Skip to main content

Border Adjustments Supplementing Nationally Determined Carbon Pricing


As agreed on in the Paris Agreement, each country determines its own contribution to combat climate change on a voluntary basis. There is no mechanism to force a country to comply with its own nationally determined contributions. This bottom-up approach builds on unilateral actions and yields a kind of carbon pricing, which is not necessarily identical across countries. As a consequence, these nationally determined climate policies have drawbacks in terms of carbon leakage and loss of competitiveness for firms producing in high carbon price countries. To reduce these negative effects, border adjustments (BAs) may be appropriate subsequent to more stringent environmental regulation. We model a three-stage game involving carbon price competition in the first stage, the introduction of BAs in the second stage and oligopolistic competition between firms in the third stage. Strategic trade theory suggests that the qualitative results about the optimal BA policy may vary with the underlying type of competition, namely Bertrand and Cournot competition. However, our results are similar for both types of competition. We conclude that BAs are suitable for supporting a more stringent environmental policy. Moreover, we find that anticipation of the implementation of BAs in the second stage yields higher average carbon prices in the first stage since high carbon price countries increase their carbon prices whereas the other countries partially offset.

This is a preview of subscription content, access via your institution.

Fig. 1
Fig. 2


  1. Numerous countries had implemented their own kind of individual carbon pricing scheme even before Paris, either by introducing a cap and trade system or by taxing carbon directly.

  2. Markusen et al. (1995) as well as Haufler and Wooton (1999) restrict their analysis to a monopoly but find similar results.

  3. Either domestic production can be replaced by imports or domestic firms can relocate to low carbon price countries. An analysis of plant relocation caused by climate policy was conducted by Mæstad (2001). He concluded that, from a global economic efficiency perspective, unilateral climate policy should always include trade measures that avoid such kind of leakage. CL can occur in several alternative ways as well, e.g. via the energy market channel or via changes in the terms of trade or factor prices (the income channel). In our model, we focus on CL as the replacement of domestic production by imports. Ritz (2009) referred to this as output leakage, which he identifies as a crucial component of CL.

  4. For details, see Mathiesen and Mæstad (2004), Ponssard and Walker (2008), Dermailly and Quirion (2008a; b), Meunier et al. (2014) as well as Monjon and Quirion (2011).

  5. Some countries might even be prevented from implementing a climate regulation or signing up to it in the first place. BAs can induce more countries to join international environmental agreements. For analytical studies on BAs and climate coalitions, see Anoulies (2015), Helm and Schmidt (2015) as well as Karp and Zhao (2008).

  6. For an analysis of global efficiency, see Keen and Kotsogiannis (2014) or Gros and Egenhofer (2011). However, their results are only applicable for governments in a bottom-up post-Paris process if there were a binding climate agreement for all countries.

  7. We thank an anonymous reviewer for suggesting this illustration.

  8. This carbon price can be implemented in several ways, e.g. via a carbon tax or some kind of cap and trade system.

  9. We do not consider implementation of an export BA as an exclusive adjusting measure because it would be similar to an export subsidy and would counteract the initial ambitious climate policy of the high carbon price country. Since we assume that climate protection remains a high priority, this scenario can be neglected.

  10. For alternative concepts of competition neutrality, see Sheldon (2011) or Sheldon and McCorriston (2012).

  11. The consumption-based approach has several advantages over the production-based approach that have already been discussed in the literature. See, for example, Peters (2008) or Steininger et al. (2014).

  12. It goes without saying that implementing BAs creates more real-world issues causing Sakai and Barrett (2016) to doubt the effectiveness of BAs as an exclusive measure to combat CL. By restricting the BA value, we have obeyed the non-discrimination rule of the WTO, which states that foreign firms may not be discriminated against compared to domestic firms. Another important point for WTO compatibility is that trade measures must be applied to like products which is fulfilled in the model framework since we consider near substitutes. In addition, if both countries have the same emission intensities, it can be guaranteed that the best available technology is applied for calculating emissions. Furthermore, trade measures cannot be applied against least-developed countries (LDCs). We consider similar agents such as industrialized or emerging economies. For a thorough legal analysis see Ismer and Neuhoff (2007) or Horn and Mavroidis (2011). For strategic effects that may occur with highly heterogenous countries like developed countries versus LDCs, see Eyland and Zaccour (2012). Moreover, as with every form of regulation, there are administrative costs in the real world that diminish the success of BAs. Nevertheless, if the BA scheme covers only a few trade-exposed, carbon-intensive commodities as proposed by Droege (2011) and Lininger (2015), these issues can be relaxed.

