Achieving Carbon Emissions Peak in China by 2030: The Key Options and Economic Impacts

Abstract

This study investigates the options and sectors that are essential for China to achieve carbon emissions peak by 2030. A dynamic computable general equilibrium (CGE) model is used to generate 14 scenarios from a scenario matrix incorporating three levels of carbon constraints and four options of low-carbon measures. Results suggest that if there is no policy intervention, China’s total CO₂ emissions would reach 22.9 Gt in 2030. To cut carbon emissions required by the latest Intended Nationally Determined Contributions (INDC) or the global two-degree target, China should not only rely on optimizing industry structure or restricting its industry output, but more importantly, it should rely on low-carbon technologies in the power and end-use sectors as well as low-carbon style consumption. We also depict how the mitigation costs can be lowered through various low-carbon countermeasures, with which the carbon mitigation cost of achieving China’s INDC target in 2030 could be reduced from 155 USD/ton-CO₂ to 35 USD/ton-CO₂. The corresponding GDP loss could fall from 6.3% to merely 0.67%, and welfare will not be affected significantly.

Appendices

Appendix 1: The CGE Model

The appendix provides a technical description of the CGE model based on Dai (2012).

6.1.1 Production

Each producer maximizes profit subject to the production technology. Activity output of each sector follows a nested constant elasticity of substitution (CES) production function. Each sector has two types of production function: one uses the existing capital stock, and another uses new investment (Dai et al. 2011). The difference between these two subsectors is the efficiency and mobility of capital among the sectors. Inputs are categorized into material commodities, energy commodities, land, labor, capital, and resource.

The producer maximizes its profit by choosing its output level and input use, depending on their relative prices subject to its technology. The producer’s problem can be expressed as

$$ \max\ {\pi}_{r, j}={p}_{r, j}\bullet {Z}_{r, j}-\left(\sum_{i=1}^N{p}_{r, i}\bullet {X}_{r, i, j}+\sum_{i=1}^N{\omega}_{r, f}\bullet {V}_{r, f, j}\right) $$

(6.5)

subject to

$$ {Z}_{r, j}={\upsilon}_{r, j}\left[{X}_{r,1, j,}{X}_{r,2, j,}\dots, {X}_{r, N, j,};{V}_{r,1, j,}\dots, {V}_{r, F, j\ }\right] $$

(6.6)

where

π_r , j::

Profit of j-th producers in region r

Z_r , j::

Output of j-th sector in region r

X_{r , i , j}::

Intermediate inputs of i-th goods in j-th sector in region r

V_{r , f , j}::

f-th primary factor inputs in j-th sector in region r

p_r , j::

Price of the j-th composite commodity

ω_r , f::

f-th factor price in region r

υ_r , j::

Share parameter in the CES production function

Industrial sectors are classified into basic, energy transformation, and power generation sectors.

6.1.1.1 Basic Sectors

For the basic production functions, activity output is determined by a fixed coefficient aggregation of non-energy and energy intermediate commodities and primary factors (Fig. 6.9). The composite of non-energy inputs is in Leontief form. Energy and the value-added bundle are nested by value-added and energy inputs. The value-added bundle is a CES function of primary factors. The composite of energy inputs is a CES aggregation of electricity and fossil fuels. Fossil fuels are further disaggregated into five types:

Fig. 6.9

Production tree of basic sectors

There are four levels in the above production tree. At each level a virtual firm is assumed, each of which aims to maximize the corresponding profit subject to the production technology.

At the top level, output is a Leontief function of the quantities of value-added and aggregate energy input and aggregate intermediate input, associated with process GHG emissions:

$$ \max\ {\pi}_{r, j}^z={p}_{r, j}^z\bullet {Z}_{r, j}-\left({p}_{r, j}^{vae}\bullet {QVAE}_{r, j}+{p}_{r, j}^{inta}\bullet {QINTA}_{r, j}+{p}_r^{ghg}\bullet {QGHG}_{r, j, act, ghg}\right) $$

(6.7)

subject to

$$ {Q}_{r, j}=\mathit{\min}\left(\frac{{ Q VAE}_{r, j}}{qvae_{r, j}},\frac{{ Q INTA}_{r, j}}{qinta_{r, j}},\frac{{ Q GHG}_{r, j, act, ghg}}{qghg_{r, j, act, ghg}}\right) $$

(6.8)

where

${\pi}_{r, j}^z$::

Profit of the j-th firm producing gross domestic output z_r , j at the top level

Z_r , j::

Gross domestic output of the j-th firm

Q_r , j::

Output in sector j of region r

QVAE_r , j::

Value-added and energy composite input

QINTA_r , j::

Composite intermediate input

QGHG_{r , j , act , ghg}::

Process emissions of GHGs per unit of output

${p}_{r, j}^z$::

Price of j-th gross domestic output

${p}_{r, j}^{vae}$::

Price of composite goods of factor and energy

${p}_{r, j}^{inta}$::

Price of composite intermediate goods

${p}_r^{ghg}$::

