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Francesca Sanna-Randaccio paper - The Business School

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production and thus on the global level of emissions. 30 <strong>The</strong> job leakage, which is not explicitly<br />

considered in the welfare function, is indirectly captured by the change in the carbon tax revenue,<br />

as both phenomena depend on the fall in the domestic production level.<br />

6.1 <strong>The</strong> NR equilibrium outcome<br />

<strong>The</strong> unilateral mitigation measure, when firm 1 location strategy does not change, leads to<br />

a fall in world production and thus emissions, although part of the contraction in domestic<br />

production is compensated by a rise in foreign output. In fact we have:<br />

ˆ NR ~ t <br />

I t II t I t II<br />

( Q W QW<br />

) <br />

0<br />

(20)<br />

3bI<br />

3bII<br />

<br />

In this scenario, the impact of the unilateral policy on consumers’ aggregate welfare is<br />

positive. Consumers’ aggregate welfare (see Cole et al. 2009, p. 1242) is given by the sum of<br />

consumers’ surplus and pollution tax revenues, less the damage from pollution. Here we assume<br />

that the revenue of the pollution tax is 100% returned to the taxpayers. 31 Although consumers’<br />

surplus narrowly defined falls, for sufficiently low values of t II , the carbon tax revenue increase<br />

is greater than the fall in consumers’ surplus, since under rather general conditions (see Appendix<br />

C):<br />

( CSˆ<br />

NR<br />

I<br />

~ ˆ NR ~<br />

CS<br />

I ) ( TI<br />

TI<br />

) <br />

t I t II 2AI<br />

11t<br />

I 3t<br />

II 8s<br />

6(<br />

AII<br />

<br />

<br />

6 3bI<br />

2t<br />

2 ) <br />

I t II s<br />

0<br />

3bII<br />

<br />

Furthermore, pollution damage decreases since (see Appendix C):<br />

( Dˆ<br />

NR<br />

I<br />

~<br />

D ) <br />

I<br />

1 1 4 3 2 4 3 2 <br />

I<br />

AI<br />

tI<br />

tII<br />

s AII<br />

tI<br />

tII<br />

s<br />

(22)<br />

( tI<br />

tII<br />

)( ) <br />

<br />

0<br />

6 bI<br />

bII<br />

3bI<br />

3bII<br />

<br />

<strong>The</strong> local firm’s profits instead diminish in both markets, as<br />

NR ~ 4 ( A ) ( 2 ) <br />

I t I s AII<br />

t I s<br />

ˆ 1 ) ( t I t II ) <br />

<br />

0<br />

(23)<br />

9 bI<br />

bII<br />

<br />

( 1<br />

<strong>The</strong> previous results allow us to state that:<br />

(21)<br />

18

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