Geography Reference
In-Depth Information
and the number of consumers captured is:
2
L
t
(
v
2
p
)
q
m
5
(3.17)
Differentiating
q
m
with respect to
p
gives:
q
m
0
0
52
2
L
t
(3.18)
p
From equation (3.18) we see that the monopoly quantity demanded and
sold falls by −
2L/t
as the firm raises its sales price
p
by $1.
We can now also apply a similar line of reasoning to the competitive
Salop case depicted in Figure 3.20. If there are
n
competing brands, then
following the logic above, if we also assume that both of a firm's immedi-
ately adjacent competitors are located at a distance of 1/
n
away and both
charge a price
P
, we can investigate how much of a market a firm captures
by selling at price of
p
.
In order to answer this question, we know already from Figure 3.20 that
the firm captures all of the market within a distance
d
c
from itself, whereby
the consumer surplus from each of the two competing brands is equal.
Therefore we can write:
v
2
td
c
2
p
5
v
2
t
c
1
2
d
c
d
2
P
(3.19)
n
in which the left hand side represents the consumer surplus from the firm's
own brand, and the right hand side represents the consumer surplus from
the competing brand. Given that:
q
c
5 2
d
c
L
(3.20a)
such that:
q
c
2
L
d
c
5
(3.20b)
We can therefore write:
tq
c
2
L
tq
c
2
L
t
n
v
2
2
p
5
v
2
1
2
P
(3.21)
and: