Climate Policy with Technology Transfers and Permit Trading

Abstract

In this paper, we analyze technology transfers (TT) and tradable emission rights, which are core issues of the ongoing climate negotiations. Subsidizing TT leads to the adoption of better abatement technologies in the South, thereby reducing the international permit price. This is beneficial for the North as long as it is a permit buyer; hence it chooses to subsidize TT. By contrast, the permit selling South suffers from the lower permit price and its welfare usually deteriorates, despite receiving subsidies. We also consider how TT affects countries’ non-cooperative choices of permit endowments and find that it tends to reduce overall emissions. Finally, a simple numerical simulation model illustrates the results and explores some further comparative statics.

Appendix

1.1 A1: Proof of Proposition 1

From the comparative statics at the end of Sect. 3.2, $p^{\prime }\left( \pi _{S}\right) >0$ and $k_{S}^{\prime }\left( \pi _{S}\right) <0$. Accordingly, if the North is a permit seller or does not trade, then the left-hand side of (13) is non-positive and we have a boundary solution with $\sigma _{S}=0$.

By contrast, if the North is a permit buyer, then $-p^{\prime }\left( \pi _{S}\right) (\omega _{N}-x_{N})>0$ so that a subsidy reduces its costs on the permit market. The subsidy payments depend on the degree of additionality. First, consider the case where subsidies can be fully restricted to additional investments, i.e., $\tilde{k}_{S}=k_{S}^{0}$. By contradiction to statement (ii), suppose that $\sigma _{S}=0$; hence $k_{S}=k_{S}^{0}$ by definition of $k_{S}^{0}$. In this case $k_{S}-\tilde{k}_{S} +\sigma _{S}k_{S}^{\prime } (\pi _{S})=0$ so that the left-hand side of (13) is strictly positive. Therefore, $\sigma _{S}=0$ can not be an optimal solution. Second, suppose that the North is not able to restrict subsidies to additional investments, i.e., $\tilde{k}_{S}<k_{S}^{0}$. In this case $k_{S}-\tilde{k}_{S}>0$ even at $\sigma _{S}=0$. If this term is sufficiently large compared to the other terms in (13), then we may have a boundary solution with $\sigma _{S}=0$ (statement iii). $\square$

1.2 A2: Proof of Proposition 3

For interior solutions with $\sigma _{S}^{c}>0$, it follows immediately from the first-order condition (13) for subsidies—or, equivalently, from Proposition 1(i)— that $\omega _{N}^{c}<x_{N}^{c}$. Turning to boundary solutions with $\sigma _{S}^{c}=0$, remember that $v_{N}^{\prime }(\omega ^{c}) >v_{S}^{\prime }(\omega ^{c})$ by assumption. Substituting from the first-order conditions for endowment choices, (20) and (19), thereby noting that $\omega _{S}^{c}-x_{S}^{c}= -\left( \omega _{N}^{c} -x_{N}^{c}\right)$, it follows that

$$\begin{aligned} 2p^{\prime }\left( \omega ^{c}\right) (\omega _{N}^{c}-x_{N}^{c})> \gamma _{S}{k_{S}^{\prime }\left( \omega ^{c}\right) .} \end{aligned}$$

(22)

Given that $p^{\prime }\left( \omega ^{c}\right) <0$, this implies $\omega _{N}^{c}<x_{N}^{c}$ for $\gamma _{S}$ sufficiently small (while the outcome is ambiguous for large $\gamma _{S}$ due to $k_{S}^{\prime }\left( \omega ^{c}\right) \le 0$). $\square$

1.3 A3: Proof of Proposition 4

We want to show that $\omega \left( \sigma _{S}^{c}\right) -\omega \left( 0\right) <0$, where $\omega \left( \sigma _{S}^{c}\right)$ and $\omega \left( 0\right)$ are endowment choices that arise in the regimes with subsidies ($\sigma _{S}=\sigma _{S}^{c}>0)$ and with no TT ($\sigma _{S} =0$). Given the lack of closed form solutions we can not directly compare these endowment levels. However,

$$\begin{aligned} \omega \left( \sigma _{S}^{c}\right) -\omega \left( 0\right) =\int \limits _{0}^{\sigma _{S}^{c}}\omega ^{\prime }\left( \sigma _{S}\right) d\sigma _{S}, \end{aligned}$$

(23)

where $\omega ^{\prime }\left( \sigma _{S}\right)$ can be determined using the implicit function theorem. In particular, we treat $\sigma _{S}$ as an exogenous variable and then track how $\omega$ evolves as subsidies rise from $\sigma _{S}=0$ to the equilibrium value $\sigma _{S}^{c}$.

