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Cap and Trade Versus Carbon Tax: An Analysis Based on a CGE Model

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Abstract

Cost-effectiveness comparisons between two typical pricing policies, i.e., cap and trade and carbon tax, are rare in the literature and are tackled in this study. We define various carbon shadow prices at different administrative levels. By using a computable general equilibrium model, the cost-effectiveness of various policies is compared in terms of the estimation of carbon shadow prices. The results show that an energy cap-and-trade policy yields a close GDP-based carbon shadow price but a lower GSPV-based (gross-social-production-value-based) carbon shadow price than a proportional energy reduction policy does. Compared to a cap-and-trade policy, a carbon tax policy yields a much lower GDP-based carbon shadow price but a higher GSPV-based price. Improving the stringency of either a cap-and-trade policy or a carbon tax policy has limit impact on the industrial structure of the whole economy despite the impact on both the GDP and the GSPV are different between these two policies. The comparison of the two carbon pricing policies mainly implies that a carbon tax is more cost-effective than cap-and-trade for a carbon- and trade-intensive economy, but cap-and-trade has lower sector-level impacts than carbon tax especially when the cap restriction is loose.

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Acknowledgements

This work was funded by the Science and Technology Project of Guangdong Province (2019A101002085). Thanks are also given to the reviewers for their valuable comments.

Author information

Authors and Affiliations

  1. School of Environmental Science and Engineering, Sun Yat-Sen University, No. 135, Xingang Xi Road, Guangzhou, 510275, People’s Republic of China

    Jin-Feng Zhou

  2. School of Public Administration, Hainan University, No. 58, Renmin Avenue, Haikou, 570228, People’s Republic of China

    Dan Wu

  3. Zhongke Environment Limited Company, Guangzhou, People’s Republic of China

    Wei Chen

Authors
  1. Jin-Feng Zhou
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  2. Dan Wu
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  3. Wei Chen
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Contributions

Jin-Feng Zhou, Dan Wu, and Wei Chen conceived and designed the methodologies, Jin-Feng Zhou wrote the program code and manuscript draft, Dan Wu revised the draft, and Wei Chen collected and analyzed the data.

Corresponding author

Correspondence to Dan Wu.

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Appendices

Appendix 1

See Tables 6, 7, 8, 9, and 10.

Table 6 Departments and codes
Full size table
Table 7 End use of energy consumption in 7 sectors (104t tce)
Full size table
Table 8 Guangdong social accounting matrix for 2017 (108 Yuan)
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Table 9 Elastic coefficients in the model
Full size table
Table 10 Balance check for the base year
Full size table

