Geography Reference
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at the extremal outcomes
x
= 0 and
x
= 1. Agglomeration is thus the most likely event
but, as simulations show, this does not mean that once agglomeration on one side has
been achieved, the situation is stable. In fact, turning points exist where the mass of i rms
moves from one location to the other. In the second scenario the long-run geographi-
cal distribution has a unique mode. In this case, the most likely occurrence is having
half of the i rms located in one region and the other half in the other region. However,
because of the stochastic nature of the process, l uctuations around this average level are
present. This scenario is typically associated with high transportation costs, and occurs,
in general, when the ef ect of externalities is weak with respect to the intrinsic proi t levels
of each location.
Summarizing, the main contribution of the foregoing analysis is to show how i rms'
heterogeneity and an individual choice process act as brakes or constraints on i rms'
agglomeration, even when strong incentives to locate in already populous locations
exist. Moreover, having introduced an explicit time dimension, we have given history a
role. Indeed the time dimension matters in two respects: i rst, the initial distribution of
activities across two locations does inl uence the subsequent observed distributions and,
second, when agglomeration is observed, because of stochastic l uctuations, it is only a
metastable phenomenon. That is, by waiting long enough, the cluster eventually disap-
pears, just to be recreated soon after, with probability 1/2, in the other location.
Our model can be extended in several directions. First of all, the 'cost sharing' assump-
tion, while useful, is admittedly ad hoc. More careful modeling is probably needed. The
ef ort should not be restricted to the notion of technological and/or knowledge spillover,
which might even be characterized by a pecuniary nature, see, for example, Antonelli
(Chapter 7, this volume), but could encompass also other, possibly negative, sources
of interactions that are not market mediated, like pollution and/or congestion ef ects.
A second extension of the model would be to generalize consumers' behavior along the
same lines we followed to describe i rms' behavior. Whereas in the present version of
the model consumers are homogeneous and maximize the same CES utility function,
it would be interesting to assume that consumers are heterogeneous and to explicitly
model their consumption decision in time. In that case, changing the size of the economy
would imply, because of varying idiosyncrasies in consumers' demand, a change in the
amplitude of proi t l uctuations. This, in turn, would impact the likelihood of observing
agglomerated outcomes, probably reducing it.
In any case, we are aware that the ultimate test will be to confront our model with
real data. An interesting aspect of the discrete choice model we implemented is that it
leads quite easily to empirical applications. An exercise in this direction has already been
performed in Bottazzi et al. (2008), where the parameters characterizing the geographi-
cal equilibrium distribution have been estimated in several sectors of the Italian manu-
facturing industry. The present work moves in the direction of developing a theoretical
framework able to provide deeper and more informative economic interpretations of
these econometric exercises.
Notes
*
Thanks to the participants to the DIMETIC Summer School 'Geography of Innovation and Growth',
Pecs, Hungary; the First DIME Scientii c Conference, Strasbourg, France; and seminars given at the
Università degli Studi di Napoli 'Parthenope' and at the Scuola Superiore S'Anna, Pisa, Italy. The research