  13. We exclude that a single firm can deter market entry of its competitor. Hence, equilibrium values under Cournot competition have to be positive. From (A.4), market exit can be avoided by assuming \((c_{i}, \varsigma _{i})<\frac{1}{\alpha -\beta }\), i.e. the effective marginal production cost have to be low enough such that even for marginal cost prices, served demand does not vanish. Thus, there is some scope left for an oligopolistic mark-up without market deterance.

  14. Throughout the paper, results of Bertrand (Cournot) competition are indicated by superscript B (C).

  15. Note that the first term of (7) is positive as the equilibrium price \(p_{A}\) always exceeds firms’ production costs \((c+t_{A})\).

  16. There are conditions such as asymmetric production costs (cf. Simpson 1995) or endogenous market structure through free market entry (cf. Katsoulacos and Xepapadeas 1995) that may result in overinternalization. However, these conditions do not apply to our model framework. Thus, we follow Ebert (1991/1992) and Kennedy (1994) by assuming underinternalization.

  17. SBA is emission-neutral. Considering Eqs. (3) and (4), it becomes apparent that global emissions decrease with the sum of effective marginal costs \((c_{A}+c_{B}+\varsigma _{A}+\varsigma _{B})\), irrespective of the type of competition. In the event of SBA, the sum of all effective marginal costs is reduced to \(c_{A}+c_{B}+\varsigma _{A}+\varsigma _{B}=4c+2t_{A}+2t_{B}\) in both equations and consequently does not change with \(\theta \) (\(\frac{\partial E}{\partial \theta }=0\)). If exports and imports are adjusted at the same rate, the increase in emissions caused by adjusting exports equals the decrease in emissions due to adjusting imports.

  18. The second-order condition (SOC) is negative for both types of competition. We can show the effect for both Bertrand \(\frac{\partial t_{A}^{B}}{\partial t_{B}^{B}}=\frac{\Gamma ^{2}4\alpha ^{2}\beta [\alpha ^{2}-\beta ^{2}]}{SOC}<0\) and Cournot competition \(\frac{\partial t_{A}^{C}}{\partial t_{B}^{C}}=\frac{\Gamma ^{2}2\beta (\alpha ^{2}-\beta ^{2})(2\alpha ^{2}-\beta ^{2})}{SOC}<0\). Furthermore, the numerator is smaller than the absolute value of the SOC in both cases.

  19. For both types of competition, global emissions decline with a stronger regulation, i.e. \(\frac{\partial E^{B}}{\partial t_{A}}= \Gamma 2\alpha (\alpha \beta +\beta ^{2}-2\alpha ^{2})<0\) and \(\frac{\partial E^{C}}{\partial t_{A}}= \Gamma 2(\alpha ^{2}-\beta ^{2})(\beta -2\alpha )<0\).

