Climate Policy: Costs and Design A survey of some recent numerical studies

Rapport 2009/

Ingeborg Rasmussen og Michael Hoel

Climate Policy: Costs and Design A survey of some recent numerical studies

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Climate Policy: 
Costs and Design 
A survey of some recent numerical studies 
 
Michael Hoel, Mads Greaker, Christian Grorud, 
Ingeborg Rasmussen 
 
 
 
 
 
 
 
 
 
 
 
 
 	
 
TemaNord 2009:550

Climate Policy: Costs and Design 
A survey of some recent numerical studies 
 
TemaNord 2009:550 
© Nordic Council of Ministers, Copenhagen 2009 
ISBN 978-92-893-1888-4 
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Content 
Preface ........................................................................\
........................................................ 7	 	
1 Introduction/Summary ........................................................................\
............................. 9	 	
2 Theoretical background ........................................................................\
......................... 21	 	
2.1 Optimization........................................................................\
................................. 21	 	
2.2 The disc ount rate ........................................................................\
.......................... 26	 	
2.3 Simulation ........................................................................\
.................................... 30	 	
2.4 Policy in struments ........................................................................\
........................ 31	 	
2.5 Fossil Fuels as Non -renewable Resources............................................................ 33	 	
3. Articles with a main focus on optimization .................................................................. 37	 	
3.1 Analyses with the DICE Model ........................................................................\
.... 37	 	
3.2 Analyses with th e ENTICE Model ....................................................................... 41	 	
3.3 Market Equilibria with Endoge nous Technological Development ...................... 45	 	
3.4 Analyses with the WITCH Model ........................................................................\
 46	 	
3.5 Production Functions for Cl imate Policy Modelling ............................................ 50	 	
3.6 Future Climate Change Costs ........................................................................\
....... 51	 	
3.7 Handling Un certainty ........................................................................\
................... 52	 	
3.8 Alternative Policies for Achieving Emi ssion Goals ............................................. 54	 	
3.9 Summary / discussion of articles with a main focus on optimization .................. 56	 	
4. Articles with a main focus on simulations ................................................................... 59	 	
4.1 The Fourth IPCC Asse ssment Report ................................................................... 59	 	
4.2 The Stern Review ........................................................................\
......................... 62	 	
4.3 Studies by the OECD ........................................................................\
................... 65	 	
4.4 Studies by the IEA........................................................................\
........................ 69	 	
4.5 Australia”s Low Pollution Future ........................................................................\
. 76	 	
4.6 Summary / discussion of studies with a main focus on simulations ..................... 84	 	
References ........................................................................\
............................................. ... 89	 	
Norsk sammendrag: Klimapolitikk: Kostnader og utforming.......................................... 93	 	
Appendices ........................................................................\
............................................. 101	 	
Appendix to Section 2.1 ........................................................................\
................... 101

Preface 
This report gives results from a project financed by the Working Group 
on Environment and Economics under the Nordic Council of Ministers. 
The aim of the project has been to give a thorough discussion of some 
recent studies on economic issues related to climate change and climate 
policies. The focus is on various numerical analyses and not on the purely 
theoretical studies. The leader the project was Michael Hoel, University of Oslo. The re-
port was written jointly by Michael Hoel and Mads Greaker (Statistics 
Norway), Christian Grorud (Vista Analyse) and Ingeborg Rasmussen 
(Vista Analyse). Many of the studies we considered report costs for stabilizing CO	
2 
emissions at about 450 ppm CO	
2, corresponding roughly to 500-550 CO	2-
e. The long-term temperature increase fo r such a concentration target will 
be about 2.5-3	
oC. The cost estimates vary considerably. For approxi-
mately the same climate targets, the total costs are in the range of 1-5% of 
GDP. The marginal cost of mitigation, often called the carbon price, tells us 
how strict climate policy must be in order to achieve the climate target. 
Under an efficient climate policy, the carbon price should increase over 
time at a rate below the discount rate. This holds in most of the studies, 
but in some of them the carbon price grows considerably faster. 
The predicted carbon price necessary to achieve a climate goal of the 
type above differs strongly between studies. Most of the studies predict a 
carbon price in 2050 in the range of 100-400 US $ per ton of CO	
2.

