Supplementing Domestic Mitigation and Adaptation with Emissions Reduction Abroad to Face Climate Change

Abstract

In this paper we focus on a long-term dynamic analysis of the optimal adaptation/mitigation mix in the presence of a pollution threshold above which adaptation is no longer efficient. We account for accumulation in abatement capital, greenhouse gases, and adaptation capital in order to better capture the arbitrage between abatement and adaptation investments. Pollution damages arise from the emissions due to the country consumption but also from the emissions of the rest of the world (ROW). A pollution threshold is then introduced, above which adaptation is no longer efficient. We obtain that if this threshold is lower than the steady-state level of pollution, there is no way for the modelled economy to avoid it. In particular, such a situation will appear if the ROW’s emissions are high. We then show that CDM may be a means to avoid a pollution threshold above which adaptation becomes of no use.

Appendix

The FOCs lead to

$$\begin{aligned} \frac{\overset{.}{\phi }}{\phi }\left( \alpha -1+\frac{(s-1)\phi }{1-\phi }\right) =(1-\alpha )\frac{\overset{.}{\theta }}{\theta }-(1-\omega )\frac{\overset{.}{c}}{c}-(\rho +\delta )+\frac{\omega m}{\beta \lambda _{M}}c^{\omega -1}K^{m-1} \end{aligned}$$

(17)

A steady-state is such that $\overset{\cdot }{A}/A=0$ $\overset{\cdot }{K}/K=0,$ $\overset{\cdot }{S}/S=0,\overset{.}{c}/c=0,$ $\overset{.}{\phi }/\phi =0$ and $\overset{\cdot }{\theta }/\theta =0$. Equations (13), (14) and (6) gives:

$$\begin{aligned} K^{*}(\theta ^{*},\phi ^{*})= & {} \left( \phi ^{*}\theta ^{*}\right) ^{\alpha }\overline{K} \end{aligned}$$

(18)

$$\begin{aligned} A^{*}(\theta ^{*},\phi ^{*})= & {} \phi ^{*\alpha }(1-\theta ^{*})^{\alpha }\overline{K} \end{aligned}$$

(19)

$$\begin{aligned} c^{*}(\theta ^{*},\phi ^{*})= & {} \left( \frac{(\rho +\sigma )\omega }{\beta }\phi ^{*\gamma \alpha }(1-\theta ^{*})^{\gamma \alpha }\overline{K}^{\gamma }\right) ^{\frac{1}{1-\omega }} \end{aligned}$$

(20)

Using the pollution accumulation process and the fact that at the steady-state $\overset{.}{S}/S=0$, we have:

$$\begin{aligned} \sigma S^{*}(\theta ^{*})=\beta \left( \frac{(\rho +\sigma )\omega }{\beta }\phi ^{*\gamma \alpha }(1-\theta ^{*})^{\gamma \alpha }\overline{K}^{\gamma }\right) ^{\frac{1}{1-\omega }}-\left( \phi ^{*}\theta ^{*}\right) ^{m\alpha }\overline{K}^{m}+\overline{E}-(1-\phi ^{*})^{s}Y^{s} \end{aligned}$$