  20. In both types of competition, the effects are positive for IBA \(\frac{\partial t_{A}^{B}}{\partial \tau }= -\frac{\Gamma ^{2}2\alpha ^{2}\beta ^{3}}{SOC}>0\) as well as \(\frac{\partial t_{A}^{C}}{\partial \tau }= -\frac{\Gamma ^{2}(\alpha ^{2}-\beta ^{2})2\beta ^{3}}{SOC}>0\) and for SBA \(\frac{\partial t_{A}^{B}}{\partial \theta }= -\frac{\Gamma ^{2}\alpha ^{2}[4\alpha (2\alpha ^{2}-\beta ^{2})+2\beta ^{3}]}{SOC}>0\) as well as \(\frac{\partial t_{A}^{C}}{\partial \theta }= -\frac{\Gamma ^{2}(\alpha ^{2}-\beta ^{2})[4\alpha (2\alpha ^{2}-\beta ^{2})+2\beta ^{3}]}{SOC}>0\). In Country B, the effects are negative for IBA \(\frac{\partial t_{B}^{B}}{\partial \tau }= -\frac{\Gamma ^{2}4\alpha ^{3}(\beta ^{2}-2\alpha ^{2})}{SOC}<0\) as well as \(\frac{\partial t_{B}^{C}}{\partial \tau }=-\frac{\Gamma ^{2}(\beta ^{2}-\alpha ^{2})4\alpha (2\alpha ^{2}-\beta ^{2})}{SOC}<0\) and for SBA \(\frac{\partial t_{B}^{B}}{\partial \theta }= -\frac{\Gamma ^{2}\alpha ^{2}[4\alpha ^{2}\beta +4\alpha \beta ^{2}-8 \alpha ^{3}-3\beta ^{3}]}{SOC}<0\) as well as \(\frac{\partial t_{B}^{C}}{\partial \theta }= -\frac{\Gamma ^{2}(\beta ^{2}-\alpha ^{2})[4\alpha (2\alpha ^{2}-\beta ^{2}-\alpha \beta )+3\beta ^{3}]}{SOC}<0\).

  21. The kinks would be weaker in the event of a partial BA.

  22. The higher carbon price in Country A is consistent with the results yielded by Yomogida and Tarui (2013), who found that, if marginal damage is sufficiently high, the environmental tax policy with BA will yield higher emission tax rates in the implementing country than such a policy without BA.

  23. Yomogida and Tarui (2013) assumed different emission intensities due to a technological gap. They also found that overall emissions would decline with a BA independent of the gap in emission coefficients between the countries.


  • Anoulies L (2015) The strategic and effective dimensions of the border tax adjustment. J Public Econ Theory 17(6):824–847

    Article  Google Scholar 

  • Barrett S (1994) Strategic environmental policy and international trade. J Public Econ 54:325–338

    Article  Google Scholar 

  • Böhringer C, Fischer C, Rosendahl KE (2010) The global effects of subglobal climate policies. B.E. J Econ Anal Policy 10(2) (Symposium), Article 13

  • Böhringer C, Balisteri EJ, Rutherford TF (2012) The role of border carbon adjustment in unilateral climate policy: overview of an Energy Modeling Forum study (EMF 29). Energy Econ 34:S97–S110

    Article  Google Scholar 

  • Brander JA, Spencer BJ (1985) Export subsidies and international market share rivalry. J Int Econ 18:83–100

    Article  Google Scholar 

  • Carraro C, Siniscalco D (1993) Strategies for the protection of the environment. J Public Econ 52:309–328

    Article  Google Scholar 

  • Dermailly D, Quirion P (2008a) Leakage from climate policies and border tax adjustment: lessons from a geographic model of the cement industry. In: Roger, Guesnerie, Henry, Tulkens (eds) The design of climate policy, papers from a Summer Institute held in Venice, CESifo Seminar Series, Chapter 16. MIT Press, Boston

  • Dermailly D, Quirion P (2008b) EU ETS and competitiveness: a case study on the iron and steel industry. Energy Econ 30:2009–2027

    Article  Google Scholar 

  • Droege S (2011) Using border measures to address carbon flows. Clim Policy 11:1191–1201

    Article  Google Scholar 

  • Ebert U (1991) Pigouvian taxes and market structure: the case of oligopoly and different abatement technologies. Finanzarchiv Public Financ Anal 49:154–166

    Google Scholar 

  • Eyland T, Zaccour G (2012) Strategic effects of a border tax adjustment. Int Game Theory Rev 14(3):1–22

    Article  Google Scholar 

  • Fischer C, Fox AK (2012) Comparing policies to combat emissions leakage: border carbon adjustments versus rebates. J Environ Econ Manag 64(2):199–216

    Article  Google Scholar 

  • Fowlie ML (2009) Incomplete environmental regulation, imperfect competition, and emissions leakage. Am Econ J Econ Policy 1(2):72–112

    Article  Google Scholar 

  • Gros D, Egenhofer C (2011) The case for taxing carbon at the border. Clim Policy 11(5):1262–1268

    Article  Google Scholar 

  • Haufler A, Wooton I (1999) Country size and tax competition for foreign direct investment. J Public Econ 71(1):121–139

