Geography Reference
In-Depth Information
two representative product markets, one for each location
l
, rather than the
N
distinct
products.
We shall compute market equilibrium prices, quantities, and proi ts for each i xed
distribution of i rms, that is, i xing
n
1
and
n
2
. First, exploiting the CES preference structure
(24.2), which gives a constant elasticity of demand, and assuming that the market struc-
ture is that of monopolistic competition, we derive i rms' pricing behavior. Then using
households' budget constraints we compute their total demand for the goods produced
in each location, taking into account that all goods are substitutes and transportation
costs impact the prices of foreign goods. Setting supply equal to demand we are able
to determine equilibrium quantities and i rms' proi ts in each location as a function of
n
1
and
n
2
. These expressions are used, in the next section, to assess i rms' geographical
distribution.
Let us start from i rms' pricing behavior. Consistently with our assumptions, the
market structure is that of monopolistic competition, that is, each i rm maximizes its
proi ts, setting its marginal revenue equal to its marginal costs, given market demand
elasticity and irrespective of other i rms' behavior. Using proi t function (24.4) and sub-
stituting (24.3) while setting marginal proi t to zero gives:
1 1
1
p
l
a
e
b
5 b
(24.5)
where e = ∂ log
c
/∂ log
p
is the demand elasticity. Given Assumption 1, it holds that:
e = −s
which together with (24.5) implies:
s
s 2 1
p
l
5 b
(24.6)
Since the price does not depend on the location index, local prices are equal and it holds
p
1
=
p
2
.
Denote the quantity demanded by an agent who resides in location
l
of a product pro-
duced in location
m
as
d
lm
. Each demand can be determined as a function of prices and
wages using the fact that relative demands under a CES utility satisfy:
d
11
d
12
p
2
p
1
t
b
d
22
d
21
p
1
p
2
t
b
s
s
5
a
and
5
a
(24.7)
while agents' budget constraints give:
p
2
t
m 5
n
1
d
11
p
1
1
n
2
d
12
µ
(24.8)
p
1
t
1
n
2
d
22
p
2
m 5
n
1
d
21
where, given the Cobb-Douglas formulation in (24.1), μ is the share of agents' (unitary)
income used to buy manufacturing goods. Solving for the demands, one i nds:
