Francesca Sanna-Randaccio paper - The Business School

Appendix C
I: We have that, under rather general conditions:
( CSˆ
NR
I
~
CS
) ( Tˆ
t
I
I
t
6
II
NR
I
~
T )
I
2 A 11 3 8 6(
2 2 )
I t I t II s AII
t I t II s
0
3bI
3bII
(C.1)
In fact, if t 0 , the second term in square brackets is positive since 2t 2s
0 for
II
AII I
NR AII
2t
I 2s
t II
q 1,
II
0 . If t II 0 , the first term is given by 2AI 11t
I 8s
. With s t I ,
b
II
2AI 11t
I 8s
> 2AI 3t
I , and 2A 3t
I AII
2t
I 2s
0
I . If I
s t , the sufficient condition
for 2AI 11t I 8s
0 becomes I t s 7
, under which 2AI 11t I 8s
2( AII 2t
I 2s)
0 .
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II: As to pollution damage:
( Dˆ
n
I
~
DI
)
2
2
n ~ 2
n
n
Qˆ W Q ~ ~
W Qˆ W QW
Qˆ W QW
with n {NR,PR,TR}. It follows that ˆ n ~ ˆ n ~
sign( DI
DI
) sign(
QW
QW
)
.
2
III: The full expressions of the net welfare effect with the NR equilibrium is given by:
( Wˆ
NR
I
1 1 4 A
I t I 3t
II 2s
4AII
t I 3t
II 2s
( )
~ ( t I t II ) bI
bII
bI
bII
W
I )
18 6 A
I 3t
I 3t
II 4AII
4t
I 63t
II 4s
bI
bII
(C.2)
(C.3)
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