This exercise is designed to illustrate some of the political and economic issues that play key roles in discussions about how to design an international treaty to avert climate change.
Imagine three countries sitting down to negotiate a global climate change agreement: the United States, Russia, and India. Consider the United States and Russia as more developed countries (MDCs), termed Annex-1 countries in the Kyoto Protocol, and India as a less developed country (LDC), or a non-Annex-1 country. Below are equations for both the marginal costs (MCs) and total costs (TCs) of reducing greenhouse gas (GHG) emissions for all three countries. As a country reduces emissions by more and more, the MC of reducing emissions rises. This is because presumably a country will use the least costly options for reducing emissions first and gradually move on to using higher-cost methods as more emissions reductions are required. It is also typically the case that the MC of emissions reduction is lower in developing countries. This is because LDCs have engaged in relatively little emissions reduction, or abatement, so many low-cost opportunities for reducing emissions still exist there.
The MC and TC of emissions reduction (abatement) for the three countries are expressed in billions of dollars, where X is the number of tons of GHG emissions reduced by each country:
| United States | MCUS = 5XUS | TCUS = 2.5XUS2 |
| Russia | MCR = 2XR | TCR = XR2 |
| India | MCI = XI | TCI = XI2/2 |
While each country has potentially unlimited “rights” to emit carbon into the upper atmosphere, the United States chooses only to “exercise” its “right” to emit 400 tons, Russia chooses only to exercise its right to emit 250 tons, and India chooses only to exercise its right to emit 200 tons. As a result, global emissions are 850 tons. The international community has identified a 10 percent reduction in global carbon emissions as necessary to minimize the risks of dangerous climate change.
1. How much emissions reduction would each country have to do?
| United States: | (.10)400 = 40 = XUS |
| Russia: | (.10)250 = 25 = XR |
| India: | (.10)200 = 20 = XI |
| Global: | (40 + 25 + 20) = 85 = XG = (.10)850 |
2. What would be the cost of the last ton of emissions reduced in each country?
| United States: | MCUS = 5XUS = 5(40) = $200 |
| Russia: | MCR = 2XR = 2(25) = $50 |
| India: | MCI = XI = 1(20) = $20 |
3. What would be the total cost for each country?
| United States: | TCUS = 2.5XUS2 = 2.5(40)2 = $4,000 |
| Russia: | TCR = XR2 = (25)2 = $625 |
| India: | TCI = XI2/2 = (20)2/2 = $200 |
4. What would be the total cost of emissions reduction for the world?
5. Comment on any inefficiencies and inequities in this treaty.
Efficiency: After each country has reduced its emissions by 10 percent, the MC of reduction is different in the three countries. We therefore know we failed to minimize the global costs of reduction, which means the pattern of reductions this treaty yields is inefficient. To illustrate: The last ton reduced in the United States (the 40th ton reduced) costs $200, while the last ton reduced in Russia (the 25th ton reduced) costs only $25. Had we reduced 39 tons in the United States (instead of 40) and 26 tons in Russia (instead of 25), we would have achieved the same level of global reductions, 850, but we could have saved $200 − $25 = $175—that is, TCG would have been $4,650 instead of $4,825.
Equity: For simplicity assume that the benefits of achieving a global reduction of 85 tons are the same for all three countries. While the United States is paying more than Russia, which is paying more than India, to achieve this global reduction, we might argue that it is still unfair for India to bear this much of the cost because India did much less to create the problem in the first place, since Indian per capita cumulative emissions are much lower than per capita cumulative emissions of the United States and Russia, and because India is less able to bear the cost of preventing climate change, since per capita gross domestic product (GDP) is much lower there. We could also argue that the treaty now explicitly limits each country’s “right” to release carbon into the upper atmosphere, but distributes the remaining rights very unfairly. The treaty implicitly awards the United States rights to emit (400 − 40) = 360 tons, but awards Russia only rights to emit (250 − 25) = 225 tons, and India only rights to emit (200 − 20) = 180 tons. We could argue this is unfair for three reasons: (1) Since per capita cumulative emissions are highest in the United States and lowest in India, India should be awarded the most rights to emit more carbon dioxide in the future and the United States should be awarded the fewest rights to emit more—whereas this treaty does just the opposite. (2) Since emission rights are a new form of wealth and per capita wealth is lowest in India and highest in the United States, India should receive the most emission rights and the United States the fewest—whereas this treaty does just the opposite. (3) It is more difficult to achieve economic development when consumption of fossil fuel is limited. Since India is least developed and the United States is most developed, India should receive the most emission rights and the United States the fewest—whereas this treaty does just the opposite.