Appendix 2

2.1 Equations

$$ \begin{gathered} {\text{QA}}\left( a \right) = e = {\text{scaleAa}}\left( a \right)*({\text{deltaAa}}\left( a \right)*{\text{QEVA}}\left( a \right)**{\text{rh}}0{\text{Aa}}\left( a \right) + \left( {1 - {\text{deltaAa}}\left( a \right)} \right) \hfill \\ *{\text{QINTA}}\left( a \right)**{\text{rh}}0{\text{Aa}}\left( a \right))**\left( {1/{\text{rh}}0{\text{Aa}}\left( a \right)} \right) \hfill \\ \end{gathered} $$
(20)
$$ \begin{gathered} {\text{PEVA}}\left( a \right)/{\text{PINTA}}\left( a \right) = e = \left( {{\text{deltaAa}}\left( a \right)/\left( {1 - {\text{deltaAa}}\left( a \right)} \right)} \right) \hfill \\ *\left( {{\text{QINTA}}\left( a \right)/{\text{QEVA}}\left( a \right)} \right)**\left( {1 - {\text{rh}}0{\text{Aa}}\left( a \right)} \right) \hfill \\ \end{gathered} $$
(21)
$$ {\text{PA}}\left( a \right)*{\text{QA}}\left( a \right) = e = {\text{PEVA}}\left( a \right)*{\text{QEVA}}\left( a \right) + {\text{PINTA}}\left( a \right)*{\text{QINTA}}\left( a \right) $$
(22)
$$ \begin{gathered} {\text{QEVA}}\left( a \right) = e = {\text{scaleEVA}}\left( a \right)*({\text{deltaEVA}}\left( a \right)*{\text{QVA}}\left( a \right)**{\text{rh}}0{\text{EVA}}\left( a \right) + \left( {1 - {\text{deltaEVA}}\left( a \right)} \right) \hfill \\ *{\text{QED}}\left( a \right)**{\text{rh}}0{\text{EVA}}\left( a \right))**\left( {1/{\text{rh}}0{\text{EVA}}\left( a \right)} \right) \hfill \\ \end{gathered} $$
(23)
$$ \begin{gathered} {\text{PVA}}\left( a \right)/\left( {\left( {1 + {\text{tvc}}\left( a \right)} \right)*{\text{WE}}} \right) = e = \left( {{\text{deltaEVA}}\left( a \right)/\left( {1 - {\text{deltaEVA}}\left( a \right)} \right)} \right) \hfill \\ *\left( {{\text{QED}}\left( a \right)/{\text{QVA}}\left( a \right)} \right)**\left( {1 - {\text{rh}}0{\text{EVA}}\left( a \right)} \right) \hfill \\ \end{gathered} $$
(24)
$$ {\text{PEVA}}\left( a \right)*{\text{QEVA}}\left( a \right) = e = {\text{PVA}}\left( a \right)*{\text{QVA}}\left( a \right) + \left( {\left( {1 + {\text{tvc}}\left( a \right)} \right)*{\text{WE}}} \right)*{\text{QED}}\left( a \right) $$
(25)
$$ \begin{gathered} {\text{QVA}}\left( a \right) = e = {\text{scaleVA}}\left( a \right)*({\text{deltaVA}}\left( a \right)*{\text{QLD}}\left( a \right)**{\text{rh}}0{\text{VA}}\left( a \right) + \left( {1 - {\text{deltaVA}}\left( a \right)} \right) \hfill \\ *{\text{QKD}}\left( a \right)**{\text{rh}}0{\text{VA}}\left( a \right))**\left( {{\text{1/rh0VA}}\left( {\text{a}} \right)} \right) \hfill \\ \end{gathered} $$
(26)
$$ {\text{WL}}/{\text{WK}} = e = \left( {{\text{deltaVA}}\left( a \right)/\left( {1 - {\text{deltaVA}}\left( a \right)} \right)} \right)*\left( {{\text{QKD}}\left( a \right)/{\text{QLD}}\left( a \right)} \right)**\left( {1 - {\text{rh}}0{\text{VA}}\left( a \right)} \right) $$
(27)
$$ {\text{PVA}}\left( a \right)*{\text{QVA}}\left( a \right) = e = {\text{WL}}*{\text{QLD}}\left( a \right) + {\text{WK}}*{\text{QKD}}\left( a \right) + {\text{tva}}\left( a \right)*{\text{PVA}}\left( a \right)*{\text{QVA}}\left( a \right) $$
(28)
$$ {\text{QINT}}(c1,a) = e = ic1a(c1,a)*{\text{QINTA}}\left( a \right) $$