To determine $\omega ^{\prime }\left( \sigma _{S}\right)$, summation of the first-order conditions for endowment choices, Eqs. (19) and (20), yields

$$\begin{aligned} 2p-\sigma _{S}k_{S}^{\prime }\left( \omega \right) +\gamma _{S} {k_{S}^{\prime } \left( \omega \right) }-v_{N}^{\prime } (\omega )-v_{S}^{\prime }(\omega )=0, \end{aligned}$$

(24)

which implicitly defines $\omega$ as a function of $\sigma _{S}$. For high values of $\omega$, we may have a boundary solution with $k_{S}=\underline{k}_{S}$ and ${k_{S}^{\prime }\left( \omega \right) =0}$. In this case, a marginal change in the subsidy level has no real effects and $\frac{d\omega }{d\sigma _{S}}=0$.

By contrast, if $\omega$ is sufficiently low, an interior solution with $k_{S}>\underline{k}_{S}$ obtains. For this case, implicit differentiation of (24) yields (remember that $d\pi _{S} /d\sigma _{S}={d\bar{\pi }_{S}/d\sigma _{S}=}-1$)

$$\begin{aligned} \frac{d\omega }{d\sigma _{S}}=\frac{2p^{\prime }\left( \pi _{S}\right) +k_{S}^{\prime }\left( \omega \right) -\left( \sigma _{S}-\gamma _{S}\right) \frac{\partial k_{S}^{\prime }\left( \omega \right) }{\partial \pi _{S}}}{2p^{\prime }\left( \omega \right) -\left( \sigma _{S}-\gamma _{S}\right) k_{S}^{\prime \prime } \left( \omega \right) -v_{N}^{\prime \prime } (\omega )-v_{S}^{\prime \prime }(\omega )}, \end{aligned}$$

(25)

where the derivatives account for the effects of endowment choices and subsidies at the subsequent stages of the game. From the comparative statics (10) and (18) we have $k_{S}^{\prime }\left( \omega \right) =-p^{\prime }\left( \pi _{S}\right)$ so that $2p^{\prime }\left( \pi _{S}\right) +k_{S}^{\prime } \left( \omega \right) =p^{\prime }\left( \pi _{S}\right)$ and $-\frac{\partial k_{S}^{\prime }\left( \omega \right) }{\partial \pi _{S}}=p^{\prime \prime }\left( \pi _{S}\right)$. Upon substitution into (25)

$$\begin{aligned} \frac{d\omega }{d\sigma _{S}}=\frac{p^{\prime }\left( \pi _{S}\right) +\left( \sigma _{S}-\gamma _{S}\right) p^{\prime \prime }\left( \pi _{S}\right) }{2p^{\prime }\left( \omega \right) -\left( \sigma _{S}-\gamma _{S}\right) k_{S}^{\prime \prime }\left( \omega \right) -v_{N}^{\prime \prime }(\omega ) -v_{S}^{\prime \prime }(\omega )}. \end{aligned}$$

(26)

Accordingly, the numerator of (25) is positive for all $\sigma _{S}$ if $p^{\prime \prime }\left( \pi _{S}\right)$ is not too small and $\gamma _{S}$ is not too large. Moreover, the denominator is negative by the second-order conditions with respect to the regions’ endowment choices. To see this, note that these conditions require (using $d\omega /d\omega _{i}=1$)

$$\begin{aligned} \frac{d}{d\omega }\left( \frac{dW_{i}}{d\omega }\right) <0,\quad i=N,S. \end{aligned}$$

(27)

Hence, summation yields

$$\begin{aligned} \frac{d}{d\omega }\left( \frac{dW_{N}}{d\omega }\right) +\frac{d}{d\omega } \left( \frac{dW_{S}}{d\omega }\right) =\frac{d}{d\omega } \left( \frac{dW_{N}}{d\omega }+\frac{dW_{S}}{d\omega } \right) <0. \end{aligned}$$

(28)

In the above calculations, $\frac{dW_{N}}{d\omega }+\frac{dW_{S}}{d\omega }$ is given by the l.h.s. of (24). The denominator of (26) is the derivative of this term with respect to $\omega$, i.e. $\frac{d}{d\omega }\left( \frac{dW_{N}}{d\omega }+\frac{dW_{S}}{d\omega } \right) <0$. $\square$