1. How much emissions reduction would each country have to do?
To make the two treaties equivalent, global reductions must be the same: XG must again be 85, but now XI = 0. Assume we require the United States and Russia to make the same percentage reduction, p, in their emissions. In this case we have:
Solving the second equation for p : 650p = 85; p = 85/650 = .13077; that is, the United States and Russia must each reduce by 13.077 percent.
| United States: | (.13077)400 = 52.308 = XUS |
| Russia: | (.13077)250 = 32.692 = XR |
| India: | 0 = XI |
| Global: | 52.308 + 32.692 + 0 = 85 = XG |
2. What would be the cost of the last ton of emissions reduced in each country?
| United States: | MCUS = 5XUS = 5(52.308) = $261.54 |
| Russia: | MCR = 2XR = 2(32.692) = $65.38 |
| India: | [Note: MCI = XI = 1(1) = $1 if India reduced emissions by 1 ton] |
3. What would be the total cost for each country?
| United States: | TCUS = 2.5XUS2 = 2.5(52.308)2 = $6,840.32 |
| Russia: | TCR = XR2 = (32.692)2 = $1,068.77 |
| India: | TCI = XI2/2 = (0)2/2 = $0.00 |
4. What would be the total cost of emissions reduction for the world?
5. Comment on the effects of excluding India from mandatory reductions on efficiency and equity.
Efficiency: Treaty #2 is even less efficient than Treaty #1 since $7,909.09 > $4,825. This is why people sometimes argue that achieving equity can come at the expense of efficiency. The cost of treating India fairly—not requiring it to reduce emissions at all—has raised the global cost of reducing emissions by 85 tons by $7,909.09 − $4,825 = $3,084.09. The reason is that none of the reduction is taking place in India, where the costs of reduction are lowest. Note that the first unit reduced in India would have cost only $1! We are also distributing reductions inefficiently between the United States and Russia since the MCs are different in these two countries. We could lower TCG by having more of the reductions in Russia, where the last unit of abatement cost only $65.38, and fewer of the reductions in the United States, where the last unit of abatement cost $261.54. But since Treaty #2 does not permit carbon trading between the United States and Russia, the inefficient pattern of abatement in those two countries will not be eliminated.
Equity: Clearly Treaty #2 treats India more fairly than Treaty #1. The implicit distribution of emissions rights—that is, new wealth—is now, for the United States, 400 − 52.308 = 347.692 (which is less than 360), and for Russia, 250 − 32.692 = 217.308 (which is less than 225). While India is given potentially limitless emission rights, under Treaty #2 India will only “exercise” its rights to emit 200 tons. That is all India chose to exercise before there was any treaty, and since this treaty does not allow India to sell any of its new wealth, India will continue to emit 200 tons, as before.
1. How much would each country have to reduce its emissions?
Once again XUS + XR = 85 and XI = 0. But now instead of 400p + 250p = 85, meaning that the United States and Russia will each reduce its emissions by the same percentage, p, the pattern of emissions reductions will be determined by the condition: MCUS = MCR. This is because the United States and Russia will keep trading emission rights until there are no longer any mutually beneficial deals to be struck, which will be the case only when MCUS becomes equal to MCR. So 5XUS = MCUS = MCR = 2XR, or XUS = (2/5)XR. Substituting for XUS in the first equation above, (2/5)XR + XR = 85, and XR = (5/7)85 = 60.714, and therefore XUS = 24.286.