(29)
$$ {\text{PINTA}}\left( a \right) = e = {\text{sum}}(c1,ic1a(c1,a)*{\text{PQ}}\left( {c1} \right))$$
(30)
$$ {\text{QINT}}(c2,a) = e = ic2a(c2,a)*{\text{QED}}\left( a \right) $$
(31)
$$ \begin{gathered} {\text{QA}}\left( a \right) = e = {\text{scaleCET}}\left( a \right)*({\text{deltaCET}}\left( a \right)*{\text{QDA}}\left( a \right)**{\text{rh}}0{\text{CET}}\left( a \right) + \left( {1 - {\text{deltaCET}}\left( a \right)} \right) \hfill \\ *{\text{QE}}\left( a \right)**{\text{rh}}0{\text{CET}}\left( a \right))**\left( {1/{\text{rh}}0{\text{CET}}\left( a \right)} \right) \hfill \\ \end{gathered} $$
(32)
$$ {\text{PDA}}\left( a \right)/{\text{PE}}\left( a \right) = e = \left( {{\text{deltaCET}}\left( a \right)/\left( {1 - {\text{deltaCET}}\left( a \right)} \right)} \right)*({\text{QE}}\left( a \right)/{\text{QDA}}\left( a \right))**\left( {1 - {\text{rh}}0{\text{CET}}\left( a \right)} \right) $$
(33)
$$ {\text{PA}}\left( a \right)*{\text{QA}}\left( a \right) = e = {\text{PDA}}\left( a \right)*{\text{QDA}}\left( a \right) + {\text{PE}}\left( a \right)*{\text{QE}}\left( a \right) $$
(34)
$$ {\text{QDA}}\left( a \right) = e = {\text{scaleQDA}}\left( a \right)*\left( \begin{gathered} {\text{deltaQDA}}\left( a \right)*{\text{QDAL}}\left( a \right)**{\text{rh}}0{\text{QDA}}\left( a \right) \, \hfill \\ + \left( {1 - {\text{deltaQDA}}\left( a \right)} \right)*{\text{QDAP}}\left( a \right)**{\text{rh}}0{\text{QDA}}\left( a \right) \hfill \\ \end{gathered} \right)**\left( {1/{\text{rh}}0{\text{QDA}}\left( a \right)} \right) $$
(35)
$$ \begin{gathered} {\text{PDAL}}\left( a \right)/{\text{PDAP}}\left( a \right) = e = \left( {{\text{deltaQDA}}\left( a \right)/\left( {1 - {\text{deltaQDA}}\left( a \right)} \right)} \right) \hfill \\ * \, \left( {{\text{QDAP}}\left( a \right)/{\text{QDAL}}\left( a \right)} \right)**\left( {1 - {\text{rh}}0{\text{QDA}}\left( a \right)} \right) \hfill \\ \end{gathered} $$
(36)
$$ {\text{PDA}}\left( a \right)*{\text{QDA}}\left( a \right) = e = {\text{PDAL}}\left( a \right)*{\text{QDAL}}\left( a \right) + {\text{PDAP}}\left( a \right)*{\text{QDAP}}\left( a \right)$$
(37)
$$ \begin{gathered} {\text{QQ}}\left( c \right) = e = {\text{scaleQq}}\left( c \right)*({\text{deltaQq}}\left( c \right)*{\text{QDC}}\left( c \right)**{\text{rh}}0{\text{Qq}}\left( c \right) \hfill \\ + \left( {1 - {\text{deltaQq}}\left( c \right)} \right)*{\text{QM}}\left( c \right)**{\text{rh}}0{\text{Qq}}\left( c \right))**\left( {1/{\text{rh}}0{\text{Qq}}\left( c \right)} \right) \hfill \\ \end{gathered} $$
(38)
$$ {\text{PDC}}\left( c \right)/{\text{PM}}\left( c \right) = e = \left( {{\text{deltaQq}}\left( c \right)/\left( {1 - {\text{deltaQq}}\left( c \right)} \right)} \right)*({\text{QM}}\left( c \right)/{\text{QDC}}\left( c \right))**\left( {1 - {\text{rh}}0{\text{Qq}}\left( c \right)} \right) $$
(39)
$$ {\text{PQ}}\left( c \right)*{\text{QQ}}\left( c \right) = e = {\text{PDC}}\left( c \right)*{\text{QDC}}\left( c \right) + {\text{PM}}\left( c \right)*{\text{QM}}\left( c \right) $$
(40)
