Geography Reference
In-Depth Information
Proposition 2
Consider an economy with two locations, l
= 1, 2
where Assumptions 1-4
are valid
.
Call x the fraction of i rms located in
1.
There always exist two,
and only two, geographical equilibria given by the border distribution
x
1
5 1
and x
0
5 0.
In particular, the unique distribution where proi ts are
equal, x
*
=
0.5
, is never an equilibrium
.
Proof
. See Appendix.
According to the previous proposition, the distribution with half of the i rms located
in 1 and the other half located in 2, which is the unique case where p
1
= p
2
, is never a geo-
graphical equilibrium: even if proi ts are equal, incentives are such that i rms move away
and agglomerate. Only when all i rms are located either in 1 or 2 are there no incentives
to change location.
Notice that, even if transportation costs do af ect the shape of each location's proi t
function, they have no impact in characterizing the geographical equilibria of the
economy. Conversely, as we shall see in the following section, transportation costs
play a major role in shaping the results of the evolutionary model, even in the long
run.
4. Evolutionary i rms' dynamics
In the previous section we have shown that, when the technological externality term is
introduced, i rms agglomerate in one of the two locations, irrespective of transporta-
tion costs t or the relevance of technological spillover as dependent on a. This abrupt
behavior would prescribe that any sector in which even a minimal level of localized non-
pecuniary externalities operate should display a so-called core-periphery structure. This
is clearly at odds with empirical observations. Notice that this conclusion would remain
a fortiori valid if instead we had considered workers' mobility with endogenous wage
setting, thus introducing a feedback ef ect that reduces (or inverts) the push of pecuni-
ary externalities towards a symmetric geographical distribution. This ef ect ultimately
reinforces the conclusion that in the presence of technological spillovers only a core-
periphery structure represents an equilibrium. We end up in the uncomfortable situation
of having a single possible equilibrium, implying the impossibility of performing an
empirical analysis or deriving policy implications. A possible way out from this impasse,
as we will show, is to extend the notion of geographical equilibrium to include an explicit
dynamics describing i rms' locational decisions. The foregoing analysis is, indeed, essen-
tially static and thus silent on the results of i rms' interactions out of equilibrium. As a
consequence, it is not clear what happens when the initial concentration of i rms is not
at an equilibrium level; in particular, whether one should expect i rms to agglomerate in
location 1 or in location 2.
In this section we extend our analysis by introducing heterogeneity in preferences at
the single i rm level and by explicitly modeling i rms' decisions in time, that is, by allow-
ing for a dynamic location-specii c mechanism. Suppose that the individual utility of i rm
i
derived from locating in
l
i
can be written as:
p
i
= p
l
i
+
e
i
,
l
i
(24.18)
where p
l
i
are as in (24.17) and
e
i
,
l
i
represents an idiosyncratic proi t component intended
to capture i rm-specii c characteristics, like dif erences in productive ei ciency leading to