    Article  Google Scholar 

  • Helm C, Schmidt R (2015) Climate coproduction with technology investments and border carbon adjustment. Eur Econ Rev 75:112–130

    Article  Google Scholar 

  • Horn H, Mavroidis PC (2011) To B(TA) or not to B(TA)? On the legality and desirability of border tax adjustments from a trade perspective. World Econ 34(11):1911–1937

    Article  Google Scholar 

  • Ismer R, Neuhoff K (2007) Border tax adjustments: a feasible way to support stringent emission trading. Eur J Law Econ 24:137–164

    Article  Google Scholar 

  • Karp LS, Zhao J (2008) A proposal for the design of the successor to the Kyoto Protocol. Discussion Paper 2008-03, Harvard Project on International Climate Agreements, Cambridge

  • Katsoulacos Y, Xepapadeas A (1995) Environmental policy under oligopoly with endogenous market structure. Scand J Econ 97:411–420

    Article  Google Scholar 

  • Keen M, Kotsogiannis C (2014) Coordinating climate and trade policies: Pareto efficiency and the role of border tax adjustments. J Int Econ 94(1):119–128

    Article  Google Scholar 

  • Kennedy PW (1994) Equilibrium pollution taxes in open economies with imperfect competition. J Environ Econ Manag 27(1):49–63

    Article  Google Scholar 

  • Lininger C (2015) Design options for consumption-based policy approaches: a literature review. In: Consumption-based approaches in international climate policy. Springer, Cham, pp 205–226

  • Mæstad O (2001) Efficient climate policy with internationally mobile firms. Environ Resour Econ 19:267–284

    Article  Google Scholar 

  • Markusen JR, Morey ER, Olewiler N (1995) Competition in regional environmental policies when plant locations are endogenous. J Public Econ 56:55–77

    Article  Google Scholar 

  • Mathiesen L, Mæstad O (2004) Climate policy and the steel industry: achieving global emission reductions by an incomplete climate agreement. Energy J 25(4):91–114

    Article  Google Scholar 

  • Mattoo A, Subramanian A, van der Mensbrugghe D, He J (2009) Reconciling climate change and trade policy. CGD Working Paper 189, Center for Global Development

  • Meunier G, Ponssard J, Quirion P (2014) Carbon leakage and capacity-based allocations: Is the EU right? J Environ Econ Manag 68:262–279

    Article  Google Scholar 

  • Monjon S, Quirion P (2011) Adressing leakage in the EU ETS: BA or output-based allocation? Ecol Econ 70:1957–1971

    Article  Google Scholar 

  • Peters GP (2008) From production-based to consumption-based national emission inventories. Ecol Econ 65(1):13–23

    Article  Google Scholar 

  • Peters GP, Hertwich EG (2008) CO$_2$ embodied in international trade with implications for global climate policy. Environ Sci Technol 42:14011407

    Article  Google Scholar 

  • Ponssard J, Walker N (2008) EU emissions trading and the cement sector: a spatial competition analysis. Clim Policy 8(5):467–493

    Article  Google Scholar 

  • Ritz RA (2009) Carbon leakage under incomplete environmental regulation: an industry-level approach. Discussion Paper Series, No. 461, Department of Economics, University of Oxford, Oxford

  • Richter PM, Runkel M, Schmidt RC (2017) Strategic environmental policy under emissions leakage and firm mobility. Mimeo

  • Sakai M, Barrett J (2016) Border carbon adjustments: addressing emissions embodied in trade. Energy Policy 92:102–110

    Article  Google Scholar 

  • Sheldon I (2011) Is there anything new about border tax adjustments and climate policy? Am J Agric Econ 93(2):553–557

    Google Scholar 

  • Sheldon I, McCorriston S (2012) Climate policy and border tax adjustments: might industrial organization matter? EconoQuantum, Revista de Economia y Negocios 9(2):7–28

    Google Scholar 

  • Simpson RD (1995) Optimal pollution taxation in a Cournot duopoly. Environ Resour Econ 6:359–369

    Article  Google Scholar 

  • Steininger K, Linninger C, Droege S, Roser D, Tomlinson L, Meyer L (2014) Justice and cost effectiveness of consumption-based versus production-based approaches in the case of unilateral climate policies. Glob Environ Change 24:75–87

