Capital mobility and environmental policy: taxes versus TEP

Abstract

Emission taxes and tradable-emission-permit (TEP) programs are two popular instruments used to regulate transboundary pollution. In a framework with capital, monopolistic competition, and interregional trade, we show that when capital is immobile, the two instruments are equivalent. When capital is mobile, the TEP program is more efficient. We also find that the presence of capital mobility reverses some conventional results. It may lead the non-revenue-raising instruments to be more efficient than the revenue-raising instruments, which counters the double-dividend hypothesis. With mobile capital, the initial allocation of permits affects the efficiency, which contrasts with the Coase theorem.

Appendix

• 1. The derivation of demand functions:

  Here we focus on region H, and the case of region F can be derived by symmetry. Using (4) and the assumption of symmetry between varieties gives the demands encountered by a representative firm located in H in the home market and in the foreign market, respectively, as follows:

  $$\begin{aligned} q_{HH} =&a - (b + c N) p_{HH} + c P_H, \end{aligned}$$

  (35)
  $$\begin{aligned} q_{HF} =&a - (b + c N) p_{HF} + c P_F, \end{aligned}$$

  (36)

  where

  $$\begin{aligned} P_H =&n_H p_{HH} + n_F p_{FH} , \end{aligned}$$

  (37)
  $$\begin{aligned} P_F =&n_H p_{HF} + n_F p_{FF} . \end{aligned}$$

  (38)

  Due to $P_j/N$ being the average price of the differentiated product in region j, the fixed N leads $P_j$ to serve as the price index in that region.

• 2. The derivations of Eqs. (6) and (7): Solving (4) gives $\partial q_{HH}/\partial p_{HH} = - (b + c)$. Then inserting this result into the first-order condition of profit maximization, we have:

  $$\begin{aligned} p_{HH} = [a + (b+ c)t + c P_H]/[2(b + c)]\,. \end{aligned}$$

  (39)

  Using a similar approach gives rise to $p_{FH} = p_{HH} + \tau /2$. Next, by inserting $p_{HH}$ and $p_{FH}$ into (37) we obtain $P_H = [a + (b + c) n _H t + (b + c) n_F (t + \tau )]$. Substituting this result into (39) leads to (6). Equation (7) can be obtained symmetrically.

• 3. The derivation of ${\hat{\theta }}$: Let the terms in the big square brackets be $A_1$. Then inserting the equilibrium price of the permit into $A_1$ gives

  $$\begin{aligned} A_1 = \frac{A_2}{c (-1 + \theta ) \tau ^2}\,, \end{aligned}$$

  (40)

  where

  $$\begin{aligned} A_2 = 2 a (1 -\delta ) \theta (\sigma ^F - \sigma ^H) - c (-1 + \theta )^2 \tau ^2 + b (-1 +\delta ) (\sigma ^F - \sigma ^H) (\sigma ^F +\delta \ \sigma ^F + \sigma ^H +\delta \sigma ^H + \theta \tau )\,. \end{aligned}$$

  We then solve $A_1 = 0$ for ${\hat{\theta }}$, which is given by:

  $$\begin{aligned} {\hat{\theta }} =&\frac{1}{2c \tau ^2}\left[ (2a - b\tau )(1 - \delta ) ( \sigma ^F - \sigma ^H) + 2 c \tau ^2 + \sqrt{ A_3 } \,\,\,\right] , \end{aligned}$$

  (41)

  where

  $$\begin{aligned} A_3=&4 b c (-1 + \delta ^2) [ (\sigma ^F)^2 - (\sigma ^H)^2] \tau ^2 - 4 c^2 \tau ^4 + [ 2 a (1 - \delta ) (\sigma ^F - \sigma ^H) \\&+ \tau (b (-1 + \delta ) (\sigma ^F - \sigma ^H) + 2 c \tau ) ]^2. \end{aligned}$$

• 4. The effects of s on welfare: By differentiating $CS_H + CS_F$ with respect to s, we obtain

  $$\begin{aligned} \frac{d(CS_H + CS_F)}{ds} = \frac{c^2 (b + c) (1 - 2 s^*) \tau ^2}{8 (2 b + c)^2}\,. \end{aligned}$$

  (42)

  We can see that if $s^*<1/2$, then $d(CS_H+CS_F)/ds > 0$; if $s^*>1/2$, then the opposite occurs.

  The effect of s on the aggregate profit is given by:

  $$\begin{aligned} \frac{d(\rho _H + \rho _F)}{ds} = \frac{ c (b + c) (4 b + c) (1 - 2 s^*) \tau ^2 }{4 (2 b + c)^2}\,. \end{aligned}$$

  (43)

  The above equation indicates that when $s^*<1/2$, the aggregate profit increases with s; when $s^*>1/2$, the opposite occurs. Finally, the effect of s on the amount of the public good is equal to $d(Z_H+Z_F)/ds = 0$, i.e., the amount of the aggregate public good is independent of s.