Table 1 Summary of regional abatement... | Emerald Publishing

Table 1

Summary of regional abatement quantities with and without dimming

Pollutant	Without dimming		With dimming
	Nash (⁠ ${\underline{\hat{q}}}_{n}^{k}$ ⁠)	Second-best (⁠ ${\underline{q}}_{n}^{k^{*}}$ ⁠)	Nash (⁠ ${\hat{q}}_{n}^{k}$ ⁠)	First-best (⁠ $q_{n}^{k^{*}}$ ⁠)
${SO}_{2}$	$\frac{r {\overset{�}{L}}_{n}}{r + c^{L}}$	$\frac{r {\overset{�}{L}}_{n}}{r + c^{L}}$	$\frac{r {\overset{�}{L}}_{n} - α_{n} \overset{�}{G}}{r + c^{L}} + \frac{α_{n}}{r + c^{L}} (\frac{y - \overset{�}{G}}{x - 1})$	$\frac{r {\overset{�}{L}}_{n} - \overset{�}{G}}{r + c^{L}} + \frac{2}{r + c^{L}} (\frac{y - 2 \overset{�}{G}}{x - 4})$
${CO}_{2}$	$\frac{α_{n} g}{c^{G}}$	$\frac{g}{c^{G}}$	$\frac{α_{n} (y - \overset{�}{G})}{x - 1}$	$\frac{y - 2 \overset{�}{G}}{x - 4}$

Notes: $x \equiv c^{G} (r + c^{L})$ and $y \equiv g (r + c^{L}) - c^{L} \overset{�}{L}$ ⁠; see also Lemma 1.