    Article  Google Scholar 

  • Veenendaal P, Manders T (2008) Border tax adjustment and the EU-ETS, a quantitative assessment, CPB Document No. 171, Central Planning Bureau, The Hague

  • Vlassis N (2013) The welfare consequences of pollution-tax harmonization. Environ Resour Econ 56(2):227–238

    Article  Google Scholar 

  • World Bank; Ecofys (2017) Carbon pricing watch 2017. World Bank, Washington, DC

  • Yomogida M, Tarui N (2013) Emission taxes and border tax adjustments for oligopolistic industries. Pac Econ Rev 18(5):644–673

    Article  Google Scholar 

Download references


We benefited from discussions held at the Public Economics Workshop in the WZB Berlin and at conferences in Dresden and Hamburg as well as from valuable comments by Daniel Becker, Michael Rauscher, Hendrik Ritter and Anna-Katharina Topp. We were able to further improve the paper following presentations at EARE 2017 in Athens and PET 2017 in Paris. In particular, we would like to thank Rabah Amir for taking the time to discuss the content of the paper. We would like to thank the editor of the Journal of Environmental and Resource Economics, Carolyn Fischer, and two anonymous referees for their valuable input. We also gratefully acknowledge the financial support given by the German Federal Ministry of Education and Research, FKZ 01LA1139A.

Author information

Authors and Affiliations


Corresponding author

Correspondence to Melanie Hecht.

Appendix A

Appendix A

A.1 Equilibrium Analysis (Second Stage)

A.1.1 Bertrand Competition

First, the presented model will be solved assuming price competition. We maximize profits with respect to domestic and foreign prices. For simplicity, we introduce \(\Gamma =\frac{1}{4\alpha ^{2}-\beta ^{2}}\) and solve for equilibrium prices

$$\begin{aligned} \left( \begin{array}{cc} p_{A}&{} q_{A} \\ p_{B} &{} q_{B}\end{array}\right) = \Gamma \left( \begin{array}{cc} 2\alpha &{} \beta \\ \beta &{} 2\alpha \end{array}\right) \left( \begin{array}{cc} 1+\alpha c_{A}&{} 1+\alpha \varsigma _{A} \\ 1+\alpha c_{B} &{} 1+\alpha \varsigma _{B}\end{array}\right) \end{aligned}$$

and equilibrium quantities

$$\begin{aligned} \left( \begin{array}{cc} x_{A}&{} y_{A} \\ x_{B} &{} y_{B}\end{array}\right) = \left( \begin{array}{cc}1 &{} 1 \\ 1 &{} 1\end{array}\right) -\Gamma \left( \begin{array}{cc}2\alpha ^{2}-\beta ^{2} &{} -\alpha \beta \\ alpha\beta &{} 2\alpha ^{2}-\beta ^{2}\end{array}\right) \left( \begin{array}{cc} 1+\alpha c_{A}&{} 1+\alpha \varsigma _{A} \\ 1+\alpha c_{B} &{} 1+\alpha \varsigma _{B}\end{array}\right) . \end{aligned}$$

A.1.2 Cournot Competition

To solve the third stage under Cournot competition, we need the inverse demand functions within the home and the foreign country

$$\begin{aligned} \left( \begin{array}{cc}p_{A}&{} q_{A}\\ p_{B} &{} q_{B}\end{array}\right) = \frac{\left( \begin{array}{cc} \alpha &{} \beta \\ \beta &{} \alpha \end{array} \right) \left( \begin{array}{cc}1-x_{A}&{} 1-y_{A}\\ 1-x_{B} &{} 1-y_{B}\end{array}\right) }{\alpha ^{2}-\beta ^{2}}. \end{aligned}$$

Maximizing profits, equilibrium quantities can be derived for the four firms that serve the domestic and foreign market

$$\begin{aligned} \left( \begin{array}{cc}x_{A} &{} y_{A} \\ x_{B} &{} y_{B}\end{array}\right) =\Gamma (\alpha +\beta ) \left( \begin{array}{cc} 2\alpha &{} -\beta \\ -\beta &{} 2\alpha \end{array}\right) \left( \begin{array}{cc}1-c_{A}(\alpha -\beta ) &{} 1-\varsigma _{A}(\alpha -\beta ) \\ 1-c_{B}(\alpha -\beta ) &{} 1-\varsigma _{B}(\alpha -\beta )\end{array}\right) . \end{aligned}$$

