand to the cost of purchasing that
brand, in order to gain the 'best buy'. The relationship between product
characteristics, demand preferences and consumption in the Salop model
can be represented with the aid of Figure 3.18.
In Figure 3.18 we denote
U
as the consumer's utility derived from con-
suming the favourite brand,
l
* as the 'location' of consumer's favourite
brand or taste defined in terms of characteristics space, and
t
as the rate of
diminishing utility associated with consuming at a 'location'
l
which is not
at
l
*. In other words, in the Salop framework, the location
l
represents a
particular sub-optimal set of product characteristics and
t
represents the
strength of preferences associated with a movement along a unit 'distance'
d
away from
l
* to
l
. As such, in product characteristics space,
t
here is
analogous to the transport costs
t
in the explicitly geographical space of
the Hotelling model above.
With this notation, we can now write a simple expression for the con-
sumer's utility
u
given as:
u
(
l
,
l
*
)
5
U
2
t
0
l
2
l
*
0
(3.12)
in which the consumer's utility
u
is a function of the preference distance
d
between
l
and
l
*. In other words the consumer's utility
u
depends on
the distance between the brand characteristics of the product actually