1 Introduction/Summary 
There is a large and growing literature focusing on economic issues re-
lated to climate change and climate policies. This report presents a dis-
cussion of some of the recent studies. Our focus has been on various nu-
merical analyses and not on the purely theoretical studies. Among the important issues in the studies we discuss are the follow-
ing: 
 
a.) What will the development of greenhouse gas emissions be and 
what climate changes will follow if no new policies are intro-
duced? 
b.) What can economic analyses tell us about climate policy goals? 
c.) What are the costs of reducing emissions? 
d.) What types of policies should be used to reduce emissions? 
e.) For a given climate goal, what are the additional costs of using 
sub-optimal policies? 
 
Each of the studies considered in this report address some or all of the\
se 
questions. In the present section we give both a non-technical discussion 
of the methodologies used to answer these questions and a summary of 
the most significant results. 
a) Emissions under BaU 
Projections of greenhouse gas (GHG) emissions and climate development 
without any change of policies are often called ‘business as usual” (BaU) 
predictions. These will be strongly influenced by assumptions made 
about population growth and the growth of per capita GDP. The latter is 
to a large extent determined by what is assumed about total factor pro-
ductivity growth. Assumptions about p opulation growth and total factor 
productivity growth are in most an alyses taken as exogenous from vari-
ous sources. Since these variables are highly uncertain for the time per-
spectives relevant for studying climat e change (at least 100 years into the 
future), many studies consider several alternatives.

The development of GDP follows from the assumptions made about 
population growth and the developm ent of GDP per capita. Total GHG 
emissions are often measured in CO	
2-equivalents (CO	2-e) and split into 
three components. The most important (currently approximately 60% of 
total emissions) is energy-related CO	
2 (sometimes called industrial CO	2), 
which include all fossil-fuel emissions plus CO	
2 emissions from indus-
trial processes. The other two components are other CO	
2 emissions 
(mostly from deforestation) and other GHG emissions. Predictions for 
these last two components are often made exogenously, while energy-
related CO	
2 is usually modelled endoge nously. The simplest way to 
model this is to assume some exoge nous development of energy-related 
CO	
2 per unit GDP. For instance, the study using the DICE model (dis-
cussed in section 3.1) assumes, based on historical trends and predictions 
of the future composition of GDP between regions, that industrial carbon 
emission per unit GDP will decline by 0.6% per year for the rest of this 
century (under BaU). A more satis factory way of modelling industrial 
carbon emissions is to have an exp licit modelling of various types of 
energy and other inputs in a productio n function explaining the develop-
ment of GDP. This is the procedure used in the studies discussed in sec-
tions 3.2 and 3.4 (ENTICE, WITCH). Predictions about BaU emissions differ quite a lot between different 
studies. For instance, in 2050 industrial CO	
2 emissions in the study using 
the ENTICE model reported in section 3.2 are about 11 Gt carbon under 
BaU, while they are about 16 Gt in the study using the WITCH model 
reported in section 3.4, in spite of th e models being relatively similar. The 
latter prediction is roughly in line w ith what is assumed in the Stern Re-
view (discussed in section 4.2). Incomplete reporting in several of the 
studies means it is in many cases not clear whether differences in CO	
2 
emissions are due to differences in GD P predictions or in predictions of 
emissions per unit of GDP. 
Different predictions of CO	
2 emissions give different predictions for 
concentration levels of GHGs in th e future, and therefore also for tem-
perature changes. In the most re cent IPCC report (discussed in section 
4.1), emission trends are based on a set of scenarios developed by the 
IPCC in a ”Special Report on Emission Scenarios” (SRES). These should 
be interpreted as BaU scenarios. Basically there are four main families of 
scenario, A1, A2, B1 and B2, each with a number of sub-scenarios. The 
parameters of the scenarios differ in four ways: size of economic growth, 
regional difference in economic growth, degree of global technology 
diffusion and success of less polluting technology. Together they cover a 
range of possible emission time paths which, according to the IPCC, will 
lead to a concentration of GHGs in the atmosphere in the year 2100 of 
between 855 and 1,130 ppm CO
2-e. Concentration levels in most of the 
studies we have considered in this report fall within this range: see table 
4.6 in section 4.6. There are, however , two exceptions. In the DICE study

