A note on pollution and reforms of domestic and trade taxes toward uniformity

Abstract

This note revisits the work of Michael and Hatzipanayotou (ITPF 20: 753–768, 2013), who show that price-neutral indirect tax reforms increase welfare and revenue via a reduction in either production pollution or consumption pollution. This note shows instead that an indirect tax reform can reduce both of these emissions while increasing government revenue. The key point is that tax rates should be adjusted to preserve aggregate demand or aggregate output. Such a reform strategy has a broader set of options for addressing distortions and renders consumption and production choices more environmentally friendly.

Appendix

The third and the last terms of (6) cancel:

$$ \begin{gathered} \mathop \Sigma \limits_{j \ne k} p_{j} R_{{p_{j} p_{k} }} (\xi_{j} - \xi_{k} ) - \mathop \Sigma \limits_{f \ne j} p_{j} R_{{p_{f} p_{j} }} (\xi_{j} - \xi_{f} )\left( {\frac{{R_{{pp_{k} }} }}{{R_{{pp_{f} }} }}} \right) \hfill \\ = \frac{{\mathop \Sigma \limits_{j \ne f,k} p_{j} R_{{p_{f} p_{j} }} R_{{p_{j} p_{k} }} \left[ {\left( {\frac{1}{{p_{f} }} - \frac{1}{{p_{j} }}} \right)\left( {\frac{{\phi_{j} }}{{p_{j} }} - \frac{{\phi_{k} }}{{p_{k} }}} \right) - \left( {\frac{1}{{p_{j} }} - \frac{1}{{p_{k} }}} \right)\left( {\frac{{\phi_{j} }}{{p_{j} }} - \frac{{\phi_{f} }}{{p_{f} }}} \right)} \right]}}{{p_{f} \left( {p_{j} } \right)^{2} p_{k} R_{{pp_{f} }} }} \hfill \\ = 0 \hfill \\ \end{gathered} $$

(13)

where $p_{i} = p^{*} - \phi_{i}$ ($i = f,j,k$).

We can simplify the fourth and the last terms in (10):

$$ \begin{aligned} \mathop \Sigma \limits_{j \ne k} q_{j} E_{{q_{j} q_{k} }} (\sigma_{j} - \sigma_{k} ) - \sum\limits_{f \ne j} {q_{j} E_{{q_{f} q_{j} }} (\sigma_{j} - \sigma_{f} )\frac{{\left\{ {\Delta E_{{qq_{k} }} + E_{qu} \left[ {\mathop \Sigma \limits_{j \ne k} p_{j} R_{{p_{j} p_{k} }} (\gamma_{j} - \gamma_{k} ) + \mathop \Sigma \limits_{j \ne k} q_{j} E_{{q_{j} q_{k} }} (\eta_{j} - \eta_{k} )} \right]} \right\}}}{{\left[ {\Delta E_{{qq_{f} }} + E_{qu} \mathop \Sigma \limits_{f \ne j} q_{j} E_{{q_{f} q_{j} }} (\eta_{j} - \eta_{f} )} \right]}}} \\ & = \mathop \Sigma \limits_{j \ne k} q_{j} E_{{q_{j} q_{k} }} (\sigma_{j} - \sigma_{k} ) - \sum\limits_{f \ne j} {q_{j} E_{{q_{f} q_{j} }} (\sigma_{j} - \sigma_{f} )\frac{{\left[ {E_{u} E_{{qq_{k} }} + E_{qu} \mathop \Sigma \limits_{j \ne k} p_{j} R_{{p_{j} p_{k} }} (\gamma_{j} - \gamma_{k} )} \right]}}{{E_{u} E_{{qq_{f} }} }}} \\ & = \underbrace {{\frac{{\mathop \Sigma \limits_{j \ne f,k} q_{j} E_{{q_{f} q_{j} }} R_{{q_{j} q_{k} }} \left[ {\left( {\frac{1}{{q_{f} }} - \frac{1}{{q_{j} }}} \right)\left( {\frac{{\theta_{j} }}{{q_{j} }} - \frac{{\theta_{k} }}{{q_{k} }}} \right) - \left( {\frac{1}{{q_{j} }} - \frac{1}{{q_{k} }}} \right)\left( {\frac{{\theta_{j} }}{{q_{j} }} - \frac{{\theta_{f} }}{{q_{f} }}} \right)} \right]}}{{q_{f} \left( {q_{j} } \right)^{2} q_{k} E_{u} E_{{qq_{f} }} }}}}_{ = 0} \\ & - \sum\limits_{f \ne j} {q_{j} E_{{q_{f} q_{j} }} (\sigma_{j} - \sigma_{f} )\frac{{E_{qu} \mathop \Sigma \limits_{j \ne k} p_{j} R_{{p_{j} p_{k} }} (\gamma_{j} - \gamma_{k} )}}{{E_{u} E_{{qq_{f} }} }}} \\ \end{aligned} $$

(14)