Geography Reference
In-Depth Information
dif erent i xed costs or individual preferences for one particular location, because of, for
instance, existing social linkages. At every time step a i rm is randomly chosen to exit the
economy. At the same time a new i rm enters and chooses whether to be located in 1 or in
2 by comparing the individual utilities in (24.18). As long as the distribution of
e
i
,
l
across
i rms is well behaved (see Bottazzi and Secchi, 2007; Bottazzi et al., 2008, for details) the
resulting probability of choosing
l
is given by:
e
p
l
e
p
1
1
e
p
2
,
l
[
{
1,
2
}
Prob
l
5
(24.19)
The fact that the locational choice is probabilistic derives from the assumption that the
new entrant possesses preferences, or faces costs, that are not i xed, but contain an indi-
vidual component that is randomly extracted from a given distribution.
When the probability of choosing location
l
is given by (24.19), Bottazzi and Secchi
(2007) show that, if the exponentials of proi ts are linearly changing in the number of
i rms, it is possible to compute the long-run stationary distribution of the entry-exit
process. Thus, to exploit this result we need a linearized version of the exponential proi t
functions. We can naturally obtain it as the deviation from the middle point
x
* = 0.5,
that is, the unique point where proi ts are equal.
Proposition 3
Consider an economy with two locations, l =
1, 2
, where Assumptions 1-4
are valid
.
Denote the linearization of location l exponential proi ts around
x
*
=
0.5
as c
l
, and the number of i rms in location l as n
l
.
Linearized expo-
nential proi ts are given by:
c
l
=
a
+
bn
l
,
l
=1, 2
(24.20)
where:
4at
s21
(
1 1 t
s21
)
2
a
5 1 2
4a
2
st
s21
I
m
(
1 1 t
s21
)
2
b
5
(24.21)
Proof
. See Appendix.
We shall call the term
a
in (24.21) the 'intrinsic proi t'. This is the part of the common
proi t that is entirely dependent on exogenously given characteristics of the location.
Conversely, the coei cient
b
in (24.21) captures the marginal contribution of a i rm to the
proi t level of the location in which it resides. We shall call it the 'marginal proi t'.
4
In our
case, this coei cient captures the total ef ect of pecuniary and technological externalities.
Because of the leading ef ect of the latter it is always positive but, because of the presence
of market mediated interactions, it is dependent on transportation costs. Specii cally,
the marginal proi t is increasing with the value of t. When transportation costs are high
(low t) each i rm's marginal contribution to the location proi t is small, whereas when
transportation costs are low (high t ) the marginal contribution is large.
Given the linearization in (24.20), the following proposition characterizes the long-run
geographical equilibrium distribution.
