Table 1 Equilibrium outcomes under the... | Emerald Publishing

Table 1

Equilibrium outcomes under the three price-based emissions reduction policies

	Single firm profits	Firm abatement level	Environmental damage	Government’s budget	Social welfare
Emissions tax	$π_{i}^{* E T} = \frac{\begin{array}{l} 8 z^{4} + 2 z^{3} (16 g^{2} + 8 g + 21) \\ + 2 z^{2} (96 g^{2} + 60 g + 25) \\ + 40 z g (9 g + 5) + 200 g^{2} \end{array}}{[8 g z (z + 5) + 8 z^{2} + 25 (z + 2 g)]}$	$k_{i}^{* E T} = \frac{2 (4 g z + 10 g - z)}{[8 g z (z + 5) + 8 z^{2} + 25 (z + 2 g)]}$	$E D^{* E T} = \frac{32 z^{2} g {(3 + z)}^{2}}{{[8 g z (z + 5) + 8 z^{2} + 25 (z + 2 g)]}^{2}}$	$G B^{* E T} = \frac{16 z^{2} (3 + z) (4 g z + 10 g - z)}{{[8 z^{2} (1 + g) + 5 z (5 + 8 g) + 50 g]}^{2}}$	$S W^{* E T} = \frac{4 (3 + z) (z + 2 g)}{8 z^{2} (1 + g) + 5 [5 z + 2 g (5 + 4 z)]}$
Abatement subsidy	$π^{* A S} = \frac{2}{25} + \frac{8 g^{2} z}{25 {(z + 2 g)}^{2}}$	$k_{i}^{* A S} = \frac{4 g}{5 (z + 2 g)}$	$E D^{* A S} = \frac{g}{2} {[\frac{4}{5} - \frac{8 g}{5 (z + 2 g)}]}^{2}$	$G B^{* A S} = - \frac{32 g^{2} z}{25 {(z + 2 g)}^{2}}$	$S W^{* A S} = \frac{12 z + (24 - 8 z) g}{25 (z + 2 g)}$
Policy mix	$π^{* P M} = \frac{4 g^{2} (1 + z) + 4 g z + z^{2}}{8 {[(z + 2) g + z]}^{2}}$	$k_{i}^{* P M} = \frac{g}{(z + 2) g + z}$	$E D^{* P M} = \frac{g}{2} {[\frac{z}{(z + 2) g + z}]}^{2}$	$G B^{* P M} = \frac{(4 g - 1) z^{2} - 4 g (g + z)}{4 {[(1 + g) z + 2 g]}^{2}}$	$S W^{* P M} = \frac{z + 2 g}{(2 z + 4) g + 2 z}$

Source(s): Authors’ own elaboration