GHG emission price

qvae_r , j::

Technical coefficient expressing the composite amounts of value-added and energy inputs required per unit of Q_r , j

qinta_r , j::

Technical coefficient expressing the composite amounts of non-energy intermediate inputs required per unit of Q_r , j

qghg_{r , j , act , ghg}::

Technical coefficient expressing the process GHG emissions per unit of Q_r , j

At the second level of the production tree, there are two virtual firms with profit-maximization problems. First, composite value-added and energy input is CES aggregation of value-added input and total energy input:

$$ \max {\ \pi}_{r, j}^{va e}={p}_{r, j}^{va e}\bullet {QVA E}_{r, j}-\left({p}_{r, j}^{va}\bullet {QVA}_{r, j}+{p}_{r, j}^{fe}\bullet {QFE}_{r, j}\right) $$

(6.9)

subject to

$$ {QVA E}_{r, j}={\alpha}_{r, j}^{vae}\bullet {\left({\delta}_{r, j}^{vae}\bullet {QVA}_{r, j}^{{-\rho}_{r, j}^{vae}}+\left(1-{\delta}_{r, j}^{vae}\right)\bullet {QFE}_{r, j}^{{-\rho}_{r, j}^{vae}}\right)}^{-\frac{1}{\rho_{r, j}^{vae}}} $$

(6.10)

Second, aggregate non-energy intermediate input is defined as Leontief function of disaggregated intermediate input:

$$ \max\ {\pi}_{r, j}^{i nta}={p}_{r, j}^{i nta}\bullet {QINT A}_{r, j}-\left(\sum_i{p}_{r, j}^q\bullet {QINT}_{r, i, j}\right) $$

(6.11)

subject to

$$ { QINT A}_{r, j}=\mathit{\min}\left(\frac{QINT_{r, i, j}}{qint_{r, i, j}}\right) $$

(6.12)

where

${\pi}_{r, j}^{vae}$::

Profit of j-th firm producing composite input of value added and energy

${\pi}_{r, j}^{inta}$::

Profit of j-th firm producing composite intermediate input

QVA_r , j::

Aggregate value-added input

QFE_r , j::

Aggregate energy input (electricity and fossil energy)

QINT_{r , i , j}::

i-th non-energy inputs in j-th firm

${p}_{r, j}^{va}$::

Price of composite value-added input

${p}_{r, j}^{fe}$::

Price of the composite energy input (including electricity and fossil fuel)

${p}_{r, j}^q$::

Price of the i-th composite goods

qint_{r , i , j}::

The amounts of each input required per unit of composite intermediate input

${\alpha}_{r, j}^{vae}$::

Shift (or efficiency) parameter in the CES function

${\delta}_{r, j}^{vae}$::

CES share parameter, $0\le {\delta}_{r, j}^{vae}\le 1,\ \sum_i{\delta}_{r, j}^{vae}=1$

${\rho}_{r, j}^{vae}$::

The CES substitution parameter, in which the elasticity of substitution between value added and energy, σ, equals $\frac{1}{1+\rho}$

${\sigma}_{r, j}^{vae}$::

Elasticity of substitution between value-added bundle and energy

At the third level of the production tree, there are two virtual firms with profit-maximization problems as well. First, composite value-added input is CES aggregation of capital and labor input:

$$ \max\ {\pi}_{r, j}^{va}={p}_{r, j}^{va}\bullet {QVA}_{r, j}-\left({ p l}_r\bullet {QLAB}_{r, j}+{ p k}_{r, j}\bullet {QCAP}_{r, j}\right) $$

(6.13)

subject to

$$ {QVA}_{r, j}={\alpha}_{r, j}^{va}\bullet {\left({\delta}_{r, j}^{cap}\bullet {QCAP}_{r, j}^{{-\rho}_{r, j}^{va}}+{\delta}_{r, j}^{lab}\bullet {QLAB}_{r, j}^{{-\rho}_{r, j}^{va}}\right)}^{-\frac{1}{\rho_{r, j}^{va}}} $$

(6.14)

Moreover, composite energy input is CES aggregation of electricity input and fossil fuel input:

$$ \max\ {\pi}_{r, j}^{fe}={p}_{r, j}^{fe}\bullet {QFE}_{r, j}-\left({p}_{r,{}^{``} ele"}^q\bullet {QELE}_{r, j}+{p}_{r, j}^{fos}\bullet {QFOS}_{r, j}\right) $$

(6.15)

subject to

$$ {QFE}_{r, j}={\alpha}_{r, j}^{fe}\bullet {\left({\delta}_{r, j}^{ele}\bullet {QELE}_{r, j}^{{-\rho}_{r, j}^{fe}}+\left(1-{\delta}_{r, j}^{ele}\right)\bullet {QFOS}_{r, j}^{{-\rho}_{r, j}^{fe}}\right)}^{-\frac{1}{\rho_{r, j}^{fe}}} $$

(6.16)

where

${\pi}_{r, j}^{va}$::

