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North–south convergence and the allocation of CO2 emissions


Mankind must cooperate to reduce GHG emissions to prevent a catastrophic rise in global temperature. How can the costs of reducing GHG emissions be allocated across regions of the world and simultaneously address growth? We postulate a two-region world and, based on sustainability and egalitarian criteria, calculate optimal paths in which a South, like China, and a North, like the United States, converge in welfare per capita to a path of sustained growth of 1 % per year by 2085, while global CO2 emissions are restricted to a conservative path, constructed from the Representative Concentration Pathway RCP3-PD scenario, that leads to the stabilization of concentrations around 450 ppm CO2, providing an expected temperature change not exceeding 2 °C. It follows from our analysis that growth expectations in the North and the South should be scaled back substantially, not only after 2085, but also in the transition period. Feasible growth paths with low levels of emissions would require heavy investments in education and knowledge. Northern and Southern growth should be restricted to about 1 % and 2.5 % per year, respectively, over the next 75 years. Politicians who wish to solve the global-warming problem should prepare their polities to accept this reality.

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  1. 1.

    The RCPs are described in the 2011 special issue of Climatic Change. For a summary see Meinshausen et al. (2011) and van Vuuren et al. (2011). The data can be obtained from

  2. 2.

    The corresponding levels in RCP3-PD are more conservative, since negative emissions after 2073 stabilize CO2 concentrations at around 375 ppm and expected surface temperature increase at around 1.2 °C. See Section S.3.2.5 of the (online) Appendix for a detailed description of our Generational Path with extended projections until the year 2500.

  3. 3.

    These are no doubt important (Arrow et al. 2004, Barnosky et al. 2012, and Vitousek et al. 1997).

  4. 4.

    In other contexts, sustainability applies to maintaining some index of natural resources (Neumayer 2013). Here we follow Solow’s (1993): “I will assume that a sustainable path for the national economy is one that allows every future generation the option of being as well off as its predecessors” (p.168).

  5. 5.

    See Llavador et al. (2011, 2013) and Roemer (2011).

  6. 6.

    Although we do not explicitly consider here Stern’s kind of uncertainty, it can be proved that, as long as the probability of extinction is not too large, our formulation is mathematically equivalent to one in which uncertainty is explicitly modeled (Llavador et al. 2010, 2011, 2013; Roemer 2011).

  7. 7.

    Since utility must grow at rate ρ, and one of the arguments of the utility function is essentially fixed (atmospheric carbon concentration), the other arguments must grow at a slightly higher rate than ρ.

  8. 8.

    Starting with different parameters for each region would require postulating a law of motion for these parameters so that they eventually converge. We do model the spillover of knowledge from North to South, but we feel that attempts to extend the approach to the parameters of the production function would be ad hoc.

  9. 9.

    North’s marginal products of capital and emissions are respectively about 1.7 and 1.6 times those in South (Section S.3.2.7 in the Appendix). The marginal product of an input is the rate at which output increases instantaneously as the amount of the input is increased, holding other inputs constant. For the Cobb-Douglas production function, this rate is proportional to the output–input ratio.

  10. 10.

    We assume that no resource is wasted; in particular, there is no involuntary unemployment.

  11. 11.

    Precisely: utility in period t is \( {c}_t^{\alpha_c}{\left({x}_t^l\right)}^{\alpha_l}{\left({S}_t^n\right)}^{\alpha_n}{\left({\widehat{S}}^m-{S}_t^m\right)}^{\alpha_m} \), where \( \left({c}_t,{x}_t^l,{S}_t^n,{\widehat{S}}^m-{S}_t^m\right) \) are consumption, leisure in units of skill, the stock of knowledge, and the non-carbon-polluted atmosphere, respectively, in period t. The four α j exponents are positive and sum to one.

  12. 12.

    Llavador et al. (2013) performs the exercise of identifying utility with consumption only, instead of the four-argument utility function, in a one-region world. The feasibility of sustaining annual growth rates around 1 % is robust to this modification but, of course, the paths for the economic variables are quite different.

  13. 13.

    Not surprisingly, in order to catch up with North, South’s consumption of output has to grow fast during the transition, see Section S.4 in the Appendix.

  14. 14.

    Values for the economic variables along the transition and in the steady state are reported in section S.4 of the Appendix.

  15. 15.

    See Table s.12 in the Appendix.

  16. 16.

    This recommendation is in line with those put forth by Skidelsky and Skidelsky (2012), Gordon (2012) and Rogoff (2012), who call for limiting growth based on different considerations.


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We are indebted to three referees and the guest editors of Climatic Change for detailed and useful suggestions. We thank the audiences in various presentations, in particular in the Workshop on Multi-disciplinary Perspectives on Climate Ethics, Como, Italy. We also thank Thomas Stoerk for very diligent research assistantship. Humberto Llavador acknowledges financial support from the Spanish Ministry of Economy and Competitiveness through the Severo Ochoa Programme for Centers of Excellence in R&D (SEV-2011-0075) and the Spanish Ministry of Science and Innovation through the research grants (ECO2011-28965) and (EC-2012-36200).

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Correspondence to Humberto Llavador.

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“This article is part of a special issue on” Multidisciplinary perspectives on climate ethics “with guest editors Marco Grasso and Ezra M. Markowitz”.

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Llavador, H., Roemer, J.E. & Silvestre, J. North–south convergence and the allocation of CO2 emissions. Climatic Change 130, 383–395 (2015).

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JEL Classification

  • D63
  • F53
  • O40
  • O41
  • Q50
  • Q54
  • Q56