| United States: | 24.286 = XUS |
| Russia: | 60.714 = XR |
| India: | 0 = XI |
| Global: | 24.286 + 60.286 + 0 = 85 = XG |
2. What would be the cost of the last ton of emissions reduced in each country?
| United States: | MCUS = 5XUS = 5(24.286) = $121.43 |
| Russia: | MCR = 2XR = 2(60.714) = $121.43 |
| India: | [Note: MCI = XI = 1(1) = $1 if India reduced emissions by 1 ton] |
3. What would be the total cost of the reductions carried out in each country?
| United States: | TCUS = 2.5XUS2 = 2.5(24.286)2 = $1,474.52 |
| Russia: | TCR = XR2 = (60.714)2 = $3,686.19 |
| India: | TCI = XI2/2 = (0)2/2 = $ 0.00 |
However, the total cost to the United States is not just the cost of reducing its own emissions by 24.286. That reduction is not sufficient to achieve a 13.077 percent reduction from 400, which is all the United States has the “right” to emit. Consequently, the United States will have to buy emission rights from Russia. Like Treaty #2, Treaty #3 gives the United States the right to emit (1 − .13077)400 = 347.692 tons. The United States will also reduce 24.286 tons, as calculated above. Therefore, the United States will need to purchase [400 − 347.692 − 24.286] = 28.022 emission rights from Russia. The price of each emission right will be $121.43 because Russia would accept no less (since that is what it will cost Russia to reduce its last ton) and the United States will pay no more (since the United States could reduce another ton itself for that amount). So $121.43(28.022) = $3,402.71, and the total cost to the United States—that is, the cost of reducing emissions internally by 24.286 tons, plus the cost of buying 28.022 emission rights from Russia—is $1,474.52 + $3,402.71 = $4,877.23.
The total cost to Russia of reducing emissions by 60.714—which exceeds a 13.077 percent reduction from 250 by 28.022 tons—is reduced by the amount Russia gains from selling 28.022 emission rights to the United States. At a price of $121.43 each, Russia reduces its total costs by $121.43(28.022) = $3,402.71 when it sells 28.022 emission rights to the United States. So the total cost to Russia—that is, the cost of reducing emissions internally by 60.714 tons, minus the revenue received from selling 28.022 emission rights to the United States—is $3,686.19 − $3,402.71 = $283.48.
4. What would be the total cost of emissions reduction for the world?
5. Comment on the effects of emission trading between Annex-1 countries on efficiency and equity.
Efficiency: Treaty #3 is more efficient than Treaty #2 because it allows reductions to be reallocated from the United States to Russia until the marginal reduction costs are equal in the two countries. TCG are lowered by $7,909.09 − $5,160.71 = $2,748.38. However, Treaty #3 is still not as efficient as it might be. The 85th ton reduced costs $121.43 (whether it is reduced in the United States or in Russia). If instead the 85th ton were reduced in India, it would cost only $1!
Equity: The distribution of emission rights under Treaty #3 is the same as under Treaty #2, so the equity implications of the wealth distribution are the same. The efficiency gain ($7,909.09 − $5,160.71 = $2,748.38) from reallocating reductions from the United States to Russia until the marginal reduction costs are equal in the two countries achieved by Treaty #3 is divided between the United States ($6,840.32 − $4,877.23 = $1,963.09) and Russia ($1,068.77 − $283.48 = $785.29). There is no change for India. Under both Treaty #2 and Treaty #3, India benefits from prevention of climate change at no cost.
1. How much emissions reduction would each country have to do? (Note: Treaty #4 does not require India to reduce emissions; however, since India can now sell emission reduction credits to the United States and Russia, India will benefit by reducing emissions, as illustrated below.)
