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Two-nation, one-pollutant model

Now consider a two-nation, one-pollutant model of the world: fossil fuel carbon dioxide from India and the USA (Smith 1989a). (Before the break-up of the USSR, these were the second most populous developing nation and developed nation, respectively, each with about 22 per cent of the population of its group.) Let us ask the seemingly straightforward question, 'What will be their relative responsibilities for increasing GG emissions over the next 35 years?'

Table 2.5 lists some of the relevant parameters for 1986, as well as projections for the year 2025, given UN population estimates and three possible future energy scenarios for the USA (annual per capita fossil fuel use grows at zero per cent, at +0.5 per cent, as it has in recent years, or at -1.5 per cent, which is what would be needed to reach a 30 per cent reduction in total emissions by 2025). The one scenario for India, 4.4 per cent growth, was chosen because it is similar to recent rates and allows the average Indian in 2025 to achieve an annual emission rate of 1 tonne of carbon per capita, about the 1990 world average, or what the United States achieved before 1900. Presumably, however, advances in technology and its application by 2025 would allow much more benefit per unit of emissions than achieved by the USA at similar emission levels.

Table 2.4 Proportion of world carbon emissions and population, by country

  1950-86 carbon emissions
(% of world)
1986, total population
(% of world)
1950-86 cumulative capita/year (% of world) 1986 per capita emissions (% of mean) 1986 undepleted natural debt (% of mean)
USA 30.1 5.3 5.9 503 572
Germany, United 7.4 1.7 2.2 352 431
Canada 2.3 0.6 0.6 412 412
Czechoslovakia 1.4 0.4 0.4 424 406
Belgium 0.9 0.2 0.3 269 398
United Kingdom 4.8 1.3 1.6 296 382
Australia 1.1 0.4 0.4 388 313
Poland 2.4 0.8 0.9 334 291
[USSR] 17.8 6.2 7 361 289
Netherlands 0.8 0.3 0.4 242 255
Bulgaria 0.5 0.2 0.2 362 253
France 2.9 1.2 1.5 180 244
Japan 5.6 2.7 3.2 212 211
Hungary 0.5 0.2 0.3 199 199
Romania 0.9 0.5 0.6 242 178
South Africa 1.2 0.7 0.7 280 162
Italy 1.9 1.3 1.6 166 148
Korea, Dem. 0.5 0.5 0.4 194 119
Spain 0.9 0.9 1 129 105
Yugoslavia 0.5 0.5 0.6 150 101
Greece 0.2 0.2 0.3 163 99
Venezuela 0.4 0.4 0.3 149 94
Argentina 0.6 0.7 0.7 85 83
Saudi Arabia 0.2 0.3 0.2 260 82
Portugal 0.1 0.2 0.3 80 57
Mexico 1 1.8 1.5 91 55
Chile 0.1 0.3 0.3 49 53
Korea, Rep. 0.5 0.9 0.9 109 51
Iran 0.4 1 0.8 68 43
Malaysia 0.1 0.4 0.2 58 40
Turkey 0.4 1.1 1 69 34
Colombia 0.2 0.6 0.6 44 33
Iraq 0.1 0.4 0.3 56 31
Syria 0.1 0.2 0.2 78 30
China 6.8 23.1 23.4 53 30
Algeria 0.1 0.5 0.4 69 27
Peru 0.1 0.4 0.4 29 26
Brazil 0.8 3 2.7 38 25
Egypt 0.2 1.1 1 42 22
Morocco 0.1 0.5 0.4 23 14
Philippines 0.2 1.2 1.1 16 14
Thailand 0.1 1.1 1 26 13
Vietnam 0.1 1.3 1.3 8 11
India 1.8 16.9 16.1 19 10
Indonesia 0.3 3.8 3.5 17 9
Ivory Coast 0.02 0.2 0.2 13 8
Pakistan 0.15 2.3 2 13 7
Sri Lanka 0.02 0.4 0.4 6 6
Kenya 0.03 0.5 0.3 5 6
Cameroon 0.01 0.2 0.2 17 6
Mozambique 0.02 0.3 0.3 2 5
Ghana 0.02 0.3 0.3 5 5
Nigeria 0.11 2.2 1.7 13 5
Sudan 0.02 0.5 0.4 4 5
Zaire 0.02 0.7 0.6 3 4
Burma 0.03 0.8 0.8 5 3
Madagascar 0.01 0.2 0.2 2 3
Tanzania 0.01 0.5 0.4 2 2
Uganda 0.01 0.4 0.3 1 2
Bangladesh 0.04 2.3 2.1 3 2
Ethiopia 0.01 1 0.9 1 1
Nepal 0.002 0.4 0.3 2 1
        Weighted means (t/cap)
Total 100 100 100 0.99 27.2

Note, for example, that the USA has a smaller fraction of present population 15.3%) and per capita emissions (503% of mean) than of cumulative population (5.9%) and natural debt (cumulative emissions, 572%). This is because the United States has been emitting at higher levels for a longer period and has a lower population growth rate than most of the world. The current weighted global per capita emissions are about 1 t/y, compared to the average nation's emission of 1.2 t/y shown in Table 2.3.

