Adaptation and International Environmental Agreements

Abstract

We study the impact of collective effort in R&D in adaptation technologies, and also spillover effects on formation and size of stable international environmental agreements (IEAs). Our results suggest that it is possible to have more than one size of stable IEA. We can achieve a superior equilibrium, i.e., the grand coalition, if countries manage to keep knowledge spillovers low and arrange a minimum ratification threshold. This threshold is defined endogenously. We also shed light on the effects of two-sided spillover on global welfare and the size of stable IEAs.

Appendices

Appendix 1: Proof of Proposition 3.1

First-order conditions for 10 and 9 provide the following 4-unknown, 4-equation system:

$$\begin{aligned} \begin{aligned} \alpha -e^{N}-\beta \left( Se^{S}+Ne^{N}+\theta \frac{\left( \kappa ^{N}+\gamma \left( S\kappa ^{S}+\left( N-1-S\right) \kappa ^{N}\right) \right) }{\overline{K}}\right)= & {} 0,\\ -c\kappa ^{NS}+\frac{\theta \left( Se^{S}+\left( N-S\right) e^{N}\right) }{\overline{K}}= & {} 0,\\ \alpha -e^{S}-S\beta \left( Se^{S}+Ne^{N}\right) +\theta S\frac{\left( S\kappa ^{S}+\gamma N\kappa ^{N}\right) }{\overline{K}}= & {} 0,\\ -c\kappa ^{S}+\theta S\frac{\left( Se^{S}+Ne^{N}\right) }{\overline{K}}= & {} 0. \end{aligned} \end{aligned}$$

Solving for the variables $e^{N}, \, \kappa ^{N},\,e^{S}$ and ${\kappa ^{S}}$ gives the result.

Appendix 2: Calibration of the Parameters $\gamma$ and $\theta$

See Figs. 5 and 6.

Fig. 5

Calibration of main parameters ($\gamma$ and $\theta$), where $M=100,$ $c=0.37$, $\beta =0.0008$, $K=7.5$ and $\alpha =0.5$. a Region with positive individual emissions ($e^{S}>0$and $e^{N}>0$), b region where adaptation doesn’t overweight environmental damages ($D\left( \mathscr {E},K_{i}\right) \ge 0$), c region with non-negative welfare for signatories ($W_{i}^{S}\ge 0$), d region with non-negative welfare for non-signatories ($W_{i}^{NS}\ge 0$)

Fig. 6

Calibration of main parameters ($\gamma$ and $\theta$), where $M=50,$ $c=0.37$, $\beta =0.0008$, $K=6$ and $\alpha =0.5$. a Region with positive individual emissions ($e^{S}>0$and $e^{N}>0$), b region where adaptation doesn’t overweight environmental damages ($D\left( \mathscr {E},K_{i}\right) \ge 0$), c region with non-negative welfare for signatories ($W_{i}^{S}\ge 0$), d region with non-negative welfare for non-signatories ($W_{i}^{NS}\ge 0$)