DRAFT

Post-Kyoto Climate Regimes: Per Capita Cumulative CO2 Emissions

versus Contraction and Convergence of CO2 Emissions

Preliminary Draft Version

Hanae Tamechika*

February 2012

Abstract

The Copenhagen Accord sets the target for the post-Kyoto international climate framework as limiting the

global temperature increase to less than 2 degrees Celsius above the pre-industrial levels. In this paper,

we construct a dynamic computable general equilibrium model and analyze the economic effects of two

methods for allocating emission quotas across all countries under the post-Kyoto international climate

framework. Two types of CO2 emission quotas are considered: “historical responsibility” (HR), which

allocates emission quotas such that the per capita cumulative CO2 emissions for the 1950–2050 period are

equalized across all countries and “contraction and convergence of CO2 emissions”(C&C), which

allocates emission quotas such that the per capita CO2 emissions in 2050 are equalized across all

countries. Meinshausen et al (2009) states that limiting the cumulative CO2 emissions over the 2000–2050

period to 1,440 Gt CO2 yields a 50% probability of warming exceeding 2 degrees Celsius, relative to the

pre-industrial levels. This paper assumes that the global cumulative CO2 emissions from 2000 to 2050 are

1,440 Gt CO2.

It is shown that the rates of decrease in the GDP of developing countries under the HR scenario are

smaller than those under the C&C scenario. In addition, the rates of decrease in the GDP of industrialized

countries under the C&C scenario are smaller than those under the HR scenario. China becomes the

importer of emission rights in the long run, even under the HR scenario, whose allocation method is based

on cumulative CO2 emissions. Moreover, GDP loss in China increases over time (GDP losses in China

worsen off over time).

Keywords: computable general equilibrium modelling; permit allocation; climate policy

* Graduate School of Economics, Osaka University, 1-7, Machikaneyama, Toyonaka, Osaka, 560-0043,

Japan. Phone: +81-6-6850-5265; Fax: +81-6-6850-5256. E-mail: tamechika@econ.osaka-u.ac.jp

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1. Introduction

The Kyoto protocol, in which the ratified Annex B countries abate CO2 emissions, ends in 2012.

Accordingly, negotiations for the international climate change policy that will come into effect after 2012,

the so-called “post-Kyoto protocol,” have begun. In these negotiations, emission targets and the

allocation of emission quotas for multiple countries are being discussed. There are also some studies that

focus on the CO2 emission quotas allocation under the post-Kyoto protocol (e.g. Böhringer and Welsch

2004).Under the Kyoto protocol framework, which a group of counties or regions abate CO2 emissions,

carbon leakage occurs. The issue of carbon leakage is defined as follows: the impact of CO2 emission

reduction on the world CO2 emissions are small when only a group of countries reduce their CO2

emissions, and this small impact could be further diminished by the increase in CO2 emissions in

non-abatement countries. Therefore, the desirable post-Kyoto protocol is one in which CO2 emission

abatement is implemented in all countries including developing countries, which tend to rapidly increase

their CO2 emissions.

The 15th Conference of the Parties (COP 15), held at Copenhagen in 2009, set the emission target as

limiting the temperature increases to less than 2 degrees Celsius above preindustrial levels in order to

prevent dangerous climate change. This requires stabilization of atmospheric CO2 emissions at 450 ppm

CO2 eq. In this paper, we focus on this “450 ppm” scenario. To achieve this target, the methods for

allocating emission quotas across countries, such as the contraction and convergence of CO2 emissions,

must be considered. In this method, emission quotas are allocated all countries such that the per capita

CO2 emissions in the terminal point are equalized across them. Developing countries argue that emission

quotas must be allocated according to “historical responsibility,” and mention that emission targets must

be set according to the amount of cumulative CO2 emissions.

In this paper, we simulate emission reduction under the post-Kyoto protocol. In accordance with the

Copenhagen Accord, we set the 450 ppm target. In this paper, the two allocation methods of CO2

emission quotas for the 2005–2050 period: per capita cumulative CO2 emissions and contraction and

convergence of CO2 emissions. Under the per capita cumulative CO2 emissions scenario, which allocates

emission quotas so as to equalize per capita cumulative CO2 emissions across all countries, industrialized

countries face negative emission quotas. That is, they are not allowed to emit CO2 emissions under this

scenario. Therefore, it is necessary to note that implementation of international emission trading is

required under the per capita cumulative CO2 emissions scenario.

The rest of this paper is organized as follows. Section 2 discusses CO2 emissions by regions and

Section 3 provides an overview of the model and the data. Section 4 describes our policy scenarios.

Simulation results are discussed in Section 5. Section 6 concludes.

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2. CO2 emissions

In this section, we survey CO2 emissions. Table 1 summarizes CO2 emissions for the 1950–2005

periods. As shown in the table, the largest emitter of cumulative CO2 emissions is United States, followed

by China, Russian Federation, Germany, United Kingdom and Japan. Since CO2 emissions correlate with

populations, we take account of population, when considering “historical responsibility” on climate

change. Therefore, we define the per capita cumulative CO2 emissions as the indicator of the historical

responsibility on climate change.