One index that could potentially answer the question of relative responsibility would be based on the expected change in national emission rates. Thus, India's annual emission rate in 1986 was 8.3 times less than that of the USA, but, at a US growth rate of zero (the middle scenario), India will catch up by 2025. Could it realistically be said that they each then have equal responsibility? Not if it is the impact on the atmosphere that is of concern, which is best indicated by natural debt.

Under the stated scenario, the USA-to-India ratio of natural debts added 1986-2025 is 2.3. In other words, this ratio might be considered their relative responsibility over the period, to be used, for example, for allocating costs of international programmes. (Higher ratios indicate that more responsibility would fall on the USA.)

Table 2.5 Emissions indices: carbon as carbon dioxide from fossil fuels and cement. India versus the USA

  1986 populationb (106) 1986 emissions/ capita (tonne) 1986 emissions/ nation (106 tonne) 1950-86 cumulative/ capita (tonne) 2025 populationb (106) (tonne) 2025 emissions/ capita (106 tonne) 2025 emissions/ nation (tonne) 1950-2025 cumulative/ capita 1987-2025 incremental cumulative/ nation (109 tonne)
USA (+05%)a 242 50 1210 155 301 6.1 1830 376 60
USA (0%) 242 50 1210 155 301 5.0 1500 355 54
USA (-15%) 242 5.0 1210 155 301 2.8 834 308 40
India (44%)a 781 0.19 150 2.8 1450 1.0 1450 22 23
Ratio, USA/India 0.31 27 8.3 55 0.21 6.1c 1.3 17 2.6
5.0 1.0 16 2.3
2.8 0.58 1 4 1 .7

Basic data from Marland et al. 1988

a Shown in parentheses are the annual growth rates in per capita carbon emissions assumed for this scenario.
b Population inputs are medium-case estimates from the UN (1988).
c The three ratios shown in these columns correspond to the three per capita USA carbon emission growth rates (+0.5%, 0%, -1.5%).

Let us now examine this index (natural debt per nation) a bit more closely. Is it really fair to allocate responsibility on the basis of national emissions (or natural debt)? To do so would imply that responsibility is somehow a function of size, that if you are lucky enough to live in a small country you are not as responsible as someone living in a large country, even if your own personal emissions are the same. Responsibility is best judged on a per capita and not on a per nation basis. Otherwise, quite perverse results can be obtained: for example that Hong Kong should have the same allotment as China until they merge in 1997, when their total allotment would drop by half. Or that the former parts of the USSR have suddenly become less responsible now that they are smaller. Clearly we do not want an index that rewards nations for splitting up or, conversely, for taking over other nations!

On the other hand, since governments, not individuals, will be actually asked to pay the bill for greenhouse remediation projects, the population size represented by the government must be considered. If the per capita emissions (or natural debt) is simply multiplied by the population size, however, we are right back to national emissions again. Chapter 4 directly addresses this dilemma.

Returning to Table 2.5, use of per capita indices changes the ratio of present USA/India emissions from 8.3 to 27. From the standpoint of natural debt, as shown in Table 2.5, the CO2 placed into the atmosphere since 1950 as part of the US industrialization process is equivalent to about 155 tonnes per person in 1986, about 50 times that of the average Indian, at 2.8 tonnes.

According to the scenarios in Table 2.5, the Indian per capita cumulative contribution would increase by a factor of about 6 over the period, while the American contribution would little more than double. Because of the large difference in initial values, however, during these 39 years, the Indian's contribution would increase by 19 tonnes, while the average US resident's contribution would rise more than 10 times as much, to 200 tonnes. The ratio of total cumulative amounts at the end of the period would, at 16, be lower than what it was in 1986 (50), but still high. At that point, the average Indian would still be responsible for only a minor part of the total atmospheric accumulation, less than 6 per cent of that of the average US resident. (See the box for a visual metaphor that may help put these points into perspective.)

Given these circumstances, even though their national emission rates would be the same at the end of the period, it seems presumptuous to expect the Indian to contribute much to an international effort to control greenhouse gases, at least relative to what might be expected of the American. Even with a drastic cut in emission rates, the growth of natural debt per capita is much higher in the USA.

The two-nation, two-pollutant model

To illustrate the importance of time horizon, we now upgrade the two nation model to include the two most important greenhouse gases: CO2 and methane. The United States and Indian emissions for 1987 are shown in Table 2.6. Note that, by the instantaneous index (time horizon = 0), the United States produces only three times as much GG as India when CH4 is included, which is much less of a relative responsibility than the factor of 7.9 for CO2 alone. Thus, it is not surprising that US negotiators tend to argue for including gases such as methane that are produced in relatively greater amounts by developing nations (Stewart and Weiner 1990).

Global change and the seawall metaphor

Used with care, an appropriate metaphor can sometimes assist in gaining insights about complicated relationships. In this spirit, consider the visualisation in Figure 2.11, which illustrates a simple two-person model of the world.

