Geography Reference
In-Depth Information
is that it doesn't modify the total i xed costs paid by the industry. This has consequences
on the computation of i rms' average proi t.
Corollary 1 Consider an economy with two locations, l
= 1, 2,
and N i rms, where
Assumptions 1-3 are valid
.
Tot
al
i xed costs in each location are equal to
a
N/
2.
The average i rms' proi t
p
does not depend either on the distribution
of i rms x or on transportation cost
t
and is given by:
p 5
2
I
m
N
s
2 a
(24.15)
Proof
. See Appendix.
Before we start to look for geographical equilibria, that is, those spatial distributions of
i rms where they have no incentives to change location, notice that, without restrictions
on the parameters' values, there could exist economies characterized by negative proi ts.
In this case, we would expect i rms to exit the economy. On the other hand, if proi ts
were positive we could expect i rms to enter the economy. As we consider the number
of i rms
N
in the model as given, if there are no barriers to entry, it seems reasonable to
set the number
N
to a level that implies zero proi ts. By force of Corollary 1 this can be
done also without knowing the geographical equilibrium distribution. Indeed proi ts at
a geographical equilibrium must be equal to average proi ts, and average proi ts (24.15),
because of Corollary 1, are independent on the geographical distribution
x
. Moreover,
as we have explained at the end of the previous subsection, zero total proi ts are needed
in order to guarantee that all markets are at an equilibrium. All together, it is enough to
have the following Assumption.
Assumption 4
: The number of i rms
N
is such that proi ts at a geographical equilibrium
are zero, that is:
N
5
2
I
m
sa
(24.16)
Even if, by construction, the previous assumption implies p = 0, outside the geograph-
ical equilibrium proi ts can be both positive or negative so that their dif erential gives
i rms the incentive to relocate. Before moving to the analysis of these incentives and to
the characterization of the geographical equilibria, it is useful to rewrite proi ts (24.12)
incorporating Assumptions 3-4:
p
1
(
x
)
5
a
1
x
1
(
1 2
x
)
t
s21
1
t
s21
x
t
s21
1
(
1 2
x
)
b
2
a
2
x
2
a
µ
(24.17)
p
2
(
x
)
5
a
1
x
t
s21
1
(
1 2
x
)
1
t
s21
x
1
(
1 2
x
)
t
s21
b
a
2
(
1 2
x
)
2
a
2
Given the i rms' production costs a, the products' elasticity of substitution s and the
transportation cost t, the distribution of i rms between the two locations,
x
, determines,
through (24.17), the levels of proi t. Notice that in (24.17), dif erently from (24.12),
both the demand driven term and the i xed cost term are functions of the geographi-
cal distribution of i rms. The i rst dependence is mediated by market forces (pecuniary
