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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

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