Profit of j-th firm producing composite input of value added

${\pi}_{r, j}^{fe}$::

Profit of j-th firm producing composite input of energy

QCAP_r , j::

Capital input required per unit of value-added input

QLAB_r , j::

Labor input required per unit of value-added input

QELE_r , j::

Electricity input required per unit of composite energy input

QFOS_r , j::

Composite fossil fuel input required per unit of composite energy input

pl _r ::

Labor price in region r

pk_r , j::

Capital price in j-th sector of region r

${p}_{r,`` ele"}^q$::

Price of the composite goods of electricity

${p}_{r, j}^{fos}$::

Price of composite fossil fuel input in j-th sector

${\alpha}_{r, j}^{fe}$::

Shift (or efficiency) parameter in the CES function

${\delta}_{r, j}^{fe},{\delta}_{r, j}^{cap},{\delta}_{r, j}^{lab}$::

CES share parameters, $0\le {\delta}_{r, j}^{\ast}\le 1,\ \sum_i{\delta}_{r, j}^{\ast }=1$

${\rho}_{r, j}^{fe}$::

CES substitution parameter, in which the elasticity of substitution between electricity and composite fossil fuel, σ, equals $\frac{1}{1+\rho}$

${\sigma}_{r, j}^{va}$::

Elasticity of substitution between capital and labor

${\sigma}_{r, j}^{vae}$::

Elasticity of substitution between electricity and fossil fuel

At the fourth level of the production function, composite fossil fuel is CES aggregation of coal, crude oil, natural gas, coke, petrol oil, and manufactured gas:

$$ \max\ {\pi}_{r, j}^{fos}={p}_{r, j}^{fos}\bullet {QFOS}_{r, j}-\left(\sum_{fos}{p}_{r, fos}^q\bullet {QFF}_{r, fos, j}\right) $$

(6.17)

subject to

$$ {QFOS}_{r, j}={\alpha}_{r, j}^{ff}\bullet {\left(\sum_{fos}{\delta}_{r, j}^{ff}\bullet {QFF}_{r, fos, j}^{{-\rho}_{r, j}^{ff}}\right)}^{-\frac{1}{\rho_{r, j}^{ff}}} $$

(6.18)

where

${\pi}_{r, j}^{fos}$::

Profit of j-th firm producing composite input of fossil fuel

QFF_{r , fos , j}::

CES shift (or efficiency) parameter

${p}_{r, fos}^q$::

Price of fossil fuel input

${\alpha}_{r, j}^{ff}$::

Shift (or efficiency) parameter in the CES function

${\delta}_{r, j}^{ff}$::

CES share parameter, $0\le {\delta}_{r, j}^{ff}\le 1,\ \sum_i{\delta}_{r, j}^{ff}=1$

${\rho}_{r, j}^{ff}$::

CES substitution parameter, in which the elasticity of substitution among fossil fuels, σ, equals $\frac{1}{1+\rho}$

${\sigma}_{r, j}^{ff}$::

Elasticity of substitution among fossil fuels

6.1.1.2 Energy Transformation Sector (Except Power Generation)

Energy transformation sectors include gas production and supply, petroleum and nuclear fuel processing, and coking. The energy bundle is linked at the top level in order to maintain the first law of thermal efficiency of the conversion of primary energy to the secondary energy (Fig. 6.10). Functions at other levels are the same as the basic sectors.

Fig. 6.10

Production tree of energy transformation sectors

Thus the problem is expressed in

$$ \begin{array}{ll} \max\ {\pi}_{r,j}^z=& {p}_{r,j}^z\bullet {Z}_{r,j}\hfill \\ {}& -\left({p}_{r,j}^{vae}\bullet {\mathit{\mathrm{QVAE}}}_{r,j}+{p}_{r,j}^{fe}\bullet {QFE}_{r,j}+{p}_{r,j}^{\mathit{\mathrm{inta}}}\bullet {\mathit{\mathrm{QINTA}}}_{r,j}+{p}_r^{ghg}\bullet {\mathit{\mathrm{QGHG}}}_{r,j, act, ghg}\right)\ \hfill \end{array} $$

(6.19)

subject to

$$ {Q}_{r, j}=\mathit{\min}\left(\frac{{ Q VAE}_{r, j}}{qvae_{r, j}},\frac{{ Q FE}_{r, j}}{qfe_{r, j}},\frac{{ Q INTA}_{r, j}}{qinta_{r, j}},\frac{{ Q GHG}_{r, j, act, ghg}}{qghg_{r, j, act, ghg}}\right) $$

(6.20)

where

QFE_r , j::

Aggregate energy input (electricity and fossil energy)

qfe_r , j::

Technical coefficient expressing the aggregate energy inputs required per unit of Q_r , j

6.1.1.3 Power Generation Sector

Electricity is generated by eight technologies, e.g., coal, gas, oil, nuclear, hydro, wind, solar PV, and biomass power. Disaggregation of the electricity sector into eight technologies in the base year follows the methodology developed by Sue Wing (2006, 2008). Production function of each technology is the same as that of energy transformation sectors. Each technology is perfectly substitutable with another. Electricity output is almost in a linear relationship with energy inputs (Fig. 6.11).

