Geography Reference
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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:
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