Download 1 Unilateral Trade Liberalization in Canonical CES/Monopolistic

1
Unilateral Trade Liberalization in Canonical CES/Monopolistic
Competition Case with Homogenous Firms
To analyze unilateral trade liberalization, in both the canonical CES/monopolistic competition case with
homogenous …rms and the case with heterogeneous …rms considered in our paper, one needs to use the
trade balance condition to solve for real wages. However, unlike the case with heterogenous …rms, the trade
balance condition in the canonical CES/monopolistic case is not that hard to analyze. The reason is that all
…rms are homogenous and choose the same option. As a result, with homogeneous …rms, there is just one
equilibrium (trade balance) condition with one unknown variable, wage at Home (Country 1), that can be
used directly to show that
Proposition 1 In the canonical CES/monopolistic competition case with homogenous …rms unilateral trade
liberalization by one of the countries bene…ts each trading partner.
Proof.
Part 1 (Derivation of the equilibrium condition). Consider the canonical CES/monopolistic competition case of 2 countries that can potentially di¤er in their sizes and all production parameters. There
are Li consumers, who supply 1 unit of labor each, and Ni identical …rms in country i, i = 1; 2. To sell qij
units of output in market j; each …rm in country i faces marginal labor costs M Cij =
iceberg transportation cost,
ii
= 1 and
ij
ij
i;
where
ij
is the
> 1. In addition, each …rm faces a …xed cost of production
i
so that its total pro…t is
i
= (pii
wi M Cii ) qii + (pij
wi M Cij ) qij
Given the CES preferences, in market j this …rm sets a price pij = wi
ij
wi
i= (
of substitution between any 2 varieties. Due to free entry in each country
as
ij
=
1
(rii + rij )
wi
i,
i
i:
1) ; where
is the elasticity
= 0: Since we can re-write
the zero pro…t condition becomes rii + rij = wi
ij
i:
Next, consider the labor market clearing condition in country i:
Ni (M Cii qii + M Cij qij +
Since M Cii qii + M Cij qij = (rii + rij ) ( w
i
1)
i)
= Li :
; from the zero pro…t condition, we get Ni = Li =
i:
This means
that a number of …rms in each country does not depend on trade costs, which signi…cantly simpli…es the
analysis.
After normalizing wage in country 2 to 1, w2
1; the only variable that remains unknown is w1 ; which
can be found from the trade balance condition, N1 r12 = N2 r21 : Note that Ni = Li =
and
i
1
rij = Rj (Pj )
1
1
(pij )
1 wi ij
= wj Lj
i
1
Nj
1 wj
1
j
1
+ Ni
1 wi
ij
i
:
Hence, the trade balance condition can be re-written as
(w1 )
1
(T B) :
1
N2 (
2)
1
12 1 )
(
1
+ N1 (w1
12 1 )
1
1
21 2 )
(
1
=
N1 (w1
2
1)
1
+ N2 (
Part 2 (Unilateral trade liberalization by Country 1). Consider a fall in
be re-written as
h
1
N1 (w1 1 )
+ N2 (
2)
21
i (w )
1
1
or
N1 (
= N2 (
2
1
"
1
12 1 )
"
1
21 2 )
or
(w1 )
(
1
1
1)
1
2)
(
(w1 )
(
where the RHS > 0 does not change with
1
h
= N2 (
1
12 1 )
(
1 2
(w1 )
(
1)
1
1
2)
(
+ N1 (w1
21 2 )
1
1
(
2)
1
2
1
(w1 )
(
2
#
1
12 1 )
1
1
21 )
(w1 )
12
1
(
2)
1
21 :
1)
;
Condition (TB) can
i(
1
21 2 )
1
;
2
#
;
1
2)
N2 (
;
(1)
1
(w1 ) ( 12 1 )
N1 ( 12 1 )
21 . Moreover, both the numerator and denominator in the LHS
1
=
1
21 2 )
1
2
are positive. (This follows from (TB),
2
where since
ij
means (w1 )
(
(
12 1 )
1
1
1
12 1 )
21
2
<
1
(
=
(
2)
1
1
1
1
1
1;
N2 ( 2 )
+ N1 (w1 12 1 )
N2 ( 2 )
+ N1 (w1 1 )
( 21 )
> 1; the denominator in the LHS is smaller than the denominator in the RHS, which
denominator.) As
21 .
(w1 )
1
2)
; i.e., the numerator in (1) has to be positive, and so does the
falls, the LHS of (1) has to remain the same since the RHS of (1) does not depend on
This means that w1 falls (the numerator of the LHS in (1) is decreasing with w1 ; while the denominator
increases with w1 ; so that the whole LHS increases with w1 for given
21 ).
Welfare in Country 2, W2 , can be found from
1
(W2 )
=
which means that it rises with lower
(W1 )
w1
What can we say about
21
1
=
1
1
P2
21 .
1
2)
= N2 (
+ N1 (w1
1
12 1 )
;
Welfare in Country 1, W1 , is
w1
P1
1
= N1 (
1
1)
1
w1
+ N2
:
21 2
? Multiplying both the numerator and denominator of the LHS of (1) by w1
yields
2
(
1
1
1)
(w1 ) (
1
21
1
w1
1
2)
2
(
(
2)
1
w1
1
12 1 )
=
N2 (
N1 (
2)
1
1
12 1 )
:
Since the denominator falls with a lower w1 , then the numerator has to fall as well, implying that
1
21
w1
has to decrease with a decline in
W1 increases as
21
21 .
Going back to the expression for (W1 )
falls.
Thus, we proved that with lower
21
both countries gain.
2
1
, this proves that