Table 1: CO2 emissions from 1950 to 2005, mt of CO2

WRI data

1950-2005

United States 318432.100

China 92949.900

Russian Federation 89892.800

Germany 73208.200

United Kingdom 55033.800

Japan 42742.000

France 28771.100

India 25895.400

Canada 24300.100

Ukraine 23893.700

Poland 21118.400

Italy 18164.700

South Africa 12414.200

Australia 12166.200

Mexico 11315.000

Regions in our model

North America　（US and Canada) 239991.877

pacific oecd (aus, nz and korea, canada) 41210.006

JAPAN 42744.222

China ( including Hong Kong) 91161.880

India 23773.297

OECD Europe 198440.592

Eastern Europe 147917.646

Rest of the world (Other Asia, 114921.633

Middle East, Africa

Latin America, Mexico)

total 900161.153

Region / Country

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Table 2 provides the projected CO2 emissions for the 2005–2050 periods. We calculate future CO2

emissions by the following procedure. First CO2 emissions from 2005 to 2035 are given by EIA (2010).

Next, CO2 emissions from 2035 to 2050 are derived by extending at the growth rate of CO2 emissions

from 2030 to 2035, as projected by EIA (2010).

Table 2: CO2 emissions projection, mt of CO2

3. Model

3.1 Model

We construct a multi-regional and multi-sector dynamic computable general equilibrium model

based on Rutherford and Paltsev (2000). The model has 8 regions and 6 sectors. In each region, there

are three types of agents; representative household, government and firms. A household determines

consumption and investment (savings) so as to maximize his utility subject to a budget constraint. A

household supplies capital, labour, land and natural resources and then allocates his factor income to

purchase of goods and investment (savings). Its investment is determined by the Ramsey infinite

horizon optimizing model. We assume that labour, land and natural resources are mobile within a

region, and that land and natural resources are sector-specific factors. We also assume that capital is

mobile between regions. Next, the government collects tax revenue from output taxes, intermediate

demand taxes, factor taxes, final demand taxes, import tariffs and export subsidies, and then,

allocates his tax revenue to purchase of goods. We assume that tax rates are constant. Finally firms

produce goods with constant returns to scale technology to maximize profits using primary factors

and intermediate inputs. To explain bilateral cross-hauling in goods trade, we use the so-called

Armington assumption: goods produced in different regions are qualitatively distinct (Armington,

1969).

We assume two types of production function which is based on the GTAP-EG model

JPN pao EEU oeu nam CHN IND row

2005 1246.6 823.0 2640.6 4137.7 6409.0 5166.9 1190.1 5032.8

2010 1191.4 889.0 2687.6 4026.1 6275.1 6309.7 1463.4 5709.7

2015 1095.6 908.4 2676.9 3867.3 6101.0 7171.7 1571.6 6206.1

2020 1106.8 943.1 2708.1 3803.2 6215.4 8422.7 1754.6 6791.8

2025 1099.8 1003.8 2755.1 3797.6 6403.9 9773.4 1910.2 7462.8

2030 1078.2 1069.2 2827.0 3812.4 6587.8 11107.1 2085.2 8256.0

2035 1056.6 1147.2 2947.2 3865.3 6758.8 12390.5 2301.9 9251.3

2040 1034.4 1231.6 3073.8 3916.4 6934.9 13818.1 2542.7 10371.1

2045 1015.9 1322.1 3202.5 3970.0 7115.0 15420.4 2809.1 11622.3

2050 997.5 1419.9 3342.6 4023.8 7310.3 17202.4 3104.3 13025.9

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(Rutherford and Paltsev, 2000); the fossil-fuel production function and the non-fossil fuel production

function. Fossil fuel production activities include extraction of coal, crude oil, and natural gas.

Production has the structure shown in Figure 1. Fossil fuel output is produced as a constant elasticity

of substitution (CES) aggregate of natural resources and non natural resources input composite. The

non natural resources input for the production is a Leontief composite of capital, labour, land,

intermediate inputs.

Non fossil fuel production (including electricity) has the structure shown in Figure 2.Output is

produced with Leontief aggregation of non-energy goods and an energy- primary factor composite.

The energy-primary factor composite is a CES function of energy composite and primary factor

composite. The primary factor composite is a CES aggregation of primary factors. The energy

composite is a CES aggregation of electricity and non-electric energy input composite. The

non-electric energy is a CES aggregation of coal and liquid energy composites and the liquid energy

composite is a CES aggregation of petroleum and coal products and natural gas. The fossil fuel

composite is a Leontief aggregate of fossil fuel goods and CO2 emissions.

The utility function for the representative household is a nested CES function, as shown in

Figure 3. Aggregate consumption is a CES aggregation of a non-energy composite and energy

composite. The non-energy composite is a Cobb-Douglas aggregate of non-energy goods, and the

energy composite is a Cobb-Douglas aggregate of electricity, petroleum and coal products, natural

gas, and coal. Moreover, the fossil fuel composite is a Leontief aggregate of fossil fuel goods and

CO2 emissions.

In our model, representative households are assumed to have an infinite horizon. Therefore,

we need set the terminal condition so as to solve the dynamic model. We assume that t

in the terminal period, the growth rate of investment is equal to that of output.

The amount of CO2 emissions is assumed to be proportional to the volume of fossil

fuels and refined oil and coal products, which are used by firms as intermediate inputs

or consumed by households. Within our model, the price per unit to CO2 emission is

determined such that the amount of the actual CO2 emissions equals CO2 emission quotas,

when the amount of CO2 in the business-as-usual (BAU) scenario exceeds emission quotas.

Then, we define the unit price to emit CO2 as “permit price”. The permit price differs by

regions when regions apply domestic CO2 taxes. On the other hand, the permit price is

equalized among countries when international emission trading is allowed.

Furthermore, a household owns CO2 emission quotas and collects permit revenue.

