A CGE Analysis on a Rate-based Policy
for Climate Change Mitigation
Shinya Kato∗ and Kenji Takeuchi†
Graduate School of Economics, Kobe University
Rokko, Kobe 657-8501, Japan

March 2014
Discussion Paper No.1414
Graduate School of Economics, Kobe University∗†

a shiny fruit sugar@yahoo.co.jp
takeuchi@econ.kobe-u.ac.jp1Abstract
We conducted a computable general equilibrium analysis of a policy to regulate carbon dioxide emissions per unit of production in
Japan. It is often claimed that regulations based on emission rates
might lead to an increase in carbon dioxide emissions but do not suppress economic growth. This study shows that in the short run, arate-based policy reduce ﬁrms’ emissions at a rate greater than thatspeciﬁed by the regulation. We also compared the rate-based policy
with the cap-and-trade policy and found that the former leads to agreater reduction in the real GDP than the latter. Furthermore, thedecrease in output is tend to be more evenly distributed under the
rate-based policy than under with a cap-and-trade policy. Our results
suggest that the rate-based policy is inferior in terms of eﬃciency but
is favorable in terms of ensuring the burden of emission reduction isshared equally.

2

1

Introduction

Although global eﬀorts toward climate change mitigation have been focusedon total emission amounts, some countries have declared emission targets
relative to their GDP. For example, China and India, who are likely to be
major arbiters of global climate change in the next century, have set suchtargets. The Chinese government is targeting to reduce the carbon dioxide
emissions as a proportion of GDP in 2020 by 40–45% compared to the proportion in 2005. India has a similar policy to bring down its carbon intensity
in 2020 by 20–25% compared to that in 2005.
The eﬀects of regulation linking emissions to output (herein referred to as
the emission rate) has been analyzed mostly by theoretical approach (Helfand
1991; Fisher 2003; Boom and Dijkstra 2009; Holland 2012)*3 . Findings fromthe existing literature suggest that a rate-based regulation is inferior due toan implicit output subsidy. Fischer (2003) shows that the total amount ofemissions tends to increase with the rate-based policy compared to a casewhere a cap-and-trade policy and the rate-based policy are used together.
Boom and Dijkstra (2009) show that the amount of output in the rate-based
policy increases compared to that in the cap-and-trade policy in the short*3

An exception is Holland (2009) that examined the eﬃciency of California’s Low Carbon

Fuel Standard.

3

term and long term. While these studies suggest that a rate-based policy
cannot restrict total emissions and does not suppress economic growth, theextent of such a policy’s impact has not been scrutinized empirically andquantitatively.
This study investigates the impact of a rate-based policy in Japan, using computable general equilibrium (CGE) analysis. While Japan’s current
target for greenhouse gas emissions are based on the total emission amount,introducing a rate-based target similar to China and India is a topic of discussion. As it allows an increase in production, the introduction of a rate-based
policy is preferred by industries and trade unions likely to be aﬀected by regulation. A report by the Japanese Ministry of the Environment on the introduction of the domestic cap-and-trade policy also referred to the possibilityof introducing a rate-based policy (Japanese Ministry of the Environment
2010).
The results of this study suggest that within the framework of static CGE
analysis, the rate-based policy can reduce emissions from ﬁrms at a greaterrate than that speciﬁed by the regulation. In addition, we show that the ratebased policy tends to reduce the production more evenly across sectors. In
contrast, the cap-and-trade policy can increase the output of sectors that emit
less carbon dioxide and thereby promote a structural shift in the economy.
The remainder of the paper is organized as follows. Section 2 introduces4the model. Section 3 explains the data used and the method of calibration.
Section 4 presents simulation results on the rate-based policy that attain a
25% reduction in the emission rate from the base case. Section 5 compares
the rate-based policy and the cap-and-trade-policy. Section 6 presents ourconcluding remarks.

2

The Model

We develop a static CGE model for the Japanese economy based on 2005
data. The model is composed of 34 sectors as listed in Table 1.
It is assumed that three sectors, crude petroleum, coking coal, and natural gas (foss), petroleum and coal products (p c), and gas and heat supply(ghs), produce energy goods and other sectors produce non-energy goods.
Firms emit carbon dioxide from their production process as they use energy goods, while households emit carbon dioxide from their consumption ofenergy goods.
The model has three economic agents: a household, ﬁrms and the government. In this analysis, a representative household that owns exogenously
given capital and labor is assumed. The household provides capital and labor
to ﬁrms and, using the income obtained, it purchases goods and saves money.
It saves at a constant rate and gains utility from the consumption of goods.

