Geography Reference
In-Depth Information
a sort of 'size' ef ect: increasing the size of the economy lowers the externalities so that,
because of the entry-exit process, the likelihood of observing agglomeration is lowered.
The right panel of Figure 24.4 shows that, keeping t i xed, an increase in the i xed
cost parameter a leads, in general, to more agglomerated economies. It is so because
an increase in a decreases the intrinsic proi t
a
while increasing the marginal proi t
b
.
More precisely, a determines the scale of the proi t dif erentials. Indeed, on the one
hand, the dif erence between the maximum and the minimum proi t is proportional to
a and, on the other hand, because of Assumption 4, the higher a the lower
N
, so that a
bigger proi t dif erence is caused by a lower number of i rms. As a result, increasing i xed
costs decreases the proi t each i rm earns irrespective of the presence of other i rms, and
increases the ef ect of each locational choice on the proi ts of others. Both ef ects go in
the direction of increasing the likelihood of agglomeration. This is a sort of 'scale' ef ect
where increasing the scale of proi ts increases the likelihood of agglomeration.
Concerning the ef ect of the transportation cost on the shape of the equilibrium dis-
tribution, notice that the expression t
s−1
/(1 + t
s−1
)
2
, which appears in (24.21) for both
a
and
b
, but with a dif erent sign, is an increasing function of t. Thus, increasing the value
of t leads to an increase in the marginal proi t
b
and a decrease in the intrinsic proi t
a
.
This means that low transportation costs, that is, high values of t , favor agglomeration,
while high transportation costs favor equidistribution. Indeed, when transportation
costs are low, the pecuniary externality is relatively weak and the technological external-
ity relatively strong. In terms of the entry-exit process, the choice of a i rm to relocate
its activity has an high impact on the level of proi ts. Consequently, it is likely to trigger
other relocations and, eventually, a strong agglomeration is observed. Conversely, when
transportation costs are high, the pecuniary and technological externalities almost of set
each other. This implies that marginal proi ts are small and intrinsic proi ts dominate,
so that each locational choice has a very small impact on the general level of proi ts. The
attracting force of each location does not depend on the externality term and, given the
symmetry of the two locations, equidistribution is likely to be observed.
5. Conclusion
We have analyzed a model of i rms' location in geographical space where i rms interact
both indirectly, through market interactions, and directly, through technological exter-
nalities, and where workers are not mobile. In this simple framework we have briel y
discussed the general equilibrium static case, identifying the possible geographical
equilibria, that is, the spatial distributions in which i rms do not have any incentive to
relocate their activities. We have showed that in this case the 'cost sharing' assumption
implies long-run agglomeration, irrespective of the number of consumers, their prefer-
ences, and transportation costs. Then we have extended the analysis to include heteroge-
neity in i rms' preferences and an explicit time dynamics in their choices, thus obtaining
a stochastic model of i rms' dynamics. We have been able to characterize the long-run
geographical distribution of the process for dif erent specii cations of the economy.
This analysis has revealed that, contrary to the static equilibrium analysis, when an
explicit entry-exit dynamics is assumed to characterize the locational decision of i rms,
the economy can evolve towards two dif erent long-run scenarios. In the i rst scenario,
where externalities are stronger than intrinsic location proi ts, which typically occurs for
low transportation costs, the long-run geographical distribution is bimodal with modes