Fig. 6.11

Production tree of electricity generation sectors

6.1.1.4 Household Consumption

Household and government are the final consumers. The representative household endows primary factors to the firms and receives income from the rental of primary factors (labor and capital), rents from fixed factors (land and natural resources), and lump-sum transfer from the government (e.g., carbon tax revenue of the government). The income is then used for either investment or final consumption. The objective of household consumption is to maximize utility by choosing levels of goods consumption following Cobb-Douglas preferences, subject to commodity prices and budget constraint. The agent’s problem is expressed as

$$ \max\ {u}_{r, h}\left[{X}_{r,1}^p,\dots, {x}_{r, i}^p\right]={A}_r^p\bullet \prod_{i=1}^N{\left({X}_{r, i}^p\right)}^{\alpha_{r, i}^p} $$

(6.21)

subject to

$$ {EH}_r=\sum_i{p}_{r, j}^q\bullet {X}_{r, i}^p=\sum_{f=1}^F{\omega}_{r, f}\bullet {V}_{r, f}+\sum_j{p ld}_r\bullet {QLAND}_{r, j}+ \sum_{r es, j}{p}_{r, j}^{r es}\bullet {QRES}_{r, j}+{T}_r^{cab}-{T}_r^d-{S}_r^p $$

(6.22)

$$ {T}_r^{cab}={pghg}_{r,`` CO2"}\bullet {\mathrm{TEMS}}_{r,`` CO2"} $$

(6.23)

$$ {T}_r^d={\tau}_r^d\bullet \sum_f{\omega}_{r, f}\bullet {V}_{r, f} $$

(6.24)

$$ {S}_r^p={sr}_r^p\bullet \sum_f{\omega}_{r, f}\bullet {V}_{r, f} $$

(6.25)

where

u_r , h::

Utility function of households

EH _r ::

Household expenditure

${X}_{r, i}^p$::

Household consumption of i-th commodity

V_r , f::

f-th primary factor endowment by household

${S}_r^p$::

Household savings

TEMS_{r ,  “ CO2”}::

CO₂ emissions in region r

pghg_{r ,  “ CO2”}::

Carbon price

${T}_r^d$::

Direct tax

${\tau}_r^d$::

Direct tax rate

${sr}_r^p$::

Average propensity to save by the household

ω_r , f::

Price of the f-th primary factor

${A}_r^p$::

Scaling parameter in Cobb-Douglas function

${\alpha}_{r, i}^p$::

Share parameter in Cobb-Douglas function, $0\le {\alpha}_{r, i}^p\le 1,\ \sum_i{\alpha}_{r, i}^p=1$

6.1.2 Government

The government is assumed to collect taxes, including a direct tax on household income, ad valorem production tax (indirect tax) on gross domestic output, ad valorem import tariff on imports, and carbon tax. Based on a Cobb-Douglas demand function (Hertel and Tsigas 2004), the government spends its revenue on public services which are provided to the whole society and on the goods and services which are provided to the households free of charge or at low prices (NBS 2006). The model assumes that the revenue from the carbon tax is recycled to the representative agent as a lump-sum transfer:

$$ \max\ {u}_{r, g}\left[{x}_{r,1}^g,\dots, {x}_{r, i}^g\right]={A}_r^g\bullet \prod_{i=1}^N{\left({x}_{r, i}^g\right)}^{\alpha_{r, i}^g} $$

(6.26)

subject to

$$ \sum_i{p}_{r, i}\bullet {x}_{r, i}^g={T}_r^d+\sum_j{T}_{r, j}^z+\sum_j{T}_{r, j}^m-{S}^g $$

(6.27)

$$ {T}_{r, j}^z={\tau}_{r, j}^z\bullet {p}_{r, j}\bullet {Z}_{r, j} $$

(6.28)

$$ {T}_{r, i}^m={\tau}_{r, i}^m\bullet {pm}_{r, i}\bullet {M}_{r, i} $$

(6.29)

$$ {S}_r^g={sr}_r^g\bullet \left({T}_r^d+\sum_j{T}_{r, j}^z+\sum_j{T}_{r, j}^m\right) $$

(6.30)

where

u_r , g::

Utility function of government

${x}_{r, i}^g$::

Government consumption of i-th commodity

${S}_r^g$::

Government savings

${T}_{r, j}^z$::

Production tax on the j-th commodity

${T}_{r, j}^m$::

Import tariff on the j-th commodity

${\tau}_{r, j}^z$::

Production tax rate on the j-th commodity

${\tau}_{r, i}^m$::

Import tariff rate on the i-th commodity

${sr}_r^g$::

Average propensity to save by the government

Z_r , j::

Gross domestic output of the j-th commodity

M_r , i::

Import of the i-th commodity

pm_r , i::

Price of the i-th imported commodity

${A}_r^g$::

