Skip to main content

Thank you for visiting You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

Utilitarian benchmarks for emissions and pledges promote equity, climate and development


Tools are needed to benchmark carbon emissions and pledges against criteria of equity and fairness. However, standard economic approaches, which use a transparent optimization framework, ignore equity. Models that do include equity benchmarks exist, but often use opaque methodologies. Here we propose a utilitarian benchmark computed in a transparent optimization framework, which could usefully inform the equity benchmark debate. Implementing the utilitarian benchmark, which we see as ethically minimal and conceptually parsimonious, in two leading climate–economy models allows for calculation of the optimal allocation of future emissions. We compare this optimum with historical emissions and initial nationally determined contributions. Compared with cost minimization, utilitarian optimization features better outcomes for human development, equity and the climate. Peak temperature is lower under utilitarianism because it reduces the human development cost of global mitigation. Utilitarianism therefore is a promising inclusion to a set of benchmarks for future explorations of climate equity.

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

Relevant articles

Open Access articles citing this article.

Access options

Buy article

Get time limited or full article access on ReadCube.


All prices are NET prices.

Fig. 1: Evaluating NDCs with the utilitarian benchmark.
Fig. 2: Human development and equity advantages of the utilitarian policy.
Fig. 3: Gains from adopting the utilitarian versus the cost-minimization optimal policy.
Fig. 4: Climate advantages of the utilitarian policy.

Data availability

All data used in our version of the model is archived54 and freely available at

Code availability

All model code used to generate results and create figures for this article is archived54 and freely available at


  1. Clarke L. et al. in Climate Change 2014: Mitigation of Climate Change (eds Edenhofer, O. et al) Ch. 6 (Cambridge Univ. Press, 2014).

  2. Adoption of the Paris Agreement FCCC/CP/2015/L.9/Rev.1 (UNFCCC, 2015);

  3. Pauw, P., Mbeva, K. & van Asselt, H. Subtle differentiation of countries’ responsibilities under the Paris Agreement. Palgrave Commun. 5, 86 (2019).

    Article  Google Scholar 

  4. Winkler, H. et al. Countries start to explain how their climate contributions are fair: more rigour needed. Int. Environ. Agreem. 18, 99–115 (2018).

    Article  Google Scholar 

  5. Nationally Determined Contributions (NDCs) (UNFCCC, 2020);

  6. Höhne, N. et al. Emissions: world has four times the work or one-third of the time. Nature 579, 25–28 (2020).

    Article  Google Scholar 

  7. Ackerman, F., Stanton, E. A. & Bueno, R. CRED: a new model of climate and development. Ecol. Econ. 85, 166–176 (2013).

    Article  Google Scholar 

  8. CSO Equity Review Fair Shares: A Civil Society Equity Review of INDCs. figshare (2018).

  9. CSO Equity Review Equity and the Ambition Ratchet: Towards a Meaningful 2018 Facilitative Dialogue. figshare (2018).

  10. Holz, C., Kartha, S. & Athanasiou, T. Fairly sharing 1.5: national fair shares of a 1.5 °C-compliant global mitigation effort. Int. Environ. Agreem. 18, 117–134 (2018).

    Article  Google Scholar 

  11. Sheriff, G. Burden sharing under the Paris Climate Agreement. J. Assoc. Environ. Resour. Econ. 6, 275–318 (2019).

    Google Scholar 

  12. van den Berg, N. J. et al. Implications of various effort-sharing approaches for national carbon budgets and emissions pathways. Clim. Change 162, 1805–1822 (2020).

  13. Zimm, C. & Nakicenovic, N. What are the implications of the Paris Agreement for inequality? Clim. Policy 20, 458–467 (2020).

    Article  Google Scholar 

  14. Robiou du Point, Y. et al. Equitable mitigation to achieve the Paris Agreement goals. Nat. Clim. Change 7, 38–43 (2017).