We now have two conditions: XUS + XR + XI = 85, and MCUS = MCR = MCI. Since MCUS = 5XUS, MCR = 2XR, and MCI = XI, from the second condition we get
Substituting into the first equation, XUS + (5/2)XUS + 5XUS = 85, giving XUS = 10.
| United States: | 10 = XUS |
| Russia: | 25 = XR |
| India: | 50 = XI |
| Global: | 10 + 25 + 50 = 85 = XG |
2. What would be the cost of the last ton of emissions reduced in each country?
| United States: | MCUS = 5XUS = 5(10) = $50 |
| Russia: | MCR = 2XR = 2(25) = $50 |
| India: | MCI = XI=1(50) = $50 |
3. What would be the total cost for each country?
Total costs for each country associated with the reductions it carries out itself are as follows:
| United States: | TCUS = 2.5XUS2= 2.5(10)2 = $250 |
| Russia: | TCR = XR2 = (25)2 = $625 |
| India: | TCI = XI2/2 = (50)2/2 = $1,250 |
However, the United States and Russia will have to buy emission rights from India as follows:
| The United States will buy: | 400 − (1 − .13007)400 – 10 = 42.308 |
| Russia will buy: | 250 − (1 − .13007)250 – 25 = 7.692 |
| India will sell: | 42.308 + 7.692 = 50 |
Emission rights will sell for $50 each because the MC of reductions is now $50 in all three countries, so no country will pay more than $50 for a credit or sell a credit for less than $50. Therefore, it will cost the United States an additional $50(42.308) = $2,115.40, it will cost Russia an additional $50(7.692) = $384.60, and India will gain $50(50) = $2,500 from selling emission rights through the CDM, and therefore the total costs for the three countries are:
| United States: | TCUS = $250 + $2,115.40 = $2,365.40 |
| Russia: | TCR = $625 + $384.60 = $1,009.60 |
| India: | TC. = $1,250 − $2,500.00 = − $1,250.00 |
4. What would be the total cost of emission reductions for the world?
5. Comment on the effects of a CDM on efficiency and equity.
Efficiency: Treaty #4 has minimized the global cost of reducing global emissions by 85 tons: TCG Treaty #4: $2,125 < TCG Treaty #1: $4,825 < TCG Treaty #3: $5,160.71 < TCG Treaty #2: $7,909.09. We also know this because the marginal costs of reduction are the same in all three countries, so there is no way to reallocate emission reductions and lower global costs. Comparing the total cost of reducing emissions by 85 tons under Treaty #4 and Treaty #3, the efficiency gain produced by the CDM is $5,160.71 -$2,125 = $3,035.71. It is distributed as follows: U.S. total costs have fallen by $4,877.23 — $2,365.40 = $2,511.83. Russian total costs have risen by $1,009.60 — $283.48 = $726.12. (This is because the CDM allowed India to replace Russia as the seller in the lucrative market for emission rights.) And India now enjoys a profit of $1,250.
Equity: Treaty #4 awards the same emission rights—that is, new wealth—as Treaty #2 and #3: the United States (347.692), Russia (217.308), and India (potentially limitless). However, the CDM in Treaty #4 allows India to make more profitable use of its emission rights by selling some of them to the United States and Russia. Under Treaty #2 and #3, India could not sell any of its new wealth to the United States and Russia. The CDM allows India to sell emission rights, which it has every incentive to do as long as reducing emissions costs less than the price India receives. In the market for emission rights, supply (50 emission rights supplied by India) will equal demand for emission rights (42.308 from the United States and 7.692 from Russia) when the price of an emission right is $50. So under this treaty, the reduction of 50 of the 85 tons reduced globally will take place in India, which will cut back on its emissions from 200 to 150 tons. However, even though the reductions are taking place in India (where they are cheaper), the costs of achieving those reductions are being paid for by the United States and Russia.