$$ \begin{gathered} {\text{QDC}}\left( c \right) = e = {\text{scaleQDC}}\left( c \right)*({\text{deltaQDC}}\left( c \right)*{\text{QDCL}}\left( c \right)**{\text{rh}}0{\text{QDC}}\left( c \right) \hfill \\ + \left( {1 - {\text{deltaQDC}}\left( c \right)} \right)*{\text{QDCP}}\left( c \right)**{\text{rh}}0{\text{QDC}}\left( c \right))**\left( {1/{\text{rh}}0{\text{QDC}}\left( c \right)} \right) \hfill \\ \end{gathered} $$
(41)
$$ \begin{gathered} {\text{PDCL}}\left( c \right)/{\text{PDCP}}\left( c \right) = e = \left( {{\text{deltaQDC}}\left( c \right)/\left( {1 - {\text{deltaQDC}}\left( c \right)} \right)} \right) \hfill \\ *\left( {{\text{QDCP}}\left( c \right)/{\text{QDCL}}\left( c \right)} \right)**\left( {1 - {\text{rh}}0{\text{QDC}}\left( c \right)} \right) \hfill \\ \end{gathered} $$
(42)
$$ {\text{PDC}}\left( c \right)*{\text{QDC}}\left( c \right) = e = {\text{PDCL}}\left( c \right)*{\text{QDCL}}\left( c \right) + {\text{PDCP}}\left( c \right)*{\text{QDCP}}\left( c \right)$$
(43)
$$ {\text{YH}} = e = {\text{WL}}*{\text{QLS}} + {\text{shifhk}}*{\text{WK}}*{\text{QKS}} + {\text{transfrhg}}0 $$
(44)
$$ {\text{PQ}}\left( c \right)*{\text{QH}}\left( c \right) = e = {\text{PQ}}\left( c \right)*{\text{shrh}}\left( c \right)*{\text{mpc}}*\left( {1 - {\text{tih}}} \right)*{\text{YH}} $$
(45)
$$ {\text{YENT}} = e = {\text{shifentk}}*{\text{WK}}*{\text{QKS}} + {\text{transfrentg}}0 $$
(46)
$$ {\text{ENTSAV}} = e = \left( {1 - {\text{tiENT}}} \right)*{\text{YENT}} $$
(47)
$$ \begin{gathered} {\text{YG}} = e = {\text{sum}}(a,{\text{tva}}\left( a \right)*{\text{QVA}}\left( a \right)*{\text{PVA}}\left( a \right)) + {\text{tih}}*{\text{YH}} + {\text{tiENT}}*{\text{YENT}} \hfill \\ + {\text{sum}}(c,{\text{tm}}\left( c \right)*{\text{pwm}}\left( c \right)*{\text{QM}}\left( {cc} \right)*{\text{EXR}}) \, + {\text{sum}}(a,{\text{tvc}}\left( a \right)*{\text{QED}}\left( a \right)*{\text{WE}}) \hfill \\ \end{gathered} $$
(48)
$$ \begin{gathered} {\text{EG}} = e = {\text{sum}}(cc,PQ\left( c \right)*QG0\left( c \right)) + {\text{transfrhg}}0 + {\text{transfrent}}G0 \hfill \\ + {\text{sum}}(a,te\left( a \right)*{\text{pwe}}\left( a \right)*{\text{QE}}\left( a \right)*{\text{EXR}}) \hfill \\ \end{gathered} $$
(49)
$$ {\text{QQ}}\left( c \right) = e = {\text{sum}}(a,{\text{QINT}}(c,a)) + {\text{QH}}\left( c \right) + {\text{QINV}}0\left( c \right) + {\text{QG}}0\left( c \right) $$
(50)
$$ {\text{sum}}(a,{\text{QLD}}\left( a \right)) = e = {\text{QLS}} $$
(51)
$$ {\text{sum}}(a,{\text{QKD}}\left( a \right)) = e = {\text{QKS}} $$
(52)
$$ {\text{sum}}(a,{\text{QED}}\left( a \right)) = e = {\text{QES}} $$
(53)
$$ {\text{GSAV}} = e = {\text{YG}} - {\text{EG}} $$
(54)
$$ {\text{sum}}(c,{\text{PDCP}}\left( c \right)*{\text{QDCP}}\left( c \right)) = e = {\text{sum}}(a,{\text{PDAP}}\left( a \right)*{\text{QDAP}}\left( a \right)) + {\text{PSAV}} $$
(55)
$$ {\text{sum}}(c,{\text{pwm}}\left( c \right)*{\text{QM}}\left( c \right)) = e = {\text{sum}}(a,{\text{pwe}}\left( a \right)*{\text{QE}}\left( a \right)) + {\text{FSAV}} $$
(56)
$$ {\text{FSAV}} = e = {\text{FSAV}}0 $$
(57)
$$ {\text{QLS}} \cdot fx = {\text{QLS}}0 $$
(58)
$$ {\text{QKS}} \cdot fx = {\text{QKS}}0 $$
(59)
$$ {\text{WE}} \cdot {\text{FX}} = 1 $$
(60)