    Article  Google Scholar 

  15. Kartha, S. et al. Cascading biases against poorer countries. Nat. Clim. Change 8, 348–349 (2018).

    Article  Google Scholar 

  16. Chichilnisky, G. & Heal, G. Who should abate carbon emissions? Econ. Lett. 44, 443–449 (1994).

    Article  Google Scholar 

  17. Anthoff, D. Optimal Global Dynamic Carbon Abatement (Univ. California Berkeley, 2011).

  18. Caney, S. Cosmopolitan justice, responsibility, and global climate change. Leiden J. Int. Law 18, 747–775 (2005).

    Article  Google Scholar 

  19. Shue, H. Climate Justice: Vulnerability and Protection (Oxford Univ. Press, 2014).

  20. Gardiner, S., Caney, S., Jamieson, D. & Shue, H. (eds) Climate Ethics: Essential Readings (Oxford Univ. Press, 2010).

  21. Bykvist, K. Utilitarianism: A Guide for the Perplexed (Continuum, 2009).

  22. Kagan, S. Normative Ethics (Routledge, 1998).

  23. Singer, P. in Climate Ethics: Essential Readings (eds. Gardiner, S. et al.) 181–199 (Oxford Univ. Press, 2010).

  24. Dooley, K. et al. Ethical choices behind quantifications of fair contributions under the Paris Agreement. Nat. Clim. Change 11, 300–305 (2021).

  25. Adler, M. Measuring Social Welfare: An Introduction (Oxford Univ. Press, 2019).

  26. Nordhaus, W. D. Economic aspects of global warming in a post-Copenhagen environment. Proc. Natl Acad. Sci. USA 107, 11721–11726 (2010).

    CAS  Article  Google Scholar 

  27. Tol, R. S. J. The damage costs of climate change towards a dynamic representation. Ecol. Econ. 19, 67–90 (1996).

    Article  Google Scholar 

  28. Global Carbon Atlas—CO2 Emissions (Future Earth; accessed October 2020);

  29. Robiou du Pont, Y. A Multidimensional Equity and Warming Assessments of National Climate Pledges (Paris Equity Check, accessed 10 September 2018);

  30. Pauw, W. P. & Klein, R. J. T. Beyond ambition: increasing the transparency, coherence and implementability of nationally determined contributions. Clim. Policy 20, 405–414 (2020).

    Article  Google Scholar 

  31. Wei, T. et al. Developed and developing world responsibilities for historical climate change and CO2 mitigation. Proc. Natl Acad. Sci. USA 109, 12911–12915 (2012).

    CAS  Article  Google Scholar 

  32. Adler, M. et al. Priority for the worse-off and the social cost of carbon. Nat. Clim. Change 7, 443–449 (2017).

    Article  Google Scholar 

  33. Fleurbaey, M. & Zuber, S. Discounting, beyond utilitarianism. Economics 9, 1–52 (2015).

  34. Broome, J. Climate Matters: Ethics in a Warming World (Norton, 2012).

  35. Weyant, J. Some contributions of integrated assessment models of global climate change. Rev. Environ. Econ. Policy 11, 115–137 (2017).

    Article  Google Scholar 

  36. Bosetti, V. & Frankel, J. Politically feasible emissions targets to attain 460 ppm CO2 concentrations. Rev. Environ. Econ. Policy 6, 86–109 (2012).

    Article  Google Scholar 

  37. Edenhofer, O., Lessmann, K., Kemfert, C., Grubb, M. & Kohler, J. Induced technological change: exploring its implications for the economics of atmospheric stabilization: synthesis report from the Innovation Modeling Comparison Project. Energy J. 27, 57–107 (2006).

