Pollution Under Hybrid Environmental Regulation: The Case of Space Heating

Abstract

Economic literature on environmental policy under imperfect competition provides controversial results. Some contributions find that under specific conditions environmental policy can increase emissions. Others find that environmental policy never increases emissions. However, these contributions are based on symmetric environmental regulation. The same environmental tool is applied to all firms and/or consumers belonging to a specific industrial or service sector. This chapter aims at studying how these results are affected by hybrid regulation when different environmental tools are applied to technologies coexisting in the same sector. This situation is well-suited to describe the structural and technological features of space heating in residential sectors. Looking at polarized market configurations (a dominant firm facing a fringe of producers), the analysis shows that increasing pollution is widely admissible in principle and does not require large environmental asymmetry of firms. However when the real conditions of markets and technologies are accounted for (by means of specific numerical simulations), the probability of increasing pollution seems to be very low in most situations where it is theoretically admissible. The results about the impact of hybrid regulation are ambiguous. Compared to symmetric regulation, hybrid regulation plays a significant role in affecting the probability of increasing pollution. However, this role cannot be generalized.

Appendix

1.1 Proof of Lemma 1

By facing the rival, the more efficient firm has two alternative strategies: (1) behaving as the residual supplier by pricing above the indifference price or (2) maximizing its own production by setting the price just below the indifference price.

Let $\pi_1^d$ and $\pi_2^d$ be the profits corresponding to the first and second strategies above, respectively. The profit the dominant firm earns by choosing the first strategy is

$$ \pi_1^d = ({p_r} - {{ M}}{{{ C}}_d})(Q({p_r}) - {\bar{q}_f}) + \tau { \ }\varGamma $$

(2.11)

where

$$ {p_r} = {\arg}{\mathrm{ ma}}{{\mathrm{ x}}_p}{ \ }(p - {{ M}}{{{ C}}_d})(Q - {\bar{q}_f}) + \tau { \ }\varGamma $$

(2.12)

and $\varGamma$ is the amount of allowances allocated free of charge where $\varGamma \ne 0$ only with benchmarking of emissions allowances.

If the leader chooses the second strategy, it earns

$$ \pi_2^d = ({p_{n_a }} - {{ M}}{{{ C}}_d})Q({p_{n_a }}) + \tau { \ }\varGamma $$

(2.13)

Thus the leader will choose the second strategy if and only if $\pi_1^d < \pi_2^d$, i.e. from (2.11) and (2.13) if and only if

$$ ({p_{n_a }} - {{ M}}{{{ C}}_d}) > \frac{{p_r - {{ M}}{{{ C}}_d}}}{{Q({p_{n_a }})}}(Q({p_r}) - {\bar{q}_f}) $$

Then, by reasoning at margin and because of environmental regulation implementation, the dominant firm will move from strategy (1) to strategy (2) (decreasing market power) if

$$ \begin{gathered} \left( {\frac{{\partial {p_{n_a }}}}{{\partial \tau }} - \frac{{\partial {\mathrm{M}}{{\mathrm{C}}_d}}}{{\partial \tau }}} \right)Q({p_{n_a }}) + ({p_{n_a }} - {\mathrm{M}}{{\mathrm{C}}_d})\frac{\partial Q }{\partial p}\frac{{\partial {p_{n_a }}}}{{\partial \tau }} \hfill \\ > \left( {\frac{{\partial {p_r}}}{{\partial \tau }} - \frac{{\partial {\mathrm{M}}{{\mathrm{C}}_d}}}{{\partial \tau }}} \right)\left( {Q({p_r}) - {{\bar{q}}_f}} \right) + \frac{\partial Q }{{\partial {p_r}}}\frac{{\partial {p_r}}}{{\partial \tau }}({p_r} - {\mathrm{M}}{{\mathrm{C}}_d}) \hfill \\ \end{gathered} $$

(2.14)

and from strategy (1) to strategy (2), vice versa.

Since from (2.12)

$$ \frac{{\partial {p_r}}}{{\partial \tau }}(Q({p_r}) - {\bar{q}_f}) + \frac{{\partial {p_r}}}{{\partial \tau }}\frac{\partial Q }{\partial p }({p_r} - {{ M}}{{{ C}}_d}) = 0 $$

condition (2.14) becomes

$$ {\mathrm{d}}{\Pi_u} = \left( {\frac{{\partial {p_{n_a }}}}{{\partial \tau }} - \frac{{\partial {\mathrm{M}}{{\mathrm{C}}_d}}}{{\partial \tau }}} \right) - \frac{{{{\left( {Q({p_r}) - {{\bar{q}}_f}} \right)}^2}}}{{Q^2 ({p_{n_a }})}}\frac{{\partial {p_{n_a }}}}{{\partial \tau }} + \frac{{\partial M{C_d}}}{{\partial \tau }}\frac{{\left( {Q({p_r}) - {{\bar{q}}_f}} \right)}}{{Q({p_{n_a }})}} > 0 $$

(2.15)

Inversely, if the leader will move from strategy (1) to strategy (2) (increasing market power).

It is to be noted that if the pollution price is very high such that the leader becomes the less efficient firm (so losing its cost and price leadership), after regulation the former leader always prefers to set its residual price since it can never undercut the rival. Therefore, demand and pollution will always decrease.

1.2 Proof of Corollary 1

If input taxes are applied to both dominant firm’s and fringe’s consumers then the residual demand curve will be:

$$ {{ QR}} = \left( {Q({p_r}) - {{\bar{q}}_f} + {r_a}\tau \frac{\partial Q }{\partial p }} \right) $$

Equation (2.11) becomes:

$$ \pi_1^d = ({p_r} - {{ M}}{{{ C}}_d})\left( {Q({p_r}) - {{\bar{q}}_f} + {r_a}(0){ \ }\tau \frac{\partial Q }{\partial p }} \right) $$

At the same time, (2.13) becomes:

$$ \pi_2^d = ({p_{n_a }} - {{ M}}{{{ C}}_d})\left( {Q({p_{n_a }}) + {r_b}(0)\tau \frac{\partial Q }{\partial p }} \right) $$

By following the same procedure adopted in the proof of Lemma 1, condition (2.5) follows.

If input taxes are applied only to the dominant firm’s consumers then the residual demand curve will be:

$$ {{ QR}} = \left( {Q({p_r}) - {{\bar{q}}_f} + {r_a}\tau \frac{\partial Q }{\partial p }} \right) $$

Equation (2.11) becomes:

$$ \pi_1^d = ({p_r} - {{ M}}{{{ C}}_d})\left( {Q({p_r}) - {{\bar{q}}_f} + {r_a}(0){ \ }\tau \frac{\partial Q }{\partial p }} \right) $$

At the same time the profit corresponding to the strategy 2 is:

$$ \pi_2^d = ({p_{n_a }} - {{ M}}{{{ C}}_d})Q({p_{n_a }}) $$

By following the same procedure adopted in the proof of Lemma 1, condition (2.6) follows.