Table 3 provides the regions and sectors incorporated in our model. The world is aggregated into 8

regions: North America (NAM), Pacific OECD, Japan (JPN), China (CHN), India (IND), OECD

Europe (OEU), Eastern Europe, and the rest of the world (ROW). Sectors are aggregated into 6

sectors: coal, crude oil, natural gas, refined oil and coal products, electricity and heat, and

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non-energy macro good aggregate.

Figure 1: Production function of fossil fuel sectors

Figure 2: Production function of non fossil fuel sectors

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Figure 3: Final demand

Table 3: Regions and sectors

3.2 Data

We employ the GTAP 7 database as the benchmark data. The GTAP 7 database provides production,

imports and exports, other activities, energy data, and CO2 emissions. Our baseline projection is

calibrated by incorporating EIA projections on CO2 emissions and the growth rates of GDP (EIA, 2010).

Sectors

NAM North America (USA and Canada)

PAO Pacific OECD (Australia, New Zealand, Korea) 　COL Coal

JPN Japan 　GAS Natural gas

CHN China 　P_C Refined oil and coal products

IND India OIL Crude oil

OEU OECD Europe 　ELY Electricity and heat

EEU Eastern Europe Non-energy

ROW Rest of the world 　ROI Non-energy macro good aggregate

Regions

Energy

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4. Scenario design

In this paper, we simulate the scenario to stabilize the atmospheric CO2 concentration at 450 parts per

million (ppm) CO2 eq. The “450 ppm scenario” limits global warming at 2 degrees Celsius or lower,

relative to pre-industrial levels. We assume that global CO2 emission budgets for the 2005–2050 periods

are set at 1,314,579.25 million tons of CO2. These global budgets of cumulative CO2 emissions are

derived by calculating the cumulative CO2 emissions for the 2005–2050 period in the contraction and

convergence case under the assumption that global CO2 emissions are to be reduced by 25% in 2050,

relative to 1990 emission levels (a detailed discussion of the procedure for calculating the global CO2

emission budgets is presented in Section 4.2). Meinshausen et al (2009) states that limiting cumulative

CO2 emissions for the 2000–2050 period to 1,440 Gt CO2 yields a 50% probability of warming exceeding

2 degrees Celsius, relative to preindustrial levels. Cumulative CO2 emissions from 2000 to 2004 are

124,451.48 million tons of CO2 (IEA, 2009). Therefore, we can maintain the increase in global

temperature below 2 degrees Celsius in 2050,relative to pre-industrial levels ,with the probability of 50% ,

if the cumulative CO2 emissions from 2005 to 2050 are 131,549 million tons of CO2. Therefore, our

global CO2 emission budgets from 2005 to 2050 fall within 50% probability of warming exceeding the 2

degrees Celsius estimated by Meinshausen et al (2009).

In this paper, all countries (regions) are assumed to reduce CO2 emissions over the 2005–2050

period. We introduce two methods for allocating CO2 emission quotas for this period: the historical

responsibility scenario and the contraction and convergence of CO2 emissions scenario. The historical

responsibility scenario allocates emission quotas among countries such that the per capita cumulative CO2

emissions over the 1950–2050 period are equalized across all countries. The contraction and convergence

of CO2 emissions scenario, on the other hand, allocates emissions quotas among countries such that the

per capita CO2 emissions in 2050 are equalized across all countries.

4.1 Emission quotas allocation formula: Historical Responsibility

The historical responsibility scenario allocates our global budgets of cumulative CO2 emissions, which

is 1,314,579.25 million tons of CO2, across all countries according to their “historical responsibility” for

climate change. Historical responsibility is often measured by the cumulative CO2 emissions since 1900.

CO2 emission data from 1900 to 1949 for many countries is, however, non-existent. Because of this data

limitation, we consider cumulative CO2 emissions from 1950 to 2050. Hence, the historical responsibility

scenario allocates emissions quotas from 2005 to 2050 among countries such that the per capita

cumulative CO2 emissions from 1950 to 2050 are equalized across all countries.

For setting emissions quotas, CO2 emission data from 1950 to 2004 and population data from 1950 to

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2050 are required. We employ the CO2 emission data from the World Resources Institute (2010), and use

data from the IDB (2010) for the population from 1950 to 2050.

The procedure for calculating emission quotas per year for each country (region) is as follows: first,

cumulative world CO2 emissions from 1950 to 2050 are calculated by adding the world cumulative CO2

emissions from 1950 to 2004 to our global budgets of 1,314,579.25 million tons of CO2; next, we

calculate the world cumulative population from 1950 to 2050 by using the IDB population data (2010).

Then, the per capita cumulative CO2 emissions are derived by dividing the world cumulative carbon

emissions from 1950 to 2050 by the world cumulative population from 1950 to 2050.

The formula for per capita cumulative CO2 emissions is

z =∑ 𝐶𝑂2𝑤𝑜𝑟𝑙𝑑

2004𝑡=1950 (𝑡) + 𝑔𝑙𝑜𝑏𝑎𝑙 𝑒𝑚𝑖𝑠𝑠𝑖𝑜𝑛 𝑏𝑢𝑑𝑔𝑒𝑡𝑠

∑ 𝑃𝑂𝑃𝑤𝑜𝑟𝑙𝑑2050𝑡=1950 (𝑡)

(1)

where z represents the level of per capita cumulative CO2 emissions, t denotes the year, 𝐶𝑂2𝑤𝑜𝑟𝑙𝑑(𝑡) is

CO2 emissions in year t, and 𝑃𝑂𝑃𝑤𝑜𝑟𝑙𝑑(𝑡) denotes world population in year t.

Then, the annual emission quotas for each country are calculated by multiplying per capita cumulative

CO2 emissions by the annual population for each country.