Figure 2.11 Growth in per capita natural debt, USA and India, 1986

The figure shows a seawall holding back a sometimes stormy and largely unpredictable sea. Occasionally, the sea overtops the wall, thus threatening to flood the average American and average Indian who live on the other side. To bolster themselves against this environmental variability, they have been building up their economic and technological infrastructure as indicated by the blocks of material an which they stand. As can be seen, the American has built a much larger base of support and thus is much less vulnerable to environmental stress than is the Indian.

One measure of the size of the support blacks is the energy that has been used to build them. In the US case, in 1986 the average American was standing on a block of 155 tonnes carbon (C in CO2 from fossil fuels since 1950). The Indian, by contrast, was standing on a block some 55 times smaller, 2.8 tonnes.

Unfortunately, a considerable part of the material for the support blocks comes from the top of the wall holding back the sea. As long as the people take material off the top at a moderate rate, the seawall can grow back enough to countered it naturally. Unfortunately, the rate of removal (5 t/year for the USA and 0.2 t/year for India) exceeds the natural rate and the top of the seawall is lowering. Consequently, the chance of the sea overtopping the wall seems to be increasing.

Now consider that the American, already being relatively well protected, had been able to implement a drastic energy efficiency and renewables effort and thus reduce the annual take from the top of the seawall by 1.5 per cent each year. Thus, as shown in Figure 2.12, at the end of 39 years, the American is taking just 2.8 tonnes per year, a cut of 44%. The Indian, an the other hand, seeing the increasing chance of overtoppage, feels the need to build up the support block even faster than before and thus takes 4.5 per cent more material off the top of the seawall each year. By the year 2025, therefore, the Indian is taking 1 tonne per year, which about equals the world average in the late 1980s and what the American was taking well before 1900. Presumably, however, due to better technology and planning, more benefit will be gained in the future from such a relatively modest rate of removal.

Seawall metaphor showing how greenhouse gas emissions can increase the likelihood of environmental stress from global warming, as well as decrease human vulnerability to the some stress.

Figure 2.11 shows conditions in 1986 when the average US and Indian residents were protected from stress by infrastructure built by, respectively, 155 and 2.8 tonnes of carbon 11950-86 natural debts).

In Figure 2.12 assuming the growth rates in Figure 2.11 ore continued until 2025, the average Indian could reach annual greenhouse emissions of 1 tonne carbon, roughly the present world average. At this point, however, the Indian's natural debt would still be 14 times less than that of the US resident, although better technology might make it possible to achieve a smaller difference in their respective environmental vulnerabilities.

Figure 2.12 Growth in per capita natural debt, USA and India, 2025

Since the Indian's annual take has grown at a healthy rate and the American's has substantially fallen, the difference in their annual takes has dropped from a factor of about 30 in 1986 to 3 in 2025. From the standpoint of both benefit and risk, however, it is the amount taken from the top of the seawall that is most crucial. This is what builds up the support base that reduces vulnerability and, at the same time, increases the likelihood of environmental stress. From this standpoint, the American has taken off about eight times as much as the Indian, even though the former is undergoing a drastic annual reduction in the rate of removal and the latter's rate is increasing rapidly.

Now, consider the question posed by this book 'If a large international programme of greenhouse remediation is to be undertaken, who should pay over the next few decades?' Looking at Figure 2. 12, it does not seem quite fair to expect the Indian to bear much of the cost during this period. Compared to the American, the Indian has not taken much material off the top of the seawall, either in total since 1950 (7 per cent of the American) or incrementally during the decades being considered (13 per cent). By starting at such a high base, even with quite rapid decline in annual rates, the American's annual and total contributions to the problem will remain much higher throughout any future period during which present policies can reasonably contend. In addition, importantly, the American will remain much mare insulated from any environmental stress as well, by virtue of the infrastructure built up over many years.

In closing, it is important to remember that these conclusions refer to who is responsible for paying for climate change remediation efforts, and not to where such efforts might best be undertaken. It is quite possible, for example, that most cost-effective programmes might be in countries that have little responsibility for payment.

On the other hand, on a 500-year basis, the ratio rises to 5.7 or 6.7 (depending on whether indirect effects are included), effectively doubling relative US responsibility. A completely integrated index (an infinite time horizon) would result in a ratio of 7.3. Note also that inclusion of indirect effects tends to obligate nations such as India with relatively high methane production, that is, the USA/India ratio decreases. Thus, US negotiators could be expected to argue for inclusion of indirect effects, for shorter rather than longer time horizons, and, perhaps, for applying a discount rate as well.

Three-nation, two-pollutant model

Figure 2.13 provides further evidence of the sensitivity to choice of time horizon. It shows the impact of time horizon on the ratio between the 1987 emissions of the United States and India compared to the ratio between the United States and the then Federal Republic of Germany (FRG). Note that with an instantaneous index, the ratios are quite different, but that with a time horizon of about 565 years, the two match. US emissions are 6.9 times either those of Germany and India, which, therefore, have equal weightings. At an infinite time horizon, however, the two are different again.

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