Parameters and Variables

Symbol Description.

a Activity department.

c Commercial department.

c1 No-energy commercial department.

c2 energy commercial department.

deltaAa(a) Share parameter of CES function of QA.

deltaEVA(a) Share parameter of CES function of QEVA.

deltaVA(a) Share parameter of CES function of QVA.

deltaCET(a) Share parameter of CET function of QA.

deltaQDA(a) Share parameter of CET function of QDA.

deltaQq(c) Share parameter of Armington function of QQ.

deltaQDC(c) Share parameter of Armington function of QDC.

EG Government expend.

EH Habitant expend.

EINV investment.

ENTSAV Enterprise saving.

EXR Exchange rate.

FSAV Foreign saving.

GDP Real gross domestic product.

GSAV Government saving.

ic1a(c1, a) Consumption coefficient of non-energy product.

ic2a(c1, a) Consumption coefficient of energy product.

mpc Marginal propensity to consume.

PA(a) Price of product a.

PDA(a) Price of domestic product for domestic use.

PDAL(a) Price of provincial product for use in the province.

PDAP(a) Price of provincial product for use out of the province.

PDC(c) Price of domestic commodity for domestic use.

PDCL(c) Price of provincial commodity for use in the province.

PDCP(c) Price of provincial commodity for use out of the province.

PE(a) Price of domestic product for export.

PM(c) Price of import commodity.

PGDP Price index of GDP.

PINTA(a) Price of intermediate input.

PQ(c) Price of domestic commodity.

PVA(a) Price of the added value.

PEVA Price of the bundle of energy and added value.

pwe(a) World price of product for out-port.

pwm(c) World price of commodity for in-port.

QA(a) Quantity of product a.

QE(a) Quantity of product a for export.

QED(a) Demand of fixed energy.

QES Total supply of energy.

QG(c) Demand of government for commodity c.

QH(c) Demand of habitant for commodity c.

QINT(c, a) Department quantity of intermediate input.

QINTA(a) Total quantity of intermediate input.

QINV(c) Final demand of investment for commodity c.

QDA(a) Quantity of domestic product used in the country.

QDAL(a) Quantity of provincial product used in the province.

QDAP(a) Quantity of provincial product used out of the province.

QDC(c) Quantity of domestic commodity used in the country.

QDCL(c) Quantity of provincial commodity used in the province.

QDCP(c) Price of provincial commodity used out of the province.

QKD(a) Demand for capital.

QKS Supply of capital.

QLD(a) Demand for labor.

QLS Supply of labor.

QM(c) Quantity of import.

QQ(c) Quantity of commodity in domestic market.

QVA(a) Quantity of added value.

QEVA Quantity of the bundle of energy and added-value.

rhoAa(a) Power parameter of CES function of QA.

rhoEVA(a) Power parameter of CES function of QEVA.

rhoVA(a) Power parameter of CES function of QVA.

rhoQq(c) Power parameter of Armington function of QQ.

rhoQDC(c) Power parameter of Armington function of QDC.

rhoCET(c) Power parameter of CET function of QA.

rhoQDC(c) Power parameter of CET function of QDA.

scaleAa(a) scale parameter of CES function of QA.

scaleEVA(a) scale parameter of CES function of QEVA.

scaleVA(a) scale parameter of CES function of VA.

scaleCET(c) scale parameter of CET function of QA.

scaleQDA(c) scale parameter of CET function of QDA.

scaleQq(c) scale parameter of Armington function of QQ.

scaleQDC(c) scale parameter of Armington function of QDC.

shifentk Share of capital revenue to enterprise.

shifhk Share of capital revenue to habitant.

shrh(c) Expanding share of habitant revenue to commodity c.

te(c) Export subsidy rate.

tiEnt Income tax of enterprise.

tih Income tax of habitant.

tm(c) Tariff of commodity c.

transfrentg Transferred revenue from government to enterprise.

transfrhg Transferred revenue from government to habitant.

tva(a) Indirect tax for department a.

tvc(a) Energy tax for department a.

VBIS Dummy variable for saving-investment check.

WE Price of fixed energy.

WK Price of capital.

WL Price of labor.

YENT Enterprise revenue.

YG Government revenue.

YH Habitant revenue.

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Zhou, JF., Wu, D. & Chen, W. Cap and Trade Versus Carbon Tax: An Analysis Based on a CGE Model. Comput Econ 59, 853–885 (2022). https://doi.org/10.1007/s10614-021-10104-x

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