Imports, Pass-Through, and the
Structure of Retail Markets
Horst Ra¤ and Nicolas Schmitt
1
Comparative Statics for the Short Run
Totally di¤erentiating
cI = cD +
(w
t)
2
2 FI
;
L(w t)
(
w cD )
;
(w + cD p)
kcD
cD
(w t) ckI
;
p=w+
+
k + 1 2(k + 1)
2 ckD
N=
and using N = NE (cD =cM )k , we have
2
32
3 2
3
a11 a12 0
dp
0
4 0
1 1 5 4 dcD 5 = 4 b2 5 dt
1 a32 a33
dcI
b3
(1)
(2)
(3)
(4)
where
(
w cD )
> 0;
(w + cD p)2
k 1
NE kcD
(
p)
+
=
< 0;
(w + cD p)2
ckM
1 + 2k
k(w t)ckI
+
< 0;
=
2(1 + k)
2ck+1
D
k(w t)ckI 1
=
> 0;
2ckD
a11 =
(5)
a12
(6)
a32
a33
(7)
(8)
and
b2 =
b3 =
1
2 FI
+
2 L(w t)2
ckI
> 0:
2ckD
1
< 0;
(9)
(10)
The value of the determinant is given by jDj =
some algebraic manipulation we can show that
jDj =
(
w
(w + cD
cD )
1
k(w
+
2
p) 2(1 + k)
a11 (a32 + a33 ) + a12 . After
t)ckI 1 (cD
2ck+1
D
(w + cD
p)
cI )
k
NE kcD
ckM
1
< 0:
Using Cramer’s Rule, we have
0 a12 0
b2
1 1
b3 a32 a33
a12 (b3 a33 b2 )
> 0;
=
jDj
dp
1
=
dt
jDj
since jDj < 0, a12 < 0 and (b3
a33 b2 ) > 0;
a11
0
1
a11 (b3
jDj
1
dcD
=
dt
jDj
=
since jDj < 0, a11 > 0 and (b3
dcI
dt
0 0
b2 1
b3 a33
a33 b2 )
> 0;
a33 b2 ) > 0;
a11 a12
0
1
1 a32
a12 b2 a11 b3
=
jDj
1
=
jDj
0
b2
b3
a11 a32 b2
< 0;
since jDj < 0, and after some algebraic transformations
a12 b2
a11 b3
a11 a32 b2
=
(
w
(w + cD
cD ) 1
p)2 2
+
cI
ckI
+1
t)
ckD
2 FI
1
+
2 L(w t)2
(w + cD
cD
(w
2
p)
> 0:
In the short run, the pass-through rate with respect to the average retail
price is also given by
dp
1 ck
k dcD
1
dcD (w t) ckI
= kI +
+
+
dt
2 cD k + 1 dt
2(k + 1) dt
2 ckD
k dcD
cD dt
k dcI
cI dt
:
(11)
It is also easy to …nd examples for which the short-term pass-through rate is
greater than one.
3