Scaling parameter in Cobb-Douglas function

${\alpha}_{r, i}^g$::

Share parameter in Cobb-Douglas function, $0\le {\alpha}_{r, i}^g\le 1,\ \sum_i{\alpha}_{r, i}^g=1$

6.1.3 Investment and Savings

Investment is an important part of the final demand. In the CGE model, a virtual agent is assumed for investment which receives all the savings from the household, the government, and the external sector to purchase goods for domestic investment. The virtual investment agent is assumed to maximize the utility based on a Cobb-Douglas demand function subject to its (virtual) income constraint. Mathematically, the investment problems can be described as follows:

$$ \max\ {u}_{r, v}\left[{x}_{r,1}^v,\dots, {x}_{r, i}^v\right]={A}_r^v\bullet \prod_{i=1}^N{\left({x}_{r, i}^v\right)}^{\alpha_{r, i}^v} $$

(6.31)

subject to

$$ \sum_i{p}_{r, i}\bullet {x}_{r, i}^v={S}_r^p+{S}_r^g+\varepsilon \bullet {S}_r^f $$

(6.32)

where

u_r , v::

Utility of virtual investment agent

${S}_r^f$::

Current account deficits in foreign currency terms (or alternatively foreign savings)

ε::

Foreign exchange rate

${x}_{r,1}^v$::

Demand for the i-th investment goods

${A}_r^v$::

Scaling parameter in Cobb-Douglas function,

${\alpha}_{r, i}^v$::

Share parameter in Cobb-Douglas function, $0\le {\alpha}_{r, i}^v\le 1,\ \sum_i{\alpha}_{r, i}^v=1$

6.1.4 International Transaction

The model is an open economy model that includes the interaction of commodity trade with the rest of the world. Like most other countries’ CGE models, this model assumes the small open economy, meaning that an economy is small enough for its policies not to alter world prices or incomes. The implicit implication of small-country assumption is that export and import prices are exogenously given for the economy. In this study, future international prices are fixed to be the same level for non-energy commodities but increase by 3% yearly for energy commodities compared to the 2005 level.

Two types of price variables are distinguished. One is prices in terms of the domestic currency ${p}_i^e$ and ${p}_i^m$; the other is prices in terms of the foreign currency ${p}_i^{We}$ and ${p}_i^{Wm}$. They are linked with each other as follows:

$$ {p}_i^e=\varepsilon \bullet {p}_i^{We} $$

(6.33)

$$ {p}_i^m=\varepsilon \bullet {p}_i^{Wm} $$

(6.34)

Furthermore, it is assumed that the economy faces balance of payments constraints, which is described with export and import prices in foreign currency terms:

$$ \sum_i{p}_i^{We}\bullet {E}_{r, i}+{S}_r^f=\sum_i{p}_i^{Wm}\bullet {M}_i $$

(6.35)

where

E_r , i::

Export of i-th commodity in region r

M_r , i::

Import of i-th commodity in region r

${p}_i^{We}$::

Export price in terms of foreign currency,

${p}_i^e$::

Export price in terms of domestic currency

${p}_i^{Wm}$::

Import price in terms of foreign currency,

${p}_i^m$::

Import price in terms of domestic currency

6.1.4.1 Substitution Between Imports and Domestic Goods

The Armington assumption is adopted, i.e., the domestic and imported goods are imperfectly substitutable for each other, which implies that households and firms don’t directly consume or use imported goods but instead a so-called Armington composite goods, which is made up of imported and locally produced goods as well as goods produced in other provinces by a two-level nested CES function (Fig. 6.12).

Fig. 6.12

Nesting of imported goods, locally produced goods, and goods produced in other provinces

Import activity is described by the bottom nesting of Fig. 6.12. In the CGE model, the Armington composite goods at this level are created by virtual firms which maximize their profits by choosing a proper combination of imported and locally produced goods. The solution of their profit-maximization problem leads to their input demands for imported and domestic goods, which depend on the corresponding relative prices of domestic and imported goods. Mathematically, this problem can be expressed as

$$ \mathrm{Max}\ {\pi}_{r, i}^{m d}={p}_{r, i}^{m d}\bullet {Q}_{r, i}^{m d}-\left[\left(1+{\tau}_{r, i}^m\right)\bullet {p}_i^m\bullet {M}_{r, i}+{p}_{r, i}^d\bullet {D}_{r, i}^d\right] $$

(6.36)

subject to

$$ {Q}_{r, i}^{m d}={\alpha}_{r, i}^{m d}\bullet {\left({\delta}_{r, i}^m\bullet {M}_{r, i}^{{-\rho}_{r, i}^{m d}}+{\delta}_{r, j}^d\bullet {D}_{r, i}^{{-\rho}_{r, i}^{m d}}\right)}^{-\frac{1}{\rho_{r, i}^{m d}}} $$

(6.37)

where

${\pi}_{r, i}^{md}$::

Profit of the firm producing the i-th Armington composite goods of import and locally produced goods