The formula for the annual emission quotas allocation is

𝑍𝑖(𝑡) = 𝑧 × 𝑝𝑜𝑝𝑖(𝑡) (2)

where 𝑍𝑖(𝑡) represents the annual emission quotas, i denotes the country, and 𝑝𝑜𝑝𝑖(𝑡) denotes the

national population in year t.

4.2 Emission quotas allocation formula: Contraction and Convergence of CO2

emissions (C&C)

Under the contraction and convergence of CO2 emissions (C&C) scenario, we set the CO2 emission

reduction target, such as reducing the world carbon emissions in 2050, to a level of 25% below 1990

levels. We assume that all countries reduce their CO2 emissions from 2005 to 2050 and that per capita

CO2 emissions in 2050 are equalized across all countries.

The formula for per capita annual CO2 emissions is

𝑧𝑖(𝑡) =46−(𝑡−2004)

46∙ 𝑧𝑖(2004) +

(𝑡−2004)

46∙ 𝑧𝑐 (3)

where 𝑧𝑖(𝑡) represents the level of per capita CO2 emissions in t in country i, t denotes the year, 𝑧𝑐 is

the level of per capita CO2 emissions in 2050 CO2 emissions.

That is, the annual per capita CO2 emissions are calculated by the weighted average of per capita CO2

emissions in 2004 and 2050.

The formula for the annual emission quotas allocation, therefore, is

𝑍𝑖(𝑡) = 𝑧𝑐 × 𝑝𝑜𝑝𝑖(𝑡) (2)

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where 𝑍𝑖(𝑡) represents the annual emission quotas, i denotes the country, and 𝑝𝑜𝑝𝑖(𝑡) denotes

the national population in year t in country i.

Our global budgets of CO2 emissions from 2005 to 2050 are obtained from the emission quotas

under this C&C scenario.

4.3 Emission trading

Table 4 summarizes the emission targets in the historical responsibility and C&C scenarios. Under the

historical responsibility scenario, industrialized countries or regions such as NAM, OEU, EEU, PAO, and

JPN have negative emission quotas, as shown in Table 3. These countries are not allowed emit any CO2

emissions. Thus, international emission trading is required in the historical responsibility scenario in order

to implement the historical responsibility scenario. In this paper, therefore, we assume that international

emission trading is adopted under the historical responsibility scenario１.

１ IEA (2008) shows that the 450 ppm scenario will not be achieved without reductions in emissions by

the non-OECD countries, even if the OECD countries were to reduce their emissions to zero .

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Table 4: Emission quotas, mt of CO2

HR scenario

C&C_NTR and C&C_TRD scenarios

4.4 Policy scenarios

In this paper, we simulate the following four scenarios:

BaU: Business as usual. All countries or regions do not reduce CO2 emissions.

HR: All countries or regions face the emission quotas such that the per capita cumulative CO2

emissions from 1950 to 2050 are equalized, and international emission trading is adopted.

C&C_TRD: All countries or regions face the emission quotas such that the per capita CO2 emissions in

2050 are equalized and gradually reduce CO2 emissions from 2005 to 2050 using

international emission trading.

C&C_NTR: All countries or regions face the emission quotas such that the per capita CO2 emissions in

2050 are equalized and gradually reduce CO2 emissions from 2005 to 2050, and

international emission trading is not adopted.

We compare the differences between the equilibrium solutions for each of the above three scenarios,

JPN pao EEU oeu nam CHN IND row world

2005 -7.17 69.24 -686.25 -205.05 -2422.32 6863.31 5854.70 12568.60 22035.04

2010 -7.13 71.27 -681.35 -208.53 -2540.83 7034.63 6295.47 13683.78 23647.30

2015 -7.02 73.09 -676.74 -211.23 -2663.79 7200.42 6717.21 14808.34 25240.29

2020 -6.84 74.64 -670.70 -213.13 -2790.35 7322.07 7116.47 15953.03 26785.18

2025 -6.63 75.87 -662.39 -214.22 -2917.67 7375.31 7491.87 17096.01 28238.15

2030 -6.39 76.61 -652.28 -214.50 -3043.80 7358.44 7839.06 18225.30 29582.45

2035 -6.12 76.75 -641.36 -214.00 -3168.18 7287.95 8154.33 19332.78 30822.15

2040 -5.84 76.36 -629.99 -212.69 -3292.26 7182.77 8434.59 20408.77 31961.71

2045 -5.55 75.52 -617.70 -210.61 -3417.60 7051.49 8678.89 21446.87 33001.32

2050 -5.27 74.32 -603.96 -207.85 -3546.50 6890.83 8889.88 22437.49 33928.94

JPN pao EEU oeu nam CHN IND row world

2005 1250.16 847.50 2595.07 4109.33 6295.21 4714.93 1212.92 4995.12 26020.24

2010 1152.48 803.35 2417.48 3918.53 5998.69 4797.76 1599.79 5907.01 26595.08

2015 1044.52 753.12 2243.15 3705.38 5655.20 4875.15 2022.31 6899.66 27198.48

2020 931.87 696.76 2066.54 3472.53 5259.99 4921.22 2476.61 7979.41 27804.92

2025 818.54 634.83 1886.31 3222.73 4805.79 4920.45 2958.97 9136.66 28384.27

2030 707.68 566.85 1705.25 2959.00 4289.34 4872.71 3464.12 10364.43 28929.39

2035 600.85 493.65 1526.99 2684.71 3710.83 4789.91 3986.26 11656.40 29449.60

2040 499.22 417.22 1352.84 2402.64 3072.85 4685.18 4519.24 13004.18 29953.36

2045 404.15 339.51 1182.26 2116.05 2376.69 4564.60 5057.58 14400.22 30441.05

2050 316.55 262.16 1014.97 1828.70 1622.53 4426.45 5597.88 15833.87 30903.10

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in which CO2emission abatement is implemented, and the equilibrium solution for BaU scenario.