Using equilibrium quantities, we solve for equilibrium prices

$$\begin{aligned} \left( \begin{array}{c}p_{A} \\ p_{B} \\ q_{A} \\ q_{B}\end{array}\right) =\frac{\Gamma }{\alpha ^{2}-\beta ^{2}} \left( \begin{array}{cc}1 &{} c_{A}(2\alpha ^{2}-\beta ^{2})+\alpha \beta c_{B} \\ 1 &{} c_{B}(2\alpha ^{2}-\beta ^{2})+\alpha \beta c_{A} \\ 1 &{} \varsigma _{A}(2\alpha ^{2}-\beta ^{2})+\alpha \beta \varsigma _{B} \\ 1 &{} \varsigma _{B}(2\alpha ^{2}-\beta ^{2})+\alpha \beta \varsigma _{A}\end{array}\right) \left( \begin{array}{c}(\alpha +\beta )(2\alpha ^{2}-\beta ^{2}) \\ \alpha ^{2}-\beta ^{2}\end{array}\right) . \end{aligned}$$

A.2 Welfare

A.2.1 General Prerequisites

First, we wish to state a number of general prerequisites that hold for both types of competition. We start with producer surplus, which consists of profits from both firms located in Country A, i.e. \(\pi _{AA}\) and \(\pi _{AB}\), and add revenues from carbon pricing

$$\begin{aligned} PS_{A}+T_{A} ={\mathop {\underset{\text {profit from domestic sales}}{\underbrace{ (p_{A}-c-t_{A})x_{A}}}+\underset{\text {profit from exports}}{\underbrace{(q_{A}-c-(t_{A}-\delta _{2}))y_{A}}}+}\limits _{ \underset{\begin{array}{c} \text {carbon pricing revenues} \\ \text {from domestic production} \end{array}}{\underbrace{t_{A}{x}_{A}+ (t_{A}-\delta _{2} ){y}_{A}}}+\underset{\begin{array}{c} \text {revenues from}\\ \text {import BA} \end{array}}{\underbrace{\delta _{1} x_{B}}}.}} \end{aligned}$$

As revenues from carbon pricing levied on domestic production are costs incurred by Country A’s producers, they cancel out to zero, and (A.6) can be simplified to

$$\begin{aligned} PS_{A}+T_{A}=(p_{A}-c)x_{A}+(q_{A}-c)y_{A}+\delta _{1} x_{B}. \end{aligned}$$

For domestic consumer surplus, we take into account domestic demand for both products (\(x_{A}\) and \(x_{B})\) and obtain

$$\begin{aligned} CS_{A}=\frac{1}{2}(p_{A}^{0}-p_{A})x_{A}+\frac{1}{2} (p_{B}^{0}-p_{B})x_{B}, \end{aligned}$$

where \(p_{i}^{0}\) is the axis intercept of the inverse demand function \((i=A,B)\). Consumer surplus can be simplified to

$$\begin{aligned} CS_{A}=\frac{x_{A}^{2}+x_{B}^{2}}{2\alpha }. \end{aligned}$$

A.2.2 Import BA

To determine the impacts of import BA on producer surplus and public revenues, we differentiate (A.7) with respect to \(\tau \). With equilibrium prices (A.1) and quantities (A.2), we can determine the derivatives for Bertrand competition

$$\begin{aligned} \frac{\partial (PS_{A}^{B}+T_{A}^{B}-\varphi _{A}E)}{\partial \tau }&= \Gamma \alpha \left[ {2\alpha \beta }(p_{A}-c-t_{A}) + \frac{4\alpha ^{2}-\beta ^{2}}{\alpha }x_{B}\right] \nonumber \\&\quad +\frac{\alpha (\alpha -\beta )}{2\alpha -\beta }\left[ \varphi _{A}-\frac{\tau (2\alpha ^{2}-\beta ^{2})-\alpha \beta t_{A}}{2\alpha ^{2}-\beta ^{2}-\alpha \beta }\right] >0. \end{aligned}$$