    Google Scholar 

  38. Nordhaus, W. D. & Sztorc, P. DICE 2013R: Introduction and User’s Manual (Yale Univ., 2013).

  39. Hope, C. W. The marginal impacts of CO2, CH4 and SF6 emissions. Clim. Policy 6, 537–544 (2006).

    Article  Google Scholar 

  40. Anthoff, D. Equity and Climate Change: Applications of FUND (Max Planck Institute, 2009).

  41. Stern, N. Stern Review: The Economics of Climate Change (HM Treasury, 2006).

  42. Dennig, F., Budolfson, M. B., Fleurbaey, M., Siebert, A. & Socolow, R. H. Inequality, climate impacts on the future poor, and carbon prices. Proc. Natl Acad. Sci. USA 112, 15827–15832 (2015).

    CAS  Article  Google Scholar 

  43. Bataille, C., Guivarch, C., Hallegatte, S., Rogelj, J. & Waisman, H. Carbon prices across countries. Nat. Clim. Change 8, 648–650 (2018).

    Article  Google Scholar 

  44. Sandmo, A. Global public economics: Public goods and externalities. Public Econ. 18–19, 3–21 (2007).

  45. Sheeran, K. A. Who should abate carbon emissions? A note. Environ. Resour. Econ. 35, 89–98 (2006).

    Article  Google Scholar 

  46. Budolfson, M. & Dennig, F. in Handbook on the Economics of Climate Change (eds. Chichilnisky, G. et al.) 224–238 (Edward Elgar Press, 2020).

  47. Rawls, J. A Theory of Justice (Harvard Univ. Press, 1971).

  48. Scanlon, T. M. What We Owe to Each Other (Harvard Univ. Press, 2000).

  49. Diaz, D. & Moore, F. Quantifying the economic risks of climate change. Nat. Clim. Change 7, 774–782 (2017).

    Article  Google Scholar 

  50. Anthoff, D. & Tol, R. S. J. Fund Documentation (2016);

  51. Lamb, W. F. & Rao, N. D. Human development in a climate-constrained world: what the past says about the future. Glob. Environ. Change 33, 14–22 (2015).

    Article  Google Scholar 

  52. Rao, N. D. & Baer, P. “Decent living” emissions: a conceptual framework. Sustainability 4, 656–681 (2012).

    Article  Google Scholar 

  53. Winkler, H. et al. Equitable Access to Sustainable Development: Contribution to the Body of Scientific Knowledge (BASIC Expert Group, 2011).

  54. Budolfson, M. et al. Utilitarian benchmarks for emissions and pledges promote equity, climate and development. Zenodo (2021).

  55. Technical Update of the Social Cost of Carbon for Regulatory Impact Analysis Under Executive Order 12866 (Interagency Working Group on the Social Cost of Carbon, United States Government, 2016).

  56. Nordhaus, W. D. & Boyer, J. Warming the World: Economic Models of Global Warming (MIT Press, 2000).

  57. Iyer, G. et al. Implications of sustainable development considerations for comparability across nationally determined contributions. Nat. Clim. Change 8, 124–129 (2018).

    Article  Google Scholar 

  58. Aldy, J. et al. Economic tools to promote transparency and comparability in the Paris Agreement. Nat. Clim. Change 6, 1000–1004 (2016).

    Article  Google Scholar 

  59. Nordhaus, W. D. & Yang, Z. A regional dynamic general-equilibrium model of alternative climate-change strategies. Am. Econ. Rev. 86, 741–765 (1996).

    Google Scholar 

  60. Dennig, F. & Emmerling, J. A Note on Optima with Negishi Weights (Princeton Univ., 2017).

  61. Stanton, E. A. Negishi welfare weights in integrated assessment models: the mathematics of global inequality. Clim. Change 107, 417–432 (2011).

    Article  Google Scholar 

  62. Broome, J. Weighing Goods: Equality, Uncertainty and Time (Blackwell, 2003).

  63. Broome, J. Equality versus priority: a useful distinction. Econ. Philos. 31, 219–228 (2015).

    Article  Google Scholar 

  64. Adler, M. Future generations: a prioritarian view. George Wash. Law Rev. 77, 1478–1519 (2009).

    Google Scholar 

  65. Voorhoeve, A. & Fleurbaey, M. Priority or equality for possible people? Ethics 126, 929–954 (2016).

    Article  Google Scholar 

  66. Monjon, S. & Quirion, P. A border adjustment for the EU ETS: reconciling WTO rules and capacity to tackle carbon leakage. Clim. Policy 11, 1212–1225 (2011).