5. Simulation results

In this section, we present the simulation results and examine them.

5.1 Emission target

Table 5 summarizes the rate of reduction of CO2 emissions. The rate of reduction varies from region

to region. India (IND) and the rest of the world (ROW) receive sufficient emission quotas in all three

scenarios, HR, C&C_TRD, and C&C_NTR. In all scenarios, emission quotas in India (IND) and the rest

of the world (ROW) are above their BaU CO2 emissions. India (IND) and the rest of the world (ROW)

own the so-called “hot air” in the scenarios HR, C&C_TRD, and C&C_NTR. Furthermore, India (IND)

and the rest of the world (ROW) receive much higher emission quotas in the HR scenario than in the

C&C_TRD and C&C_NTR scenarios. Under HR, the reduction rates in the industrial countries other than

Pacific OECD (PAO) exceed 100%, meaning that the industrialized countries other than Pacific OECD

(PAO) are not allowed to emit CO2 emissions.

China (CHN) increases its CO2 emissions at a rapid rate. China (CHN) faces emission targets in the

HR scenarios, unlike India (IND) and the rest of the world (ROW). China receives higher emission quotas

under HR than under C&C_TRD and C&C_NTR. Under HR, China (CHN)’s emission target in the

beginning is lower, however becomes high over time.

5.2 Permit price

In this section, we examine the permit prices under HR and C&C_TRD. Table 6 shows permit prices.

Under HR, the permit price in 2005 is $2/t CO2. The permit price in the HR scenario rises over time,

resulting in the permit price in 2050 being $7/t CO2. Under C&C_TRD, on the other hand, the permit

price in 2005 is $21.75/tCO2. The permit price in the C&C scenario declines over time, resulting in the

permit price being around $5/tCO2 after 2025.

In this way, the difference between permit price in HR and C&C_TRD scenarios is caused by reduction

rates. In 2005, the global reduction rate under HR is 17% and under C&C_TRD is 2%, as shown in Table

4. In the beginning, the high reduction rate is imposed under the HR scenario and the low reduction rate

under the C&C_TRD scenario. In addition, under the HR scenario, countries or regions need to devote

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much effort to abate emissions in the beginning because they must reduce emissions substantially at that

time, before they can abate emissions with ease during the latter half of the 2005–2050 periods. Therefore,

the permit price declines. Under the C&C_TRD scenario, the reduction rate of CO2 emissions increases

over time, resulting in the rise of the permit price.

5.3 Volumes of exports and imports of emission permits

Table 7 shows the volume of exports and imports of emission permits under the HR and C&C_TRD

scenarios. In the C&C_TRD scenario, India (IND) and the rest of the world (ROW) are exporters of

emission permits. On the other hand, the largest importer of emission permits is North America (NAM).

North America (NAM) will import 1,299.14 million tons of emission permits in 2030 and 3,544.18

million tons in 2050. The second largest importer of emission permits is China (CHN). China (CHN) will

import 2,437.91 million tons of emission permits in 2030 and 3,472.68 million tons in 2050.

In the HR scenario, India (IND) and the rest of the world (ROW) are exporters of emission permits from

2005 to 2050. In the HR scenario, North America (NAM) is the largest importer of emission permits as

well. North America (NAM) will import 8,697.56 million tons of emission permits in 2030 and 9,099.17

million tons in 2050. The second largest importer of emission permits under the HR scenario is OECD

Europe (OEU). OECD Europe (OEU) will import 3,668.27 million tons of emission permits in 2030 and

3,564.99 million tons in 2050. In the HR scenario, China (CHN), who increases its future CO2 emissions

at a rapid rate, becomes the importer of emission permits in the long run. The China’s volume of imports

of emission permits in the HR scenario is smaller than that in the C&C_TRD scenario.

Compared with the C&C_TRD scenario, India (IND) and the rest of the world (ROW) under the HR

scenario, which export emission permits, increase the volume of exports of emissions permits from 2005

to 2050. All industrial countries under the HR scenario increase their volume of imports of emission

permits compared to the C&C_TRD scenario. This is because the reduction rates of CO2 emissions for

industrial countries in the HR scenario are higher than those in the C&C_TRD scenario.

5.4 GDP·GNI

Table 8 provides the percentage changes in GDP from BaU. The rate of decrease in the GDP of Japan

(JPN) in the HR scenario is smaller than that in the C&C_TRD scenario. In terms of GDP, the HR

scenario is desirable for JPN. In the beginning of the 2005–2050 period, the rates of decrease in the GDP

of countries or regions other than Japan (JPN) in the C&C_TRD scenario are smaller than those in the HR

scenario. Then, in the latter half on this period, the rates of decrease in the GDP of countries or regions

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other than Japan (JPN) in the C&C_TRD scenario are larger than those in the HR scenario.

Table 9 shows the percentage changes in gross national income (GNI) from BaU. GNI is derived by

adding permit revenue to GDP. The rates of decrease in the GDP of emission permit exporters such as

India (IND) and the rest of the world (ROW) in the HR scenario are smaller than those in the C&C_TRD

scenario from 2005 to 2050. In terms of GNI, the HR scenario is desirable for India (IND) and the rest of

the world (ROW).