With equilibrium quantities (A.4) and prices (A.5), we can determine the derivatives for Cournot competition

$$\begin{aligned} \frac{\partial (PS_{A}^{C}+T_{A}^{C}-\varphi _{A}E)}{\partial \tau }&=\Gamma \left[ 2\alpha x_{A}+(4\alpha ^{2}-\beta ^{2})x_{B}\right] \nonumber \\&\quad +\frac{\alpha ^{2}-\beta ^{2}}{2\alpha +\beta }\left[ \varphi _{A}-\frac{2\alpha \tau -\beta t_{A}}{2\alpha -\beta } \right] >0. \end{aligned}$$

In order to compute the effect on consumer surplus, we use equation (A.9) with equilibrium quantities (A.2) to obtain the impact for Bertrand competition

$$\begin{aligned} \frac{\partial CS_{A}^{B}}{\partial \tau }= \Gamma \left[ \alpha \beta x_{A}-(2\alpha ^{2}-\beta ^{2})x_{B}\right] <0, \end{aligned}$$

which decreases with \(\tau \) as \(x_{A}-x_{B}=-\Gamma \alpha (\Delta +\delta _{1}) (2\alpha ^{2}-\beta ^{2}-\alpha \beta )\le 0\) and \(\alpha \beta <2\alpha ^{2}-\beta ^{2}\). In Cournot competition, we obtain

$$\begin{aligned} \frac{\partial CS_{A}^{C}}{\partial \tau }=\frac{\Gamma }{\alpha }(\alpha ^{2}-\beta ^{2})(x_{A}\beta -2\alpha x_{B})<0, \end{aligned}$$

which decreases with \(\tau \) as \(x_{A}-x_{B}=\Gamma (\alpha ^{2}-\beta ^{2})(2\alpha +\beta )(\delta _{1}-\Delta )\le 0\) and \(\beta <2\alpha \).

A.2.3 Symmetric BA

For SBA, we differentiate (A.7) with respect to \(\theta \) to obtain the impact on domestic producer surplus and public revenues. With equilibrium prices (A.1) and quantities (A.2), we obtain the impact for Bertrand competition

$$\begin{aligned} \frac{\partial (PS_{A}^{B}+T_{A}^{B})}{\partial \theta }=\Gamma \left[ \begin{array}{c} {\alpha ^{2}\beta [2(p_{A}-c)-t_{A}]}\\ +\alpha [ 2\alpha ^{2}(t_{A}-\theta )-(q_{A}-c)\beta ^{2}]-\theta (2\alpha ^{2}-\beta ^{2})\alpha \end{array}\right] +x_{B}. \end{aligned}$$

With equilibrium quantities (A.4) and prices (A.5), we obtain the impact for Cournot competition

$$\begin{aligned} \frac{\partial (PS_{A}^{C}+T_{A}^{C})}{\partial \theta } =\Gamma \left[ \begin{array}{c} {\beta t_{A}(\alpha ^{2}-\beta ^{2})+2\alpha \beta x_{A}+2\alpha (\alpha ^{2}-\beta ^{2})(t_{A}-\theta )}\\ +\beta ^{2}y_{A}-\theta (\alpha ^{2}-\beta ^{2})2\alpha \end{array}\right] +x_{B}. \end{aligned}$$

The effect of SBA on consumer surplus is equal to the effect of IBA since including an additional export BA only influences the foreign market. Hence, the only relevant effect is that of the import BA which is captured in \(\frac{\partial CS_{A}}{\partial \tau }=\frac{\partial CS_{A}}{\partial \theta }\).

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Hecht, M., Peters, W. Border Adjustments Supplementing Nationally Determined Carbon Pricing. Environ Resource Econ 73, 93–109 (2019).

Download citation

  • Accepted:

  • Published:

  • Issue Date:

  • DOI:


  • Unilateral climate policy
  • Carbon pricing
  • Environmental tax competition
  • Border adjustment
  • International trade
  • Oligopolistic competition

JEL Classification

  • C72
  • H41
  • F12