Geography Reference
In-Depth Information
alternative whose utility is fixed and which is also unaffected by the product
or location strategies played by the firms in the Salop model. We denote
the consumer surplus associated with consuming the outside good as
w
.
If the consumer is 'located' at the location of their ideal brand tastes or
preferences, in that the consumer is consuming their ideal good, the surplus
gained by consuming this good can be written as (
U - p
*). However, we
also know that the consumer will only consume this ideal good within the
Salop model rather than the outside good if (
U - p
*) .
w
, or alternatively
if (
U -
w
) .
p
*. Therefore, the consumer's reservation price or reserva-
tion value
v
can be written as
v
5 (
U - w
), and this is the maximum utility
gained by consuming the ideal good, allowing for the opportunity costs of
consuming the outside good. As such, this also represents the minimum
consumer surplus which a consumer will need to gain by consuming an
alternative good which is not ideally located in product space, in order for
the consumption of any alternative good in the Salop model to take place.
Therefore, if we denote the price paid for the good located at a distance
d
5
l
−
l
* in the Salop model as
p
l
, then we know that the behaviour of the con-
sumer in terms of consuming the good in the Salop model can be written as:
Max
[
u
(
l
,
l
*
)
2
p
l
]
$
w
(3.13)
which means that the consumer will maximize the net utility gain (con-
sumer surplus) from consuming an alternative good within the Salop
model, if the consumer surplus gained is greater than that which would be
gained by consuming the ideal good instead of the outside good.
Assuming that
L
consumers are distributed evenly around the circle,
and that a firm has a monopoly region as depicted in Figure 3.19, then we
can write:
u
(
l
,
l
*
)
2
p
l
5
v
2
td
m
2
p
l
$ 0
(3.14)
i.e.:
v
2
p
t
5
d
m
(3.15)
This is the maximum distance between the firm and the edge of its
market boundary in a Salop monopoly region model. From Figure 3.19
we know that each brand therefore captures:
2
(
v
2
p
)
t
2
d
m
5
(3.16)