In the beginning of the 2005–2050 period, the rates of decrease in the GNI of countries or regions

other than India(IND) and the rest of the world (ROW) in the C&C_TRD scenario are smaller than those

in the HR scenario. Then, in the latter half of this period, the rates of decrease in the GNI of countries or

regions other than India(IND) and the rest of the world (ROW) in the C&C_TRD scenario are larger than

those in the HR scenario.

5.5 C&C_NTR case

Table 10 shows the simulation results of the C&C_NTR scenario. In this section, we examines that

results. The marginal abatement costs vary by region and range from $0/tCO2 to $208/tCO2. The marginal

abatement costs in India (IND) are $0/tCO2 from 2005 to 2050. The marginal abatement costs in the rest

of the world (ROW) are $0/tCO2 from 2010 to 2050. This is because BaU CO2 emissions in India (IND)

are below the emission quotas during the 2005–2050 period and because BaU CO2 emissions in the rest

of the world (ROW) are below the emission quotas during the 2010–2050 period. Regions other than

India (IND) and the rest of the world (ROW) increase their marginal abatement costs over time. These

results are due to the increase in the reduction rate over time.

The rates of decrease in the GDP of regions other than India (IND) and the rest of the world (ROW) in

the C&C_NTR scenario are smaller than those in the C&C_TRD scenario. This is because international

emission trading lowers the burdens of emission reduction in these regions.

6. Conclusions

In this paper, we analyzed the post-Kyoto scenario using a dynamic general equilibrium model. To

achieve the 450 ppm target, we establish two types of methods to allocate emission quotas. We simulate

the HR and C&C scenarios. Developing countries argue that the rate of emission reduction for a country

must be set according to the cumulative CO2 emissions in that country. This paper shows that the HR

scenario, which allocates emission quotas across all countries on the basis of cumulative CO2 emissions,

is preferable for developing countries compared to the C&C scenario. Even under the HR scenario, China,

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however, becomes the importer of emission rights in the long run, and the reduction rate of CO2

emissions in China increases over time.

Reference

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Böhringer, C. and Welsch, H., (2004). Contraction and convergence of carbon emissions: an

intertemporal multi-region CGE analysis. Journal of Policy Modeling, 26, 21–39.

EIA (2010), International Energy Outlook 2010, Energy Information Agency

(EIA).

GTAP (2005), Global Trade Analysis Project, GTAP 7 Data Package, University

of Purdue.

IEA (2008), World Energy Outlook (2008 edition), International Energy Agency, OECD/IEA, Paris,

France.

IEA (2009), CO2 Emission from Fuel Combustion (2009 edition), International Energy Agency,

OECD/IEA, Paris, France.

Meinshausen, M, Meinshausen, N, Hare, W, Raper, S C B,Frieler, K, Knutti, R,

Frame, D J and Allen, M R (2009). Greenhouse gas emission targets for limiting

global warming to 2 °C. Nature, 458, 1158–1162.

Rutherford, T. F. and S. V. Paltsev (2000). GTAP in GAMS and GTAP-EG: Global Datasets for

Economic Research and Illustrative Models, Department of Economics, University of Colorado,

Working Paper.

United States Census Bureau (2010). International Data Base (IDB), United States Census

Bureau.

WRI (2010). Earth Trends Searchable Database: Climate and Atmosphere -- CO2 Emissions: Total

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CO2 emissions. World Resources Institute (WRI).

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Table 5: Emission reduction in percentage of BaU emissions

HR scenario

C&C_NTR and C&C_TRD scenarios

JPN pao EEU oeu nam CHN IND row world

2005 100.58 91.59 125.99 104.96 137.80 -32.83 -391.93 -149.74 17.31

2010 100.60 91.98 125.35 105.18 140.49 -11.49 -330.20 -139.66 17.18

2015 100.64 91.95 125.28 105.46 143.66 -0.40 -327.41 -138.61 14.72

2020 100.62 92.09 124.77 105.60 144.89 13.07 -305.58 -134.89 15.63

2025 100.60 92.44 124.04 105.64 145.56 24.54 -292.20 -129.08 17.45

2030 100.59 92.83 123.07 105.63 146.20 33.75 -275.94 -120.75 19.66

2035 100.58 93.31 121.76 105.54 146.88 41.18 -254.24 -108.97 22.40

2040 100.56 93.80 120.50 105.43 147.47 48.02 -231.71 -96.79 25.54

2045 100.55 94.29 119.29 105.30 148.03 54.27 -208.96 -84.53 28.99

2050 100.53 94.77 118.07 105.17 148.51 59.94 -186.38 -72.25 32.72

JPN pao EEU oeu nam CHN IND row world

2005 -0.28 -2.97 1.72 0.69 1.78 8.75 -1.91 0.75 2.35

2010 3.27 9.63 10.05 2.67 4.41 23.96 -9.32 -3.46 6.85

2015 4.67 17.09 16.20 4.19 7.31 32.02 -28.68 -11.18 8.11

2020 15.80 26.12 23.69 8.70 15.37 41.57 -41.15 -17.49 12.41

2025 25.57 36.76 31.53 15.14 24.95 49.65 -54.90 -22.43 17.02

2030 34.36 46.98 39.68 22.38 34.89 56.13 -66.13 -25.54 21.44

2035 43.14 56.97 48.19 30.54 45.10 61.34 -73.17 -26.00 25.85

2040 51.74 66.12 55.99 38.65 55.69 66.09 -77.73 -25.39 30.22

2045 60.22 74.32 63.08 46.70 66.60 70.40 -80.04 -23.90 34.50

2050 68.27 81.54 69.64 54.55 77.80 74.27 -80.33 -21.56 38.72

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Table 6: Permit price in $US per ton CO2