(section 3.1) BaU concentration of CO	2 in 2100 is only 685 ppm (even 
adding other GHGs not reported in the study would probably keep the 
number below 800 ppm). The second exception is the Australian study 
reported in section 4.5, which gives a BaU concentration in 2100 of 1,560 
ppm CO	
2-e. This study also assumes much more rapid growth in GDP per 
capita than other studies and we suspect that this is the reason for the high 
long-term concentrations of CO	
2 in the atmosphere. 
Predicted climate change under BaU obviously depends on the pre-
dicted development of GHG concentr ation in the atmosphere. The rela-
tionship between atmospheric concentr ation and climate change is often 
characterized by so-called climate sensitivity, which tells us by how 
much the global average temperature will ultimately increase as a re-
sponse to a doubling of the atmospheric concentration of CO	
2-e. Accord-
ing to IPCC (2007), climate sensitivity is “likely to be in the range 2	oC to 
4.5	oC with a best estimate of 3	oC, and is very unlikely to be less than 
1.5	oC. Values substantially higher than 4.5	oC cannot be excluded, but 
agreement of models with observations is not as good for those values.” 
Almost all studies use the point estimate of 3
oC, implying that stabiliza-
tion of atmospheric concentrations at 550 ppm CO	
2-e will give a long-
term temperature increase of 3	oC (and that, e.g., 450 ppm CO	2-e will give 
a long-term temperature increase of about 2	oC). However, due to the un-
certainty about the para meter characterizing climate sensitivity, there is 
roughly a 50% chance that the long- term temperature increase will be 
higher than 3	
oC even if one succeeds in st abilizing atmospheric concen-
tration at 550 ppm CO	
2-e. 
b) Optimal development of emissions 
Uncorrected climate change may give la rge future costs, in particular in 
the next century. Mitigating emissions also have costs and these will oc-
cur immediately (and in the future). A sensible climate policy goal needs 
to find the right balance between present mitigation costs and future cli-
mate change costs. Ideally, one sh ould aim at minimizing the discounted 
sum of mitigation costs and climate change costs. This type of optimiza-
tion is discussed in detail in section 2. 1. In addition to giving the optimal 
time path for emissions, optimization of this type will give a time path for 
the marginal mitigation cost, often ca lled the carbon price. This price tells 
us how emissions should be reduced: any emission reduction that costs 
less than this price should be carri ed out, while potential emission reduc-
tions that would cost more than the carbon price should not be carried 
out. As shown in section 2.1, the carbon price will typically grow over 
time at a rate less than the discount rate.	
1 
 	
 	1 Strictly speaking, less than the sum of the discount rate and a rate refl ecting how carbon depreci-
ates from the atmosphere. However, this latter term is low – less than 1%.