The United States and Russia are paying more than it costs India to reduce 50 tons. The total cost of reducing the 50 tons in India is 502/2 = $1,250. The United States and Russia pay India $50(50) = $2,500. But this does not mean the United States and Russia are overpaying India by $1,250. We could just as easily argue the United States and Russia are underpaying India because it would have cost the United States and Russia much more than $2,500 to reduce those 50 tons themselves. By comparing the total costs under Treaty #3 and Treaty #4, we can calculate how much more it would have cost the United States and Russia: From Treaty #3 we know the total cost to the United States and Russia combined of reducing all 85 tons themselves is $5,160.71. From Treaty #4 the total cost to the United States and Russia combined (when they can purchase 50 of the 85 tons from India) is $2,365.40 + $1,009.60 = $3,375. Therefore the United States and Russia have saved $5,160.71 — $3,375 = $1,785.71 by purchasing 50 emission rights from India. Rather than speak of over- or underpaying, it is more accurate to say that the United States and Russia are sharing with India the efficiency gain from relocating 50 tons of reduction from the United States and Russia to India. In this case, the United States and Russia are getting $1,785.71 of the efficiency gain, and India is getting $1,250 of the efficiency gain. If the division of the efficiency gain were allocated through some political process or even through direct negotiation, it could be divided differently. However, this is how the efficiency gain will be allocated if we leave it to be settled by the laws of supply and demand in a free market for emission rights. The efficiency gain from this market transaction, like the efficiency gains from all market transactions, is divided between sellers and buyers according to the relative price elasticities of supply and demand. Whoever has the lower price elasticity will always capture more of the efficiency gain.
Warning: There is an important implicit assumption in the above analysis and an explicit warning is in order. We have assumed that India will actually reduce its emissions by 50 tons when it sells 50 emission rights to the United States and Russia. Of course this is what the executive board of the CDM in the Kyoto Protocol is supposed to ensure when it certifies emission rights for sale, namely that there was actually that number of tons reduced additional to what would have occurred in any case. But Treaty #4 gives India unlimited emission rights. When India could not sell emission rights, it only found it in its interest to “exercise” its right to emit 200 tons. But since India can now sell emission rights at $50 apiece, why would India not want to “exercise” its right to emit more than 200 tons—in which case global emissions would no longer decline by 85 tons? As long as India has unlimited emission rights, there will be what economists call a perverse incentive for India to try to sell bogus emission rights. Selling a real reduction that cost only $15, say, for $50 is a good deal. But if you can sell a “pretend” reduction that cost nothing for $50, that is an even better deal! We began to evaluate this problem in Chapter 8 but devote more attention to it in Chapters 9 and 10.
However, even if the CDM avoids cheating—that is, selling rights to emit that do not correspond to real reductions—it is sometimes criticized for other reasons we review in Chapter 9. Some people criticize it precisely because it does what it is designed to do—lower the cost of emissions reductions for MDCs. These critics argue that by lowering the cost of carbon emissions in the United States and Russia—in our exercise from $121.43 to $50 a ton—the CDM has reduced incentives for MDCs to search as hard as they would have otherwise for new renewable energy and energy conservation technologies. As discussed in Chapter 9, supporters of the CDM respond by saying, “If you want to keep the marginal cost of emissions high in the MDCs, it is better to do so by reducing emission caps on MDCs by more than 13.077 percent rather than by making it more costly for them to reduce emissions by limiting their use of the CDM.” To see how this might work, we consider Treaty #5.
1. How much emissions reduction would each country have to do?
MCUS = 5XUS = 121.43, which gives Xus = 24.29
MCR = 2XR = 121.43, which gives XR = 60.72
MCI = XI = 121.43, which gives XI = 121.43
XG = 24.29 + 60.72 + 121.43 = 206.44, which is much greater than 85 and therefore moves us much further in the direction of reducing global emissions. While an 85-ton reduction was a 10 percent reduction from pretreaty emission levels, 206.44/850 = .24287 is a 24.287 percent reduction. While unlimited trading guarantees that we will achieve this much larger reduction at the lowest possible global cost, nonetheless the global cost will be considerably higher because the overall reduction is considerably higher.
2. What would be the cost of the last ton of emissions reduced in each country?
By design the MC of emission reductions in each country is $121.43 in order to keep the pressure on the United States and Russia to search for renewable and energy efficiency as high as it was under Treaty #3.