HR scenario

C&C_TRD scenario

JPN pao EEU oeu nam CHN IND row

2005 21.75 21.75 21.75 21.75 21.75 21.75 21.75 21.75

2010 12.77 12.77 12.77 12.77 12.77 12.77 12.77 12.77

2015 7.28 7.28 7.28 7.28 7.28 7.28 7.28 7.28

2020 5.88 5.88 5.88 5.88 5.88 5.88 5.88 5.88

2025 5.30 5.30 5.30 5.30 5.30 5.30 5.30 5.30

2030 4.97 4.97 4.97 4.97 4.97 4.97 4.97 4.97

2035 4.87 4.87 4.87 4.87 4.87 4.87 4.87 4.87

2040 4.90 4.90 4.90 4.90 4.90 4.90 4.90 4.90

2045 5.02 5.02 5.02 5.02 5.02 5.02 5.02 5.02

2050 5.21 5.21 5.21 5.21 5.21 5.21 5.21 5.21

JPN pao EEU oeu nam CHN IND row

2005 2.24 2.24 2.24 2.24 2.24 2.24 2.24 2.24

2010 3.86 3.86 3.86 3.86 3.86 3.86 3.86 3.86

2015 3.21 3.21 3.21 3.21 3.21 3.21 3.21 3.21

2020 4.06 4.06 4.06 4.06 4.06 4.06 4.06 4.06

2025 4.90 4.90 4.90 4.90 4.90 4.90 4.90 4.90

2030 5.55 5.55 5.55 5.55 5.55 5.55 5.55 5.55

2035 6.14 6.14 6.14 6.14 6.14 6.14 6.14 6.14

2040 6.67 6.67 6.67 6.67 6.67 6.67 6.67 6.67

2045 7.12 7.12 7.12 7.12 7.12 7.12 7.12 7.12

2050 7.49 7.49 7.49 7.49 7.49 7.49 7.49 7.49

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Table 7: Permit exports and imports, mt of CO2 positive: exports, negative: imports

HR scenario

C&C_TRD scenario

JPN pao EEU oeu nam CHN IND row

2005 -1141.01 -630.77 -2779.05 -3948.34 -7965.36 3325.06 4950.55 8188.93

2010 -1093.69 -684.30 -2826.94 -3863.25 -7969.78 2610.74 5146.10 8681.12

2015 -1022.52 -716.76 -2893.17 -3789.42 -8086.02 1865.55 5421.05 9221.29

2020 -1026.02 -737.49 -2889.79 -3723.44 -8285.36 1123.90 5671.21 9866.98

2025 -1006.36 -771.91 -2871.64 -3691.09 -8500.49 405.34 5939.75 10496.41

2030 -972.40 -804.97 -2856.86 -3668.27 -8687.56 -236.84 6173.56 11053.33

2035 -935.38 -840.29 -2855.94 -3664.53 -8829.81 -732.95 6359.38 11499.53

2040 -894.92 -872.57 -2837.24 -3645.62 -8946.27 -1209.35 6503.34 11902.63

2045 -854.83 -900.90 -2798.17 -3613.92 -9034.44 -1673.11 6603.12 12272.24

2050 -812.58 -925.52 -2745.57 -3564.99 -9099.17 -2117.11 6660.24 12604.70

JPN pao EEU oeu nam CHN IND row

2005 15.31 40.57 32.58 3.23 -16.87 -179.03 71.00 33.21

2010 -2.12 -34.33 -68.84 12.64 23.54 -671.28 280.60 459.79

2015 -11.08 -92.25 -203.73 -25.98 -110.14 -1209.73 623.21 1029.69

2020 -109.54 -145.22 -291.30 -119.34 -425.33 -1672.87 998.79 1764.80

2025 -188.24 -219.86 -384.31 -278.12 -835.94 -2094.96 1436.64 2564.79

2030 -250.99 -301.24 -496.75 -471.36 -1299.13 -2437.91 1879.94 3377.44

2035 -309.13 -391.52 -629.72 -701.08 -1795.20 -2666.29 2317.26 4175.67

2040 -360.87 -483.63 -750.88 -929.24 -2337.91 -2917.79 2753.78 5026.54

2045 -408.58 -575.27 -861.16 -1154.95 -2923.58 -3189.23 3183.78 5928.99

2050 -448.74 -664.87 -967.54 -1369.41 -3554.18 -3472.68 3604.93 6872.49

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Table 8: GDP (% change from BaU)