5Figure 1 shows that the household gains utility from consumption ofenergy and non-energy goods. The number in Figure 1 denotes the elasticity
of substitution and it is assumed to equal 1. The household determines its
consumption of goods so as to maximize its utility under budget constraints.
Figure 2 shows the production structure of ﬁrms. A ﬁrm produces a primary production factor by using capital and labor, then produces a secondary
production factor by using energy goods, and produces a ﬁnal product byusing non-energy goods. It is assumed that carbon dioxide emissions occur
owing to the use of energy goods. To maximize proﬁts, ﬁrms determine theproduction quantity in this structure.
The ﬁnal products are transformed into domestic goods and export goods.
The domestic goods are transformed into Armington composite goods in combination with imported goods, on the assumption that there is an imperfect
substitution between them (Armington 1969). The elasticity of substitution
between domestic goods and imported goods and the elasticity of transformation between domestic goods and export goods are set at 4. The value ofthe elasticity of substitution in our model comes from the reference value in
Takeda (2007).
The government is supposed to collect three types of tax: a production
tax, tariﬀ, and tax on household income. It is assumed that the government
consumes or saves the tax revenue at a constant rate.
6

For simplicity, a small country is assumed. As a result, the foreign currency prices of imported and exported goods are constant. As for the balanceof payments, the amount of the current account imbalance is constant. In
addition, the current account deﬁcit is interpreted as foreign savings.
From the above settings, the government spending, the household consumption, and the current account deﬁcit is determined, and hence the total
amount of saving. The total amount of savings is spent on investment goods
at a constant rate.

3

Data and calibration

We perform a CGE simulation using the benchmark data of the base year.
In the present study, the data comprise economic data and emissions data.
The economic data comprise data on intermediate inputs, ﬁnal consumption, investment, government expenditure and exports and imports from “the2005 Input-output Tables for Japan” (Statistics Bureau, Japanese Ministryof Internal Aﬀairs and Communications 2009). In addition, we use data on
government savings in “Income and Outlay Accounts Classiﬁed by Institutional Sector in 2005” (Economic and Social Research Institute 2007). We
construct a social accounting matrix from these data for the CGE analysis.
Emissions data are taken from the consumption and input of energy goods

7from the 3EID database (Nansai and Moriguchi 2012).
In a CGE analysis, calibration refers to a model estimation method thatexactly reproduces the initial equilibrium of the estimated model. From thesocial accounting matrix, we can obtain the parameters for the production
function, utility function, saving rate, tax rate, income, and emissions coefﬁcient.
As data in the social accounting matrix are only expressed in terms ofthe value added, we must separate the value data into quantity and pricedata. For convenience, it is assumed that labor is the numeraire good, andthe price for all production factors and all products are take the value one in
the base year. Numerical computation is done with GAMS (general algebraic
modeling system) and its solver, PATH.

4

Impacts of the rate based policy

Using the CGE model, we analyze the characteristics of emission regulations
by the rate-based policy. When emissions trading by the rate-based policy
is introduced, the proﬁt function of the representative ﬁrm in the sector isexpressed as follows:
max Px x − {Py1 y1 + Py2 y2 + PCO2 (hy2 y2 − αx)}
y1 ,y28(1)

where x is output, y1 is the input of non-energy goods, y2 is the input ofenergy goods, hy2 is the emission coeﬃcient, and α is the emission rate.
Px , Py1 , Py2 , and PCO2 represent prices of x, y1 , y2 , and emission permits,
respectively. We assume that emission regulations are imposed only on ﬁrms
and not on the household. This is realistic since it is costly to allocate
emission permits to households and allow them to trade. The ﬁrm’s carbon
dioxide emissions are represented by hy2 y2 , while αx denotes the initiallyallocated emission permits. When the amount of emissions is larger thanthat allowed under the allocated emission permits (hy2 y2 − αx > 0), theﬁrm must be a buyer of permits at the permit price PCO2 . By contrast,
when the amount of emissions is smaller than the allocated emission permits(hy2 y2 − αx < 0), the ﬁrm must be a seller of permits. Under the rate-based
policy, the price of permits is determined by the demand and supply foremission permits, as:∑i