3. What would be the total cost for each country?
Total costs for each country associated with internal reductions are as follows:
| United States: | TCUS = 2.5XUS2= 2.5(24.29)2 = $1,475.01 |
| Russia: | TCR = XR2 = (60.72)2 = $3,686.92 |
| India: | TCI = XI2/2 = (121.43)2/2 = $7,372.62 |
However, the United States and Russia will have to buy emission rights from India. If we continue to exempt India from any mandatory reductions and reduce emission rights in the United States and Russia by the same percentage, we can calculate the percentage reduction, p that will be necessary as follows:
400p + 250p = 206.44, which gives p = .3176. In other words, the United States and Russia will both have to reduce emissions by 31.76 percent in order to achieve a global reduction of 24.287 percent since we are not limiting India’s emission rights at all.
| The United States will buy: | 400 − (1 − .3176)400 – 24.29 = 102.75 |
| Russia will buy: | 250 − (1 − .3176)250 – 60.72 = 18.68 |
| India will sell: | 102.75 + 18.68 = 121.43 |
Emission rights will sell for $121.43 each. Therefore it will cost the United States an additional $121.43(102.75) = $12,476.93, it will cost Russia an additional $121.43(18.68) = $2,268.31, and India will gain $121.43(121.43) = $14,745.24 from selling emission rights through the CDM:
| United States: | TCUS = $1,475.01 + $12,476.93 = $13,951.94 |
| Russia: | TCR = $3,686.92 + $2,268.31 = $5,955.23 |
| India: | TCI = $7,372.62 − $14,745.24 = − $7,372.62 |
4. What would be the total cost for the world?
5. Comment on the effects of creating a high price on emissions in An-nex-1 countries to stimulate research and innovation in energy conservation and renewables.
Efficiency: Treaty #5 is efficient in the sense that it minimizes the global cost of achieving a 24.287 percent reduction in global emissions. But a larger efficiency question is what percentage global reduction is efficient in the first place! This depends, of course, on how great the benefits of avoiding climate change are compared to the costs associated with doing so. In theory, we should keep reducing emissions up to the point where the global benefit of the last ton reduced is equal to the cost of reducing it. Depending on how large the benefits of reducing emissions may be, that may mean that only a 10 percent reduction in emissions is warranted (i.e., efficient) or it may mean that a 24.287 percent reduction is warranted (i.e., efficient).
However, all attempts to estimate and quantify the benefits of avoiding climate change have proved very unsatisfactory—and without such an estimate, a cost-benefit analysis (CBA) is impossible. So instead of deploying a CBA approach to answering the question of what percentage reduction in global emissions is efficient, more and more analysts are approaching this part of the policy debate as an insurance issue, as explained in Chapter 2. We ask scientists to tell us what percentage reductions are necessary to reduce the risk of possibly cataclysmic climate change to a level we find acceptable. If they tell us we need a 10 percent reduction, then we design a policy to achieve that target. If they tell us we need a 24.287 percent reduction, we make that our target. Right now, most climate scientists believe that the percentage global reduction that is considered politically realistic is significantly below the level science says is necessary to reduce risk to an acceptable level. In this case, something more along the lines of a 24.287 percent reduction would be more efficient than a 10 percent reduction.
Equity: Because Treaty #5 leads to a larger global reduction and still gives India potentially unlimited emission rights, there are fewer emission rights to be awarded to the United States and Russia. The United States is awarded (1 − .3176)400 = 272.96, which is less than the 347.692 the United States received under Treaty #4. Russia is awarded (1 − .3176)250 = 170.60, which is also less than the 217.308 Russia received under Treaty #4. Notice that while the total cost of Treaty #5 to the United States and Russia is much higher, tightening global reductions from 10 percent to 24.287 percent benefits India by allowing India to sell more emission rights (121.43 > 50) at a much higher price ($121.43 > $50)! This means that non-Annex-1 countries stand to gain a considerable amount financially if the global reduction target is reduced under a Kyoto-type treaty, in addition to all the benefits they will enjoy by reducing the amount of climate change they must live with.