Geography Reference
In-Depth Information
externality), whereas the second dependence is brought in by the 'cost sharing' hypoth-
esis (technological externality).
3. Geographicalequlibria
In this section we investigate the static geographical equilibria of the system, that is,
those distributions of i rms
x
such that, in the search for higher proi ts, each i rm located
in 1 has no incentives to move to 2 and vice versa. Geographical equilibria can be of two
types: 'border' equilibria and 'interior' equilibria. A border equilibrium occurs when
i rms concentrate in one location, say 1, and proi ts in 1 are higher than proi ts in 2. As
all the i rms are in 1, no other i rm can respond to this dif erence in proi t opportunities.
Candidates for border equilibria are
x
= 1, when all i rms are in 1, and
x
= 0, when all
i rms are in 2. Conversely, an interior equilibrium occurs when i rms distribute between
the two locations, that is
x
[ (0, 1), proi t levels are equal in both regions, and i rms do
not have any incentive to change their location. Using proi ts in (24.17) we will derive
results for the existence and uniqueness of geographical equilibria, border and interior,
for all the dif erent parameterizations of the economy. This static
3
analysis, which owes
considerably to Bottazzi and Dindo (2008) where more details can be found, is useful
to understand the interplay of pecuniary and technological externalities and constitutes
a useful step for the development of the evolutionary dynamic analysis of the next
section.
The respective role of each externality in determining proi t dif erentials and thus the
aggregate geographical equilibrium can be judged by looking at the shape of the proi t
functions and by keeping in mind that, because of transportation costs, local prices are
lower than foreign prices, and thus local demand impacts i rms' level of output more
than foreign demand. Consider the pecuniary externality term alone, for example, set
a = 0 in (24.17). For dei niteness, consider proi ts in 1 (results for proi ts in 2 follow in
the same way). For small
x
, that is, few i rms in location 1 and many i rms in location 2,
each i rm in 1 faces high local demand and low foreign demand. Because of the dif erent
impact of local and foreign demand, the level of output of i rms in 1 is high and proi ts
are high too. As
x
increases, the local demand for these i rms decreases, so that proi ts
decrease too. As the concentration of i rms in 1 increases further, for a sui ciently large
value of
x
, the demand coming from the consumers in 2, where very few i rms are left, is
more and more directed to 1 and the proi ts and the proi ts of i rms located in 1 increase
again. Proi ts are thus U-shaped, with p
1
(
x
)|
a=0
i rst decreasing and then increasing in
x
.
Since a i rm makes the most proi ts when alone in one location, we have p
1
(
x
= 0)|
a=0
>
p
1
(
x
= 1)|
a=0
so that the border distributions 0 and 1 are never an equilibrium. In fact,
when all i rm's are located in one region it is always more proi table to move to the other
region. If the transportation cost is increased (decreased), the variation in proi ts as a
function of
x
is more (less) pronounced but the general shape of the proi t function is pre-
served. As a result, the overall agglomeration ef ect of the pecuniary externality is always
'negative', in the sense that it works against concentration of production.
The above picture changes completely when one considers also the technological
externality terms introduced by the 'cost sharing' assumption, that is, a > 0 in (24.17).
The panels in Figure 24.1 show graphs of p
1
(
x
) and p
2
(
x
) in this case. Proi ts are given
by the superposition of a monotonically increasing technological externality to the
U-shaped market-driven pecuniary externality term. With low transportation costs (high