hy2i yy2i =∑αi x i(2)iwhere i is the index of the ﬁrm. The LHS of (2) denotes the total demandfor emission permits and the RHS denotes the total supply. PCO2 is determined so as to satisfy this equation. In the rate-based policy simulation,
the business-as-usual (BaU) emission rate is calculated by dividing the BaU
emissions by the BaU output. A rate-based policy is expressed by multiplying
9the BaU emission rate by a factor less than one. For example, a rate-based
policy that requires a 10% reduction in the emission rate is expressed by multiplying the BaU emission rate by 0.9. This means that the ﬁrm must reduce
emissions by 10% from the BaU emissions when it maintains its output at
the BaU level.
Table 2 shows the results of a simulation for a 25% reduction in theemission rate. Note that the policy requires a 25% reduction from the BaU
emission rate. Since the BaU data is of the Japanese economy in 2005, itmeans that the reference of the policy is emissions and output in 2005. Aftera 25% reduction in the emission rate, emissions from ﬁrms are reduced bymore than 25%, with the actual value being −26.6%. Because the rate-based
policy in this simulation is imposed only on ﬁrms, the emission reduction
from the household is small at 0.59%. As a result, the total emission ofcarbon dioxide is reduced by 22.9%.
The total supply of emission permits is∑

αi xi . By requiring αi to beireduced by 25%, the output also becomes lower than the BaU output, andthe emission is reduced by 26.6%, by more than the reduction required by therate-based policy. Even though it seems the rate-based policy allows ﬁrms
to increase emissions and output, it is not possible in the short run. Because
capital and labor is limited, the economy does not grow beyond the BaU.
Thus, emissions from ﬁrms is reduced by 26.6%, by more than the required10

reduction in emission rate (25%) by the rate-based policy in this analysis.
We can conﬁrm that this result is robust to required emission rate. Figure
3 shows the impact of requiring lower emission rate on total emissions andﬁrms’ emissions of carbon dioxide. By requiring lower emission rate, total
emissions and ﬁrms’ emissions are reduced. Emissions from ﬁrms is always
reduced by larger percentage than the required reduction in emission rate.
The impact of requiring lower emission rate on the permits price is shownin Figure 4. The permit price is increasing due to an increase in marginal
abatement cost.
Figure 5 shows the realized emission rate in each sector with 25% reduction in emission rate. Although the total reduction in emission rate is 25%,
the reduction in emission rate is diﬀerent among sectors. Emission rate is
greatly reduced in sectors such as pulp, paper, and wood products (pulp),
ceramic, stone, and clay products (nmm), and iron and steel (iron). It suggests that marginal cost of reducing the emission rate is relatively lower inthese sectors.

11

5Comparison of the cap-and-trade policy andthe rate-based policy

In this section, we compare the rate-based policy with the cap-and-trade
policy, assuming that both policies reduce the total amount of emission by
25% from 1990 levels. There are some diﬀerences regarding to the settings ofpolicy between this section and the previous section. The reference year ofpolicies examined in this section is 1990, while that in the previous section is2005. Policies in this section is targeting at total amount of emission, whilethat in the previous section is focusing on the emission rate of ﬁrms. We
assume that regulations of emissions are imposed only on ﬁrms and not on
the household in both policies.
When emissions trading using the cap-and-trade policy is introduced, theproﬁt function of the ﬁrm is represented as follows:
max Px x − (Py1 y1 + Py2 y2 + PCO2 hy2 y2 )y1 ,y2(3)

We assume that emission permits are supplied by the government by auction
and the household receives the revenue. In the cap-and-trade policy, permits
price PCO2 is determined by the demand and supply of emission permits as
the following equation:∑

hy2 i y2i = Ē

(4)

