Geography Reference
In-Depth Information
m
n
1
p
1
1
n
2
p
1
p
12s
mt
s
d
11
5
t
s21
d
12
5
n
1
p
12s
p
2
1
n
1
p
2
t
s21
2
1
m
mt
s
n
1
p
1
t
s21
1
n
2
p
1
p
12s
d
22
5
p
2
t
s21
1
n
2
p
2
d
21
5
(24.9)
n
1
p
12s
1
2
Equating, location by location, i rms' supply and consumers' demand, gives:
y
1
5
Id
11
1
Id
21
t
y
2
5
Id
22
1
Id
12
t
µ
(24.10)
where t discounts the demand of imported goods. Plugging (24.9) in (24.10) and using
(24.6) one can solve for market equilibrium quantities:
y
1
5
I
m
(
s 2 1
)
bs
1
n
1
1
n
2
t
s21
1
t
s21
n
1
t
s21
1
n
2
b
a
µ
(24.11)
y
2
5
I
m
(
s 2 1
)
bs
1
n
2
1
n
1
t
s21
1
t
s21
n
2
t
s21
1
n
1
b
a
Proi ts in each location can now be found using the latter expression together with (24.4)
and (24.6). Introducing the fraction of i rms in location 1,
x
=
n
1
/
N
(so that
n
2
= (1 −
x
)
N
),
and normalizing the level of wages to one, proi ts can be i nally written as a function of
x
:
p
1
(
x
)
5
I
m
1
x
1
(
1 2
x
)
t
s21
1
t
s21
x
t
s21
1
(
1 2
x
)
b
N
s
a
2 a
1
µ
(24.12)
p
2
(
x
)
5
I
m
1
x
t
s21
1
(
1 2
x
)
1
t
s21
x
1
(
1 2
x
)
t
s21
b
N
s
a
2 a
2
Each location-specii c proi t function in (24.12) has a positive term proportional to
the total demand for goods produced in that location and a negative term equal to the
location- specii c i xed costs. In turn, the total demand has a domestic component, the i rst
term in the parentheses, and an import component, the second term in the parenthesis.
Both components depend on i rms' geographical distribution and transportation costs.
When the transportation cost is zero, t = 1, they are equal irrespective of i rms' distribu-
tion. When the transportation cost increases, the domestic component increases, as local
consumers substitute foreign goods with local ones. For the same reason, the export com-
ponent decreases. For any given positive transportation cost, when local i rm concentra-
tion increases, the local component decreases as agents have more local goods to consume,
all at the same price. In the same situation the export component increases, because foreign
consumers have fewer local goods to consume and i nd it convenient to import more.
The net ef ects of the transportation cost on the relative proi ts of the two locations are
appraised in the next section. However, even without knowing this ef ect, it can immedi-
ately be seen that market forces make the average proi ts independent of transportation
costs. Indeed one has the following:
