Francesca Sanna-Randaccio paper - The Business School
Francesca Sanna-Randaccio paper - The Business School
Francesca Sanna-Randaccio paper - The Business School
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<strong>The</strong> condition for global pollution to rise is<br />
t<br />
I<br />
s<br />
t<br />
II<br />
b<br />
<br />
b<br />
II<br />
I<br />
, which is not too restrictive as<br />
PR requires moderate market asymmetry. 33 By comparing Eqs (20) and (25) we find that the<br />
emission leakage is always greater with PR than with NR.<br />
<strong>The</strong> sign of the impact on consumers’ aggregate welfare is undetermined. <strong>The</strong> sum of<br />
consumers’ surplus and the carbon tax revenue is given by<br />
PR ~<br />
PR ~ t <br />
I t II 2AI<br />
11t<br />
I 3t<br />
II 8s<br />
( AII<br />
t II 2s)<br />
( CSˆ<br />
I CS<br />
I ) ( Tˆ<br />
I TI<br />
) <br />
t II <br />
(26)<br />
6 3bI<br />
3bII<br />
<br />
which for t 0 is positive, although lower than in the no strategy shift case.<br />
II<br />
However, as world production may increase, and thus pollution damage may grow, we<br />
cannot say what will be the overall impact on consumer aggregate welfare. <strong>The</strong> change in damage<br />
is given by:<br />
( Dˆ<br />
PR<br />
I<br />
~ <br />
<br />
I s ( t I t II ) 4AI<br />
t I 3t<br />
II 2s<br />
4AII<br />
4t<br />
II s<br />
DI<br />
) <br />
<br />
<br />
6 bII<br />
bI<br />
<br />
3bI<br />
3bII<br />
<br />
which with b b is positive as under this assumption overall emissions increase.<br />
bI II<br />
Firm 1 profits fall in the domestic market but rise abroad, furthermore the firm faces<br />
additional fixed costs. We thus have:<br />
PR ~ 4 ( AII<br />
t II s)<br />
( AI<br />
t I s)<br />
<br />
( ˆ 1 1)<br />
s<br />
( t I t II )<br />
G1,<br />
f<br />
(28)<br />
9 bII<br />
bI<br />
<br />
As to the overall welfare impact, assuming b b and t 0 we have:<br />
( Wˆ<br />
PR<br />
I<br />
~<br />
W<br />
) <br />
I<br />
1 <br />
<br />
18b<br />
<br />
bI II<br />
I<br />
3tI( 2AI<br />
t I ) 8s(<br />
AII<br />
s)<br />
( s t I )( 4AI<br />
4AII<br />
t I 3s)<br />
G1,<br />
f<br />
<strong>The</strong>refore the sufficient condition for a fall in welfare becomes:<br />
II<br />
(27)<br />
<br />
(29)<br />
<br />
b<br />
<br />
3t( 2A<br />
t ) 8s(<br />
A s)<br />
( s t )( 4A<br />
4A<br />
t 3s)<br />
0<br />
b I I<br />
II<br />
I I I II I<br />
I (30)<br />
As expected, a high value of I enhances the negative effect on welfare (since with<br />
b b world pollution increases).<br />
bI II<br />
To summarize, an unilateral environmental policy shifting the equilibrium to PR may lead<br />
to higher global emissions. It is thus possible that, when transport costs are very high and the<br />
20