i

12

where Ē is the total supply of emission permits by the government. The LHSof (4) denotes total demand for emission permits, and the RHS denotes total
supply. Permits price PCO2 is determined according to this equation.
Table 3 shows the results. In order to achieve the same target of total
emissions, the real GDP under the rate-based policy is lower by 0.1% thanthat under the cap-and-trade policy. This means that the rate-based policy
is ineﬃcient. The permits price and the marginal abatement cost are higher
in the rate-based policy than the cap-and-trade policy. Regardless the target
in this section is the total emissions, the rate-based policy is focusing on
the emission rate. Since the rate-based policy is a mixture of policies on
emissions and output, it induces ineﬃcient allocation of resources to attainthe total emission target.
The reduction of emissions by 25% compared to the 1990 levels means the
reduction by 28.8% compared to the 2005 levels. Total emissions from ﬁrms
and the household are regulated to be 28.8% lower than the 2005 levels. Emissions from ﬁrms are reduced by 32.9% with the cap-and-trade policy and by
33.4% with the rate-based policy. Emissions from the household are reduced
by 4.6% with the cap-and-trade policy and by 1.1% with the rate-based policy. Although the household are not required to reduce the emissions, theiremissions are reduced because of the reduction in consumption due to the
reduction in output of ﬁrms.
13

Figure 6 and Figure 7 show the changes in output for each sector, under
the cap-and-trade policy and the rate-based policy. Under the both policies,
output of three sectors that produce energy goods are signiﬁcantly aﬀected
negatively: crude petroleum, coking coal, and natural gas (foss), petroleum
and coal products (p c), and gas and heat supply (ghs). On the other hand,
output of iron and steel (iron) and electricity (ely) is reduced signiﬁcantlywith the cap-and-trade policy while modestly with the rate-based policy.
In the rate-based policy, sectors with large outputs, such as iron and steel
and electricity, can get many permits free of charge from the government
according to their BaU emission rate, so the drop in output is small. Thus,
these sectors does not signiﬁcantly reduce output in the rate-based policy.
Reductions in output are more evenly distributed among sectors withthe rate-based policy than that with the cap-and-trade policy. Comparing
Figure 6 and Figure 7, it is apparent that the decrease in output with therate-based policy is smaller than that in the cap-and-trade policy. This canbe understood by arranging the equation (1) as:max (Px + αPCO2 )x − (Py1 y1 + Py2 y2 + PCO2 hy2 y2 ).
y1 ,y2(5)

Since αPCO2 in the ﬁrst term of the equation (5) is positive, the rate-based
policy has features of subsidy for output while imposing tax on emissions.
For this reason, the reduction rates of output in the rate-based policy can be14

smaller in many sectors than that in the cap-and-trade policy.
There are three sectors that output increases in the cap-and-trade policy but decreases in the rate-based policy: information and communicationelectronics equipment (iteq), electronic components (semi), and precision
instruments (preq). Carbon dioxide emissions from these sectors are verysmall. Of the total emissions in Japan of 2005, the share of iteq is 0.03%,
semi is 0.25%, and preq is 0.03%. Therefore, with the introduction of thecap-and-trade policy, demand for these products increased. This suggests thepossibility of changes in the industrial structure towards a low-carbon economy. The cap-and-trade policy can promote the growth in sectors related to
information technology while the rate-based policy does not have such eﬀect.
We can summarize our result as follows. There is a tendency that thedecrease in output is more evenly distributed in the rate-based policy compared with the cap-and-trade policy. Regarding to the sectors with lower
emission of carbon dioxide (iteq, semi, and preq), output is increased withthe cap-and-trade policy while it decreases with the rate-based policy. Since
the rate-based policy aims to reduce emissions by setting the emission rate,
there is an ineﬃciency in emission reduction. As a result, the real GDP in
the rate-based policy is smaller, albeit slightly in our case, than that in the
cap-and-trade policy.

15

6

Sensitivity analysis

We conduct a sensitivity analysis to check the robustness of the results. Wechange the elasticity of substitution σE = 0.5 in the input of energy goods to
σE = 0.3 or 0.7, and analyze how the results of static analysis would change.
Table 4 shows the result in the case of a 25% reduction of the emission
rate. From this table, we can see that the emissions fall by more than 25%
regardless of the value of σE . Thus, the result of Section 4 is robust to theelasticity of substitution. When the elasticity of substitution σE is large, thereal GDP is large and the emission reduction is small. This is because theproduction becomes more eﬃcient.
Table 5 show the comparison of the cap-and-trade policy and the ratebased policy when σE changes. The reduction in the real GDP in the ratebased policy is higher than that in the cap-and-trade policy regardless of thevalue of σE . Thus the result is in line with Section 5. We can also conﬁrm
that the real GDP becomes larger for larger σE . This is the same result asthat in Table 4, while the lower permits price suggests that the marginal
abatement cost is lower because of the increase in production eﬃciency. The
permits price changes signiﬁcantly according to σE , suggesting that technological change would have signiﬁcant impact on the cost of climate change
mitigation.