    Article  Google Scholar 

  67. Lockwood, B. & Whalley, J. Carbon-motivated border tax adjustments: old wine in green bottles? World Econ. 33, 810–819 (2010).

    Article  Google Scholar 

  68. Aldy, J. E. & Pizer, W. A. The competitiveness impacts of climate change mitigation policies. J. Assoc. Environ. Resour. Econ. 2, 565–595 (2015).

    Google Scholar 

  69. Felder, S. & Rutherford, T. F. Unilateral CO2 reductions and carbon leakage: the consequences of international trade in oil and basic materials. J. Environ. Econ. Manage. 25, 162–176 (1993).

    Article  Google Scholar 

  70. Flannery, B., Hillman, J., Mares, J. W. & Porterfield, M. Framework Proposal for a US Upstream Greenhouse Gas Tax with WTO-Complaint Border Adjustments (Resources for the Future, 2018).

  71. Golosov, M., Hassler, J., Krusell, P. & Tsyvinski, A. Optimal taxes on fossil fuel in general equilibrium. Econometrica 82, 41–88 (2014).

    Article  Google Scholar 

Download references


Research by D.S. is supported by the National Institute of Child Health and Human Development (NICHD) grants K01HD098313 and P2CHD042849. The content is solely the responsibility of the authors and does not necessarily represent the official views of the National Institutes of Health.

Author information

Authors and Affiliations



All authors contributed equally to this work. M.B.B., D.A., F.D., N.K.D., F.E. and D.S. designed the research. F.D., F.E. and K.K. led the computer modelling, M.B.B., F.E., K.K. and D.S. designed the figures and F.E., K.K. and D.S. constructed the figures. M.B.B., N.K.D. and D.S. wrote the main paper and M.B.B. wrote the Supplementary Information. All authors discussed the results and implications and commented on the manuscript.

Corresponding authors

Correspondence to Mark B. Budolfson or Dean Spears.

Ethics declarations

Competing interests

N.K.D. is a member of the committee advising the Government of India on analysis of low carbon trajectories. All other authors declare no competing interests.

Additional information

Peer review information Nature Climate Change thanks Diane Coyle and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Extended data

Extended Data Fig. 1 Cumulative emissions per capita converge over the 21st century under utilitarianism.

The vertical axis plots, for each year, (cumulative emissions by region since 1900 up to that year) divided by (the total population, measured as person-years, lived in that region since 1900 up to that year). The high levels for USA in 2020 are the result of far higher emissions through the 20th century than the poorer regions plotted. Only countries are presented for which we have adequate population and emissions data going back to 1900.

Extended Data Fig. 2 Multi-Model Robustness.

Implementing the utilitarian method in the FUND model. The top row replicates Fig. 2c-d for RICE, while the bottom row displays the analogous results in the FUND model, which is known to have substantively different assumptions and structure.50 (See FUND documentation for details of the FUND model.51) The main results of the paper—that regional emission allocations are heavily tilted towards developing countries in the utilitarian optimum—also hold in the FUND model. (See also Anthoff 2011.18) We optimize FUND through 2300 with the same discounting parameters and utilitarian objective function used to generate our main results with RICE. The FUND results assume that regional carbon taxes can go no higher than $5000/ton CO2 and remain constant after 2200.

Supplementary information

Supplementary Information

Supplementary Information.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Budolfson, M.B., Anthoff, D., Dennig, F. et al. Utilitarian benchmarks for emissions and pledges promote equity, climate and development. Nat. Clim. Chang. 11, 827–833 (2021).

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI:

This article is cited by


Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing