Geography Reference
In-Depth Information
Proposition 1
Consider an economy with two locations, l
= 1, 2,
a
nd N i rms, where
Assumptions 1-2 are valid
.
The average i rm's proi t
p
does not depend on
transportation costs and is given by:
p 5
2
I
m
N
s
2
x
a
1
2
(
1 2
x
)
a
2
(24.13)
Proof
. See Appendix.
If now one assumes that a
1
= a
2
, since location-specii c indexes have disappeared from
any variable, only market forces are at work and our model becomes close to the one of
Forslid and Ottaviano (2003). Following Bottazzi and Dindo (2008) we take a dif erent
route.
Before doing so, a last remark is necessary concerning the general equilibrium setting. In
our framework, labor and goods markets are at equilibrium only when total i rms' proi ts
are zero, and only provided that the demand for labor in both locations is not higher
than
I
. Concerning the former condition, notice that proi ts are already zero for the com-
petitive agricultural i rms but not necessarily so for manufacturing i rms. Nevertheless
it is possible to set zero proi t for the manufacturing sector, imposing a long-run equi-
librium condition on the size of the economy. We shall do so in Assumption 4 below.
Concerning the latter condition, one has that, because of labor market segmentation
(no mobility), labor demand in both locations should be lower than
I
. Straightforward
computations show that this amounts to imposing a restriction on the preferences for
manufacturing goods, namely μ < s/(2s − 1), which we will assume to hold from now
on.
2
As a result, provided that preferences for manufacturing goods are not too strong
and on imposing a long-run zero proi t condition on the number of i rms, prices and
quantities as in (24.6) and (24.11) guarantee that both labor and good markets are at
equilibrium.
Technological externalities
By retaining a dependency of the i xed cost a on the location index, we introduce a local-
ized technological externality because of direct i rms' interaction, that is, not mediated
by market forces (Scitovsky, 1954).
Assumption 3
: 'Cost sharing' hypothesis. Firms' i xed costs a
l
decrease with the number
of i rms located in
l
according to:
, where
x
l
5
n
l
a
1
5
a
2
x
1
N
,
l
[
{
0,
1
}
(24.14)
Assumption 3 represents a positive technological externality in the form of a baseline
'cost sharing': the larger the number of i rms in one location, the lower the i xed costs
these i rms bear in the production activity. Since the i xed cost paid by i rms in a given
location decreases proportionally with the number of i rms populating that location, the
total i xed cost paid remains, location by location, constant. This ef ect can be thought
of as an up-front cost paid to improve access to skilled labor, the more i rms in one loca-
tion, the smaller each i rm's investment in training, or as a cost for services or infrastruc-
ture use, which is evenly shared among all the active i rms in one location.
An important feature of the specii c form of 'cost sharing' introduced in Assumption 3