16

7

Conclusion

This study examined the eﬀect of rate-based policy with the emissions tradingin Japan. By using the static CGE analysis, it is shown that emissions fromﬁrms is reduced by 25% or more when the emission rate is required to be
reduced by 25% from the base year. This is caused by that the reductionof the emission rate and the output occur at the same time. In the shortrun, technological innovation is not taken into consideration and the emission
reduction eﬀect is large.
Furthermore, we compared the rate-based policy with the cap-and-trade
policy assuming the same level of emissions reduction. The result suggeststhat the rate-based policy reduces the real GDP more than the cap-and-trade
policy. This is due to the fact that the rate-based policy forces a reductionin emissions even in sectors whose marginal abatement costs are high.
The rate based policy does not promote a reduction in emissions for thesector with higher BaU emission rate even though their emissions are large
and has lower marginal abatement cost. In contrast, the cap-and-trade policy
forces a signiﬁcant emission reduction for the sector which has a low marginal
abatement cost. Our result suggest that the rate-based policy is inferior interms of eﬃciency, but favored in terms of equality of burden sharing among
sectors.

17

Acknowledgement
The earlier version of this paper was presented at the 2013 Fall meetingof the Japan Association for Applied Economics held at Hosei University,
Tokyo. Our heartfelt appreciation goes to Shiro Takeda whose comments
and suggestions were innumerably valuable throughout the course of ourstudy. The responsibility of any errors is of course ours.

References[1] Armington, PS (1969) “A theory of demand for products distinguishedby place of production”, IMF Staﬀ Paper, 16 (1), pp.159-178.
[2] Boom JT, Dijkstra B (2009) “Permit Trading and Credit Trading: A
Comparison of Cap-Based and Rate-Based Emissions Trading Under Perfect and Imperfect Competition”, Environmental and Resource Economics,
44, pp.107-136.
[3] Economic and Social Research Institute (2007) “Income and Outlay Accounts Classiﬁed by Institutional Sector”, Economic and Social ResearchInstitute, Cabinet Oﬃce, Government of Japan.
[4] Fischer, C (2003) “Combining rate-based and cap-and-trade emissions
policies”, Climate Policy, 3S2, pp.S89-S109.
18

[5] Helfand, GE (1991) “Standards versus standards: the eﬀects of diﬀerent
pollution restrictions”, American Economic Review, 81(3), pp.622?634.
[6] Holland SP, Hughes JE, Knittel C (2009) “Greenhouse gas reductions under low carbon fuel standards?”, American Economic Journal: Economic
Policy, 1(1), pp.106-146.
[7] Holland, SP (2012) “Emissions taxes versus intensity standards: Secondbest environmental policies with incomplete regulation”, Journal of Environmental Economics and Management, 63, pp.375-387.
[8] Japanese Ministry of the Environment (2010) “Domestic emissions trading scheme by the cap-and-trade approach in Japan”, Paper presented at
the 11th Meeting of the Domestic Emissions Trading Subcommittee, theCentral Environment Council, the Japanese Ministry of the Environment.
[9] Nansai, K, Moriguchi, Y (2012) “Embodied energy and emission intensity data for Japan using input-output tables (3EID): For 2005 IO table”,
CGER, National Institute for Environmental Studies, Japan.
(available at: http://www.cger.nies.go.jp/publications/report/d031/index-j.html).
[10] Statistics Bureau, Japanese Ministry of Internal Aﬀairs and Communications (2009) “The 2005 Input-output Tables for Japan”, Statistics Bu19

reau, Japanese Ministry of Internal Aﬀairs and Communications.
[11] Takeda, S (2007) “The double dividend from carbon regulations inJapan”, Journal of the Japanese and International Economies, 21(3),pp.336-364.