${Q}_{r, i}^{md}$::

The i-th Armington composite goods of import and locally produced goods

${D}_{r, i}^d$::

The i-th locally produced goods

${p}_{r, i}^{md}$::

Armington price of the i-th imported and locally produced goods

${p}_{r, i}^d$::

Price of the i-th locally produced goods

${\tau}_{r, i}^m$::

Import tariff rate on the i-th commodity

${\alpha}_{r, i}^{md}$::

Shift (or efficiency) parameter in the Armington composite goods production function

${\delta}_{r, i}^m$, ${\delta}_{r, j}^d$::

Input share parameters in the Armington composite goods production function (${0\le \delta}_{r, i}^m\le 1$, $0\le {\delta}_{r, j}^d\le 1$, ${\delta}_{r, i}^m+{\delta}_{r, i}^d=1$)

${\rho}_{r, i}^{md}$::

The CES substitution parameter, in which the elasticity of substitution between imported and domestic goods, σ, equals $\frac{1}{1+\rho}$

Then the composite imported and locally produced goods will be further aggregated with the goods produced in other provinces to form the final Armington composite goods that are consumed by households and the government and as intermediate inputs by firms, which will be introduced in section F.

6.1.4.2 Transformation Between Exports and Domestic Goods

On the supply side, the produced commodities are distributed to the international market, local market, and market in other provinces by a two-level nested constant elasticity of transformation function. Similar to the treatment of import, a virtual firm is assumed for each commodity which transforms the gross domestic output into exports and domestic goods as follows:

$$ \mathrm{Max}\ {\pi}_{r, i}^{dx}=\left({p}_i^e\bullet {E}_{r, i}+{p}_{r, i}^{dd}\bullet {D}_{r, i}^s\right)-\left(1+{\tau}_{r, i}^z\right)\bullet {p}_{r, i}^z\bullet {Q}_{r, i}^{dx} $$

(6.38)

subject to

$$ {Q}_{r, i}^{d x}={\alpha}_{r, i}^{d x}\bullet {\left({\delta}_{r, i}^e\bullet {E}_{r, i}^{\rho_{r, i}^{d x}}+{\delta}_{r, j}^d\bullet {D_{r, i}^s}^{\rho_{r, i}^{d x}}\right)}^{\frac{1}{\rho_{r, i}^{d x}}} $$

(6.39)

where

${\pi}_{r, i}^{dx}$::

Profit of the firm engaged in the i-th transformation

${Q}_{r, i}^{dx}$::

Gross domestic output of the i-th goods

${D}_{r, i}^s$::

i-th goods supplied to domestic market

${p}_{r, i}^z$::

Price of the i-th gross domestic output

${p}_{r, i}^{dd}$::

Price of domestically supplied goods

${\tau}_{r, i}^z$::

Production tax rate on the i-th commodity

${\alpha}_{r, i}^{dx}$::

Shift (or efficiency) parameter in the transformation function

${\delta}_{r, i}^e$, ${\delta}_{r, j}^d$::

Share parameters in the transformation function (${0\le \delta}_{r, i}^e\le 1$, $0\le {\delta}_{r, j}^d\le 1$, ${\delta}_{r, i}^e+{\delta}_{r, i}^d=1$)

${\rho}_{r, i}^{dx}$::

Transformation elasticity parameter, in which the elasticity of substitution between imported and domestic goods, σ, equals $\frac{1}{\rho -1}$

It should be noted that the goods supplied to the domestic market at this level, ${D}_{r, i}^s$, will be further distributed to local market and market in other provinces through interprovincial trade, which will be described in the next section.

6.1.5 Interprovincial Trade

An important feature of this model is that it is a country model in which interprovincial trade is treated. Similar to the case of international trade, Armington assumption is adopted to distinguish between locally produced commodity and commodity produced by firms in other provinces, and CES and CET functions are employed to describe commodity inflow from and outflow to all provinces, respectively.

6.1.5.1 Substitution Commodity Between Local Market and Inflow from Other Provinces

This section describes the top-level nesting of Fig. 6.12 which treats interprovincial inflow of commodity. By this stage the commodity in the local market is an aggregation of locally produced and imported goods, which needs to be further aggregated with goods produced in other provinces to form the final Armington composite goods to be consumed by the final consumers and firms. The treatment is similar to import:

$$ \mathrm{Max}\ {\pi}_{r, i}^{dd}={p}_{r, i}^a\bullet {Q}_{r, i}^{dd}-\left[{p}_{r, i}^{md}\bullet {Q}_{r, i}^{md}+\sum_{r r}{p}_{r r, i}^{inf}\bullet {D}_{r r, r, i}^{inf}\right] $$

(6.40)

subject to

$$ {Q}_{r,i}^{dd}={\alpha}_{r,i}^{dd}\bullet {\left({\delta}_{r,i}^{md}\bullet {Q_{r,i}^{md}}^{{-\rho}_{r,i}^{dd}}+\sum_{rr}{\delta}_{rr,r,i}^{inf}\bullet {D_{rr,r,i}^{inf}}^{{-\rho}_{r,i}^{dd}}\right)}^{-\frac{1}{\rho_{r,i}^{dd}}} $$

