How to Allocate CO2 Emissions

Delivering on his election pledge to tackle the climate change issue, President Barack Obama today instructed the US Environmental Protection Agency to establish carbon emission standards for both new and existing power plants. Important as this is, the unilateral move will have a limited impact as the world struggles over how to limit carbon emissions. Any global plan will lead to economic winners and losers. A streamlined plan to enlist global cooperation on a carbon budget – emphasizing sustainability, convergence, equality and efficiency – is put forward by Humberto Llavador, John Roemer and Joaquim Silvestre. The economists suggest that a realistic plan should be forward-looking, not striving to repair inequities of the past. “From a purely ethical viewpoint, it’s perhaps attractive to believe that countries should be allocated budgets a priori that are, let us say, proportional to their populations,” they write. “But we do not believe schemes of this sort, although much discussed, are politically realistic. What is realistic, we claim, is to maintain the relative speeds of countries in their efforts to grow.” The analysis concludes that, to contain emissions, all nations must inevitably sacrifice some growth. – YaleGlobal

How to Allocate CO2 Emissions

A fair, realistic proposal for allocating carbon emissions is needed to stem climate change
Humberto Llavador, John Roemer, Joaquim Silvestre
Tuesday, June 25, 2013

Balancing growth and emissions:  Industrial pollution in the US (top); Chinese workers in a factory

NEW HAVEN: The various rounds of global negotiations concerning climate change and the control of carbon emissions have met with limited success. Countries in the global South rightly believe that they have a right to attain the standard of living of those in the global North, and most in the global North believe that they are not to blame for the rise in atmospheric concentration, because it was not understood until the late 1980s that carbon emissions cause global warming.

If we are to keep carbon concentration sufficiently low to prevent possibly catastrophic climate change, international cooperation is required in limiting emissions. Indeed, it’s commonly estimated that global emissions per capita must be reduced to approximately 2 metric tons by 2050, from a present value of 4.7 metric tons. In 2010, US emissions were 17.6 tons per capita. An automobile that travels 25 miles per gallon of gasoline, driven for 18,000 miles, emits approximately 6.4 metric tons of CO2.

How should the global carbon budget that remains be allocated to regions of the world during the next century, in order to stabilize atmospheric CO2 concentration at 450 ppm? We describe a proposal for what we hope is a politically realistic solution to this problem.

To simplify the analysis, we suppose that the world consists of two regions: a global South, with the population of the current developing countries and a global North, with the population of the developed countries. These regions are postulated to grow at UN-estimated rates over the next 50 years. Again for simplicity, we assume that the South has the economic characteristics of China, and the North, those of the United States. Suppose that these two regions are negotiating how to allocate emissions between them when they have already agreed to a global path of emissions. We take that path to be one which engenders convergence to 450 ppm CO2. We are interested in an allocation of emissions to the global North and South which implements four desirable ends: a) sustainability, b) convergence, c) equality and d) efficiency.

Sustainability means that the growth of human welfare across generations continues at a constant rate; convergence means that the date at which the global South, or China, converges to the US in GDP per capita will occur in three generations, 75 years; equality means that, after convergence, both regions’ welfare per capita grow at the same rate; efficiency means that no path of resource allocation can implement higher welfare for every generation in every region than the one we propose. 

We model the economies of the global North and South as consisting of three production sectors: a sector that produces a consumption/investment good from labor, knowledge and capital; an education sector, in which adult labor educates children, producing skilled workers for the next generation; and a knowledge sector, producing the arts and technological knowledge, the latter determining technological progress. The only sector that produces carbon emissions is the first one. Human welfare is a function of commodity consumption, leisure, the level of education and two public goods: the stock of accumulated human knowledge and biospheric quality, the latter of which is diminished by accumulated atmospheric carbon. Our analysis produces paths of resource use for the global North and South, in which all these variables are determined. Thus, we can specify not only the allocation of the carbon budget between North and South, but also the allocation of labor to commodity production, the production of knowledge, including research and development, and the education of youth.

Our guiding principle, which determines the precise form of the optimization problem, is that the ratio of the growth factors[1] of the North and South should be equal to what it would have been, absent the climate-change problem. This implies, in particular, that the date at which the South converges to the North in GDP per capita will not change. We argue that this principle is one that’s required to gain assent of negotiators for, and polities of, the global North and South.  

Suppose that, absent the climate-change problem, China would converge to the US in GDP per capita in 75 years, and further suppose a path of regional emissions was proposed in which that convergence would occur in 100 years. China can persuasively argue that this is unfair and unacceptable. Its citizens would not accept this delay in convergence. Or suppose a path was proposed upon which convergence would occur in 50 years. Likewise, US negotiators would not agree to this, and their polities would not accept it. The only solution that survives is that the date of convergence be maintained at what it would have otherwise been. Preserving the ratio of growth factors until the date of convergence, whenever that occurs, will maintain the date of convergence at what it would have otherwise been.

Note that our principle is forward looking: We do not define “rights” that countries might have to levels of carbon emission, and we do not ask what has happened in the past. From a purely ethical viewpoint, it’s perhaps attractive to believe that countries should be allocated budgets a priori that are, let us say, proportional to their populations. But we do not believe schemes of this sort, although much discussed, are politically realistic. What is realistic, we claim, is to maintain the relative speeds of countries in their efforts to grow; hence, our stated principle.

Maintaining the relative growth factors of global regions subject to the constraint that global emissions converge to a concentration of not more than 450 ppm, suffices to determine growth paths of welfare of the global South and North that converge in 75 years. Thereafter, welfare grows at a constant rate. We show that, upon this path, the welfare per capita of the global North grows at 1.2 percent per year, during the transition – the next 75 years – and welfare per capita of the global South grows at an average of 2.9 percent per year. After convergence, both regions’ welfare grows at 1.2 percent per year.

The optimal allocation of emissions per capita in the two regions is for each generation in Figure 1.  Note that emissions per capita are greater in Generation 1 in the North, greater in Generation 2 in the South, and equalized in Generation 3. 

Furthermore, there is nopath of resource allocation which satisfies our desiderata, which maintains the convergence of CO2 to 450 ppm and which maintains the date of convergence of the global North and South, at which growth rates are appreciably larger than these. Indeed, our analysis demonstrates the necessity of addressing growth and emissions’ allocation simultaneously.

We therefore believe that, in order to successfully meet the challenge of maintaining the stated concentration of carbon, given reasonable expectations of convergence in the South, Northern polities must accept a growth rate not much larger than 1 percent per annum. Likewise, Southern growth rates will be scaled back from what expectations might have been. Absent this understanding, we see no acceptable resolution to global climate negotiations. Growth and emissions must be addressed simultaneously if negotiations for international cooperation are to succeed.


[1] The growth factor of per capita income is one plus the growth rate of per capita income. 


Humberto Llavador  is with the University of Pompeu Fabra, Barcelona;  John Roemer  is with Yale University; and Joaquim Silvestre is with the University of California, Davis.

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