20

Table 1: Sector identiﬁers (34 sectors)
Identiﬁers
agr
foss
omn
food
tex
pulp
chem
pc
nmm
iron
nfm
fmp
mch
eleq
iteq
semi
treq
preq
omf
cns
ely
ghs
wat
trd
ﬁn
dwe
trp
itc
pubs
edu
mhs
opub
bsrv
psrv

Sector description
Agriculture, forestry and ﬁshery
Crude petroleum, coking coal and natural gas*
Other minings
Beverages and Foods
Textile products
Pulp, paper and wooden products
Chemical products
Petroleum and coal products*
Ceramic, stone and clay products
Iron and steal
Non-ferrous metal
Metal products
General machinery
Electrical products
Information and communication electronics equipment
Electronic components
Transportation equipment
Precision instruments
Other industrial products
Construction
Electricity
Gas and heat supply*
Water supply and waste disposal services
Commerce
Finance and insurance
Real estateTransport
Information and communications
Public administration
Education and research
Medical service, health, social security and nursing care
Other public services
Business services
Personal services

Note: * indicates energy goods.

21

Table 2: Emissions with a −25% emission rate
Total CO2
−22.9%

Emissions (ﬁrm)−26.6%

Emissions (household)−0.59%

Permits price
1,327 yen

Real GDP−0.45%

Note: Comparison with the actuals of 2005.

Table 3: Comparison of cap-and-trade policy and rate-based policy
Emissions (ﬁrm) Emissions (household) Permits price Real GDP
Cap-and-trade−32.9%−4.6%
1,434 yen−0.64%
Rate-based−33.4%−1.1%
2,096 yen
−0.74%
Note: GDP is change from BaU. Emissions is reduced 25% from 1990 level.

Table 4: Sensitivity analysis: −25% emission rate
Elasticity of substitution σE = 0.3 σE = 0.5 σE = 0.7
Emissions (ﬁrm)−27.6% −26.6% −26.3%
Real GDP
−0.84% −0.45% −0.34%
Note: Comparison with the actuals of 2005.

Table 5: Sensitivity analysis: comparison of policies
Cap-and-trade policy
σE = 0.3 σE = 0.5 σE = 0.7
Real GDP
−0.89%−0.64% −0.52%
Permits price 2,659 yen 1,434 yen 943 yen

Rate-based policy
σE = 0.3 σE = 0.5 σE = 0.7−1.35%−0.74%−0.54%
6,020 yen 2,096 yen 1,202 yen

Note: GDP is change from BaU. Emissions is reduced 25% from 1990 level.

22

Utility1Non-energy goods

Energy goods

Figure 1: Consumption structure

Output0
0.5
1CapitalNon-energy goods

Energy goods
Labor

Figure 2: Production structure

Changes in emission rate (%)
0

-5

-10

-15

-20

-25

-30

-35

-40

-45

-50

Changes in CO2 emissions (%)

0
-10
-20

Total emissions-30

Emissions (firm)

-40
-50
-60

Figure 3: Changes in emission rate and CO2 emissions

23Permit price (yen/tCO2)

9,000
8,000
7,000
6,000
5,000
4,000
3,000
2,000
1,000
0
-5

-10

-15 -20 -25 -30 -35
Changes in emission rate (%)

-40

-45

-50

Figure 4: Changes in emission rate and permit price

Change in emission rate (%)

0
-5
-10
-15
-20
-25
-30
-35
-40
-45

agr
foss
omn
food
tex
pulp
chem
p_c
nmm
iron
nfm
fmp
mch
eleq
iteq
semi
treq
preq
omf
cns
ely
ghs
wat
trd
fin
dwe
trp
itc
pubs
edu
mhs
opub
bsrv
psrv

-50

Figure 5: Changes in realized emission rates (−25% emission rate)

24

agr
foss
omn
food
tex
pulp
chem
p_c
nmm
iron
nfm
fmp
mch
eleq
iteq
semi
treq
preq
omf
cns
ely
ghs
wat
trd
fin
dwe
trp
itc
pubs
edu
mhs
opub
bsrv
psrv

Change in output (%)

agr
foss
omn
food
tex
pulp
chem
p_c
nmm
iron
nfm
fmp
mch
eleq
iteq
semi
treq
preq
omf
cns
ely
ghs
wat
trd
fin
dwe
trp
itc
pubs
edu
mhs
opub
bsrv
psrv

Change in output (%)

10

5

0

-5

-10

-15

-20

-25

Figure 6: Changes in output under cap-and-trade policy (−25% total emis-

sions)

0

-5

-10

-15

-20

-25

Figure 7: Changes in output under rate-based policy (−25% total emissions)25