Francesca Sanna-Randaccio paper - The Business School

Proof:
Straightforward, as (given a c )
ˆ ˆ
NR
1
TR
1
iff
Ai i
4
( A ) ( )
I t I AII
t I
s
( t I
9 bI
bII
and
NR
ˆ ˆ 1
a
TR
( 1
II
)
4
9
t
II
t t
s
I
b
II
II
2
( A ) ( )
I t I AII
s t I s
)
0
bI
bII
bII
0
NR TR
(
ˆ ˆ 1 1 ) 4
( A ) ( ) 2
I t I AII
t I t I t II s
with
0
s
9 bI
bII
bII
bII
while:
ˆ ˆ
NR
1
and
PR
1
NR
ˆ ˆ 1
a
4 s ( t I t II )
iff G , f AII
s t I
9 bII
PR
( 1
II
(11)
(12)
(13)
1 (14)
)
4
9
t t
s
I
b
II
II
0
NR PR
(
ˆ ˆ 1 1 ) 4 A 2 2
II s t I t II
with
0
s
9 bII
We may observe from Eq. (11) that no relocation will be chosen instead of total relocation
if the two centripetal forces due to the “market asymmetry” effect (first term in curly brackets)
and to the “lower competition” effect (i.e.
s
bII
2
(15)
(16)
) prevail on the centrifugal effect due to the
environmental policy asymmetry (second term in curly brackets). If both Eqs. (11) and (14) hold,
a more stringent pollution tax in the large country (country I) will not modify the local firm’s
location strategy.
When the size of the foreign market falls, being it measured by a decrease in a II , and thus
ceteris paribus the gap in market size becomes larger, the probability of choosing the no relocation
strategy increases, as both conditions (11) and (14) are decreasing in a II (see (12) and (15)). As to
12