HR scenario

C&C_TRD scenario

JPN pao EEU oeu nam CHN IND row

2005 0.052 -1.173 -8.952 -0.132 -1.020 -9.698 -5.052 -3.849

2010 -0.086 -1.014 -6.217 -0.218 -0.769 -6.134 -3.683 -2.767

2015 -0.194 -0.844 -4.491 -0.298 -0.578 -3.823 -2.423 -2.061

2020 -0.336 -0.918 -4.276 -0.395 -0.584 -3.573 -2.324 -2.086

2025 -0.538 -1.077 -4.512 -0.503 -0.653 -3.773 -2.490 -2.318

2030 -0.677 -1.292 -4.984 -0.630 -0.749 -4.211 -2.778 -2.671

2035 -0.839 -1.575 -5.771 -0.776 -0.872 -4.877 -3.235 -3.191

2040 -1.033 -1.925 -6.761 -0.949 -1.024 -5.692 -3.814 -3.842

2045 -1.270 -2.353 -7.947 -1.158 -1.209 -6.652 -4.529 -4.634

2050 -1.552 -2.869 -9.337 -1.417 -1.428 -7.727 -5.402 -5.573

JPN pao EEU oeu nam CHN IND row

2005 0.016 -0.139 -0.982 -0.010 -0.111 -1.137 -0.592 -0.423

2010 -0.134 -0.465 -2.157 -0.193 -0.315 -2.225 -1.361 -1.054

2015 -0.281 -0.621 -2.345 -0.354 -0.382 -2.074 -1.387 -1.238

2020 -0.447 -0.909 -3.353 -0.523 -0.542 -2.868 -1.952 -1.814

2025 -0.536 -1.279 -4.530 -0.715 -0.740 -3.851 -2.623 -2.525

2030 -0.760 -1.665 -5.786 -0.914 -0.944 -4.907 -3.332 -3.285

2035 -1.018 -2.130 -7.302 -1.137 -1.171 -6.139 -4.191 -4.213

2040 -1.317 -2.674 -8.966 -1.392 -1.422 -7.471 -5.164 -5.271

2045 -1.664 -3.297 -10.728 -1.688 -1.697 -8.869 -6.252 -6.444

2050 -2.055 -4.004 -12.577 -2.041 -1.997 -10.282 -7.474 -7.719

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Table 9: GNI (% change from BaU)

HR scenario

C&C_TRD scenario

JPN pao EEU oeu nam CHN IND row

2005 -0.588 -2.323 -15.971 -1.004 -2.636 -5.061 14.219 0.362

2010 -0.525 -1.817 -10.671 -0.808 -1.876 -4.371 7.022 -0.045

2015 -0.488 -1.382 -7.522 -0.703 -1.335 -3.189 3.713 -0.283

2020 -0.636 -1.417 -6.998 -0.770 -1.288 -3.279 2.853 -0.447

2025 -0.877 -1.611 -7.260 -0.900 -1.398 -3.676 2.675 -0.615

2030 -1.057 -1.891 -7.901 -1.068 -1.569 -4.267 2.610 -0.842

2035 -1.282 -2.281 -9.025 -1.283 -1.812 -5.060 2.622 -1.161

2040 -1.559 -2.771 -10.451 -1.547 -2.124 -6.023 2.657 -1.549

2045 -1.903 -3.375 -12.158 -1.870 -2.508 -7.159 2.668 -2.017

2050 -2.313 -4.103 -14.143 -2.266 -2.967 -8.441 2.609 -2.576

JPN pao EEU oeu nam CHN IND row

2005 0.017 -0.131 -0.973 -0.010 -0.112 -1.164 -0.563 -0.422

2010 -0.134 -0.478 -2.190 -0.193 -0.314 -2.364 -1.182 -1.009

2015 -0.283 -0.652 -2.441 -0.356 -0.386 -2.257 -1.073 -1.149

2020 -0.469 -0.977 -3.545 -0.532 -0.567 -3.174 -1.314 -1.609

2025 -0.595 -1.421 -4.875 -0.743 -0.809 -4.316 -1.454 -2.136

2030 -0.870 -1.918 -6.357 -0.977 -1.083 -5.553 -1.482 -2.655

2035 -1.204 -2.549 -8.212 -1.260 -1.414 -6.989 -1.476 -3.275

2040 -1.609 -3.319 -10.298 -1.602 -1.818 -8.564 -1.409 -3.944

2045 -2.097 -4.231 -12.562 -2.015 -2.299 -10.243 -1.312 -4.642

2050 -2.667 -5.292 -15.003 -2.515 -2.871 -11.970 -1.219 -5.359

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Table 10: Simulation results under the C&C_NTR scenario

Marginal abatement cost in $US per ton CO2

GDP (GNI) (% change from BaU)

JPN pao EEU oeu nam CHN ind row

2005 1.45 0.84 2.26 2.34 3.58 1.91

2010 4.95 5.80 4.84 3.63 3.38 8.17

2015 5.54 9.27 6.69 3.98 4.26 9.75

2020 18.85 15.11 9.20 7.06 8.62 13.20

2025 31.43 25.58 12.29 12.29 15.02 16.98

2030 41.94 39.93 16.08 19.11 23.37 20.16

2035 55.13 60.05 21.01 27.79 34.63 22.41

2040 73.01 88.17 26.56 37.37 52.25 24.71

2045 97.97 131.60 33.20 48.53 85.81 27.20

2050 135.60 208.42 42.07 62.35 175.05 30.07

JPN pao EEU oeu nam CHN IND row

2005 0.516 0.028 -0.322 -0.088 -0.160 -2.043 0.119 -0.459

2010 0.545 -1.014 -2.965 -0.382 -0.381 -4.904 -0.039 -0.252

2015 1.022 -1.949 -4.939 -0.697 -0.640 -6.009 -0.317 -0.632

2020 1.220 -3.275 -7.300 -1.158 -1.233 -8.378 -0.420 -0.959

2025 -0.177 -5.231 -10.120 -1.728 -2.027 -10.871 -0.303 -0.910

2030 -3.042 -7.870 -13.731 -2.530 -3.080 -13.288 -0.107 -0.609

2035 -5.793 -11.901 -18.719 -3.804 -4.570 -15.858 0.035 -0.418

2040 -8.273 -17.285 -24.321 -5.424 -6.732 -18.785 0.115 -0.357

2045 -11.562 -24.227 -30.375 -7.379 -10.077 -21.903 0.210 -0.281

2050 -15.922 -33.455 -37.019 -9.681 -16.334 -25.106 0.415 -0.146