(6.41)

where

${\pi}_{r, i}^{dd}$::

Profit of the firm producing the i-th Armington composite goods of local market and inflow from other provinces

${Q}_{r, i}^{dd}$::

Armington composite goods

${D}_{rr, r, i}^{inf}$::

The i-th goods inflowing from region rr to region r

${p}_{r, i}^a$::

Armington price taken by the final consumers and firms

${p}_{rr, i}^{inf}$::

Price of the i-th goods inflowing from province rr to region r

${\alpha}_{r, i}^{dd}$::

Shift (or efficiency) parameter in the Armington composite goods production function

${\delta}_{r, i}^{md}$, ${\delta}_{rr, r, j}^{inf}$::

Input share parameters in the Armington composite goods production function (${0\le \delta}_{r, i}^{md}\le 1$, $0\le {\delta}_{rr, r, j}^{inf}\le 1$, ${\delta}_{r, i}^{md}+\sum_{r r}{\delta}_{r r, r, i}^{inf}=1$)

${\rho}_{r, i}^{dd}$::

The CES substitution parameter, in which the elasticity of substitution between imported and domestic goods, σ, equals $\frac{1}{1+\rho}$

6.1.5.2 Transformation Between Goods Sold in Local Market and Outflowing to Other Provinces

Goods supplied to the domestic market, ${D}_{r, i}^s$, will be further distributed to local market and market in other provinces through, similar to the treatment of export, a CET function as follows:

$$ \mathrm{Max}\ {\pi}_{r, i}^{p p}=\left({p}_i^d\bullet {D}_{r, i}^{local}+\sum_{r r}{p}_{r r, i}^{out}\bullet {D}_{r, rr, i}^{out}\right)-{p}_{r, i}^{d d}\bullet {D}_{r, i}^s $$

(6.42)

subject to

$$ {\mathrm{Q}}_{\mathrm{r},\mathrm{i}}^{\mathrm{pp}}={\upalpha}_{\mathrm{r},\mathrm{i}}^{\mathrm{pp}}\bullet {\left({\updelta}_{\mathrm{r},\mathrm{i}}^{\mathrm{local}}\bullet {D_{r,i}^{\mathit{\mathrm{local}}}}^{\rho_{r,i}^{pp}}+\sum_{rr}{\updelta}_{\mathrm{r},\mathrm{rr},\mathrm{i}}^{\mathrm{out}}\bullet {{\mathrm{D}}_{\mathrm{r},\mathrm{rr},\mathrm{i}}^{\mathrm{out}}}^{\uprho_{\mathrm{r},\mathrm{i}}^{\mathrm{pp}}}\right)}^{\frac{1}{\uprho_{\mathrm{r},\mathrm{i}}^{\mathrm{pp}}}} $$

(6.43)

where

${\pi}_{r, i}^{pp}$::

Profit of the firm engaged in the i-th transformation

${Q}_{r, i}^{pp}$::

Out of the i-th goods supplied to local and other provinces’ markets

${D}_{r, i}^{local}$::

i-th goods supplied to local market

${D}_{r, rr, i}^{out}$::

i-th goods outflowing from region r to other province rr

${p}_{rr, i}^{out}$::

Price of the i-th goods outflowing to other province rr

${\alpha}_{r, i}^{pp}$::

Shift (or efficiency) parameter in the transformation function

${\delta}_{r, i}^{local}$, ${\delta}_{r, rr, i}^{out}$::

Share parameters in the transformation function (${0\le \delta}_{r, i}^{local}\le 1$, $0\le {\delta}_{r, rr, j}^{out}\le 1$, ${\delta}_{r, i}^{local}+\sum_{r r}{\delta}_{r, rr, i}^{out}=1$)

${\rho}_{r, i}^{pp}$::

Transformation elasticity parameter, in which the elasticity of substitution between imported and domestic goods, σ, equals $\frac{1}{\rho -1}$

6.1.6 Market Clearance Conditions

The above sections describe the behavior of economic agents such as the households, firms, government, and investment agents and the interactions with other provinces and the rest of the world. The final step is to impose the market-clearing conditions to all commodities and factor markets as follows:

$$ {Q}_{r, i}={x}_{r, i}^p+{x}_{r, i}^g+{x}_{r, i}^v+\sum_j{x}_{r, i, j} $$

(6.44)

$$ \sum_j{v}_{r, f, j}={V}_{r, f} $$

(6.45)

6.1.7 Macro Closure

In a CGE model, the issue of macro closure is the choice of exogenous variables among all variables in the model, mainly including investment and saving macro closure and current account balance macro closure. In this model, investment is exogenously assumed. In addition, foreign exchange rate is fixed and thus balance of payment is an endogenous variable.

Appendix 2: The Decomposition Method

The appendix describes how carbon reduction can be attributed to each countermeasure in section 4.3.1 by decomposition techniques. As shown in Eq. 6.46, the total carbon emission (EM) is the summation of emissions from power generation (EM_ele) and end-use sectors (EM_end) minus emissions captured by CCS technology (EM_ccs). EM_end and EM_ele can be further broken down into subcomponents. In Eq. 6.47, EM_end is a product of the underlying factors of activity levels (GDP), industry structure (STR = VA_i/GDP), end-use energy efficiency (EFF = E_i/VA_i), and fuel-switch factor (FS = EM_i/E_i). Similarly, in Eq. 6.48, emission from power generation (EM_ele) is a product of the underlying factors of total electricity demand (ELE_tot), non-fossil-fired electricity (NF = ELE_fos/ELE_tot), and power generation efficiency (EFF = EM_ele/ELE_fos):

$$ \mathrm{EM}={\mathrm{EM}}_{\mathrm{end}}+{\mathrm{EM}}_{\mathrm{ele}}\hbox{--} {\mathrm{EM}}_{\mathrm{ccs}} $$

(6.46)

$$ {\mathrm{E}\mathrm{M}}_{\mathrm{end}}={\Sigma}_{\mathrm{i}}\left(\mathrm{GDP}\ast {\mathrm{VA}}_{\mathrm{i}}/\mathrm{GDP}\ast {\mathrm{E}}_{\mathrm{i}}/{\mathrm{VA}}_{\mathrm{i}}\ast {\mathrm{E}\mathrm{M}}_{\mathrm{i}}/{\mathrm{E}}_{\mathrm{i}}\right)=\mathrm{ACT}\ast \mathrm{STR}\ast \mathrm{EFF}\ast \mathrm{FS} $$

(6.47)

$$ {\mathrm{EM}}_{\mathrm{ele}}={\mathrm{ELE}}_{\mathrm{tot}}\ast {\mathrm{ELE}}_{\mathrm{fos}}/{\mathrm{ELE}}_{\mathrm{tot}}\ast {\mathrm{EM}}_{\mathrm{ele}}/{\mathrm{ELE}}_{\mathrm{fos}}=\mathrm{EL}\ast \mathrm{NF}\ast \mathrm{EFF} $$

(6.48)

where

EM::

Total emission

EM_end::

Emission from end-use sectors

EM_ele::

Emission from power generation

EM_ccs::

Emission captured by CCS technology

VA_i::

Value added of sector i

E_i::

Energy consumption of sector i

EM_i::

Emission from sector i

ELE_tot::

Total electricity demand

ELE_fos::

Fossil-fired electricity production

ACT::

Activity level effect

STR::

Industry structure effect

EFF::

Energy efficiency effect

FS::

Fuel-switching effect

EL::

Total electricity demand effect

NF::

Non-fossil power effect

A change in emissions from the reference to countermeasure scenarios, △EM, can be expressed as a change in emission from end-use sectors, power generation, CCS absorption, and emissions trade (Eq. 6.49). Using the Laspeyres index method (Sun and Ang 2000), a change in emissions from end-use sectors and power generation can be expressed as the joint contribution of the underlying effects indicated by _f in Eqs. 6.50 and 6.51, in which each effect can be derived from multiplication, as shown for total electricity demand in Eq. 6.52. The first part of Eq. 6.52, △ELE_tot*NF*EFF, can be interpreted as the partial effect of the total electricity demand component on the change of CO₂ emissions between the reference and mitigation scenarios. The following parts capture interactions between the remaining variables and form the so-called residual term:

$$ \triangle \mathrm{EM}=\triangle {\mathrm{EM}}_{\mathrm{end}}+\triangle {\mathrm{EM}}_{\mathrm{ele}}-\triangle {\mathrm{EM}}_{\mathrm{ccs}} $$

(6.49)

$$ \triangle {\mathrm{EM}}_{\mathrm{end}}={\mathrm{ACT}}_{\mathrm{f}}+{\mathrm{STR}}_{\mathrm{f}}+{\mathrm{EFF}}_{\mathrm{f}}+{\mathrm{FS}}_{\mathrm{f}} $$

(6.50)

$$ \triangle {\mathrm{EM}}_{\mathrm{ele}}={\mathrm{EL}}_{\mathrm{f}}+{\mathrm{NF}}_{\mathrm{f}}+{\mathrm{EFF}}_{\mathrm{f}} $$

(6.51)

$$ {\mathrm{EL}}_{\mathrm{f}}=\triangle {\mathrm{EL}\mathrm{E}}_{\mathrm{tot}}\ast \mathrm{NF}\ast \mathrm{EFF}+1/2\ast {\mathrm{EL}\mathrm{E}}_{\mathrm{tot}}\ast \left(\triangle \mathrm{NF}\ast \mathrm{EFF}+\mathrm{NF}\ast \triangle \mathrm{EFF}\right)+1/3\ast \left(\triangle \mathrm{NF}\ast \triangle \mathrm{EFF}\right) $$

(6.52)