The resulting climate goal, emission development and carbon price 
will depend on three factors: (i) mitigations costs, (ii) climate change 
costs and (iii) the discount rate (for translating all costs into a p\
resent 
value). The optimization performed in the studies discussed in sections 
3.1-3.3 all suggest that optimal clim ate policies should be quite moderate: 
according to the optimization with DICE, it is optimal to let CO	
2 concen-
trations increase to 659 ppm in the end of the next century, implying a 
temperature increase of 3.5 degrees	
2. The study using ENTICE gives 
about the same result for emissions , while the study discussed in section 
3.3 gives even higher GHG concentrations than the previous two. All 
these studies use roughly the same estimates for the costs of climate 
change. In particular, in the analysis with DICE the total costs for the 
world of a temperature of 3, 4 and 6 degrees are assumed to be 2.5%, 
4.5% and 10% respectively. It is di fficult to judge whether these numbers 
are ‘low” or ‘high”. The assumed cost of a 4-degree temperature increase 
is well within the bounds suggested by the IPCC report, and considerably 
higher than the mean cost suggested in the Stern Review.	
3 
As already mentioned, the assumed discount rate is important for the 
result of an optimization, since most of the climate change costs occur in 
the distant future. The studies above use discount rates of the magnitude 
of 4–5%. The Stern Review argues for a much lower discount rate and 
uses 1.4%. The Stern Review does not give a formal optimization in or-
der to find an optimal emission path. However, it discusses the costs of 
stabilizing GHGs at levels between 500 and 550 ppm CO
2-e: i.e. at the 
high end, about twice the pre-industrial level. Due to very high costs of 
adopting a target below 500 ppm, the Review recommends a target be-
tween 500 and 550 ppm CO	
2-e. Given a climate sensitivity of 3 (the ‘best 
guess” of the IPCC), this would limit the global mean temperature in-
crease to 3 degrees Celsius (while it would increase to 7–9 degrees by 
2200 under the BaU scenario of the Stern Review). A lot of the debate in the literature regarding the optimal climate goal 
focuses on what is assumed about the discount rate. We address this issue 
in section 2.2. The question of determ ining the ‘correct” size of the dis-
count rate in dynamic optimization problems has been discussed at length 
for many decades in the economics literature, one of the issues being the 
extent to which observations of market data can give us useful informa-
tion. There is relatively broad agreement that observed market rates of 
return are important for determining th e discount rate to be used in public 
decision-making about projects with a time horizon up to about 20 years. 
However, for projects giving costs and/or benefits further into the futu\
re 
it is not clear that there are any good market data. Moreover, even if such 
data exist, it is not obvious that they should be used for analyses with a 
 	
 	2 Throughout the report, temperature changes are given in degrees Celcius. 3 Table 13.2 in the Stern Review gives the mean cost of a 4–degree temperature increase as 2.6% of 
world GDP, but with a range from 0.4% to 15.5%.

very long time horizon. Put very simply, there are two camps in this dis-
cussion: one argues that the discount rate should reflect ethical considera-
tions regarding equity across generations; the other argues that the dis-
count rate should be roughly equal to expected rates of return on other 
investments. While the discount rate clearly is important, and explains the differ-
ence between the results of the Stern Review and the DICE model, it is 
not the only important factor. Some costs of climate change will come in 
the form of reductions in non-market goods, such as loss of biodiversity, 
effects on human well-being (health, amenities), various forms of ex-
treme weather events, risk of conflicts etc. Non-market goods of this type 
grow only slowly over time, and might even decline. If, simultaneously, 
the number of produced market goods increases rapidly, we should ex-
pect an increased marginal valua tion of non-market goods as time passes. 
This suggests that climate change co sts might be much higher in the fu-
ture than is assumed in most analy ses. In section 3.6 we discuss a study 
that incorporates issues of this type into a model that in other respects is 
practically identical to Nordhaus”s DICE model. With this modification 
of the DICE model, the optimal climate policy is much stricter than 
Nordhaus suggests. Even with the hi gh discount rate used by Nordhaus 
(4.1%), optimal emissions decline shar ply in the second half of this cen-
tury, implying that CO	
2 concentrations reach about 450 ppm in 2100 and 
then decline. This is an even stricter goal than that suggested by the Stern 
Review. 
We mentioned above that there is a considerable degree of uncertainty 
with regard to the parameter for climate sensitivity. In section 3.7 we 
discuss an important contribution by Martin Weitzman (2009), who fo-
cuses on the possibility of ‘values substantially higher than 4.5	
oC”. Based 
on the scientific literature on this topic, he argues that there is a 5% prob-
ability of climate sensitivity higher than 7 degrees	
 Celsius and a 1% prob-
ability of climate sensitivity higher than 10 degrees Celsius. He combines 
this with a model in which climate costs become very high for large tem-
perature increases. Moreover, the probability distribution of temperature 
increases is ‘fat-tailed” in the sense that, as we move towards higher tem-
perature increases, the probabilities d ecrease less rapidly than the dam-
ages increase. As a consequence, he finds that expected climate costs will 
be ‘infinitely high”. This is of course not meant literally, but it implies 
that actual expected climate costs will be very sensitive to both details of 
the probability distribution of the climate sensitivity and the exact costs 
of very large temperature increases. Weitzman argues that most analyses 
of optimal climate policy (such as the studies discussed in sections 3.1-
3.3) ignore this important feature and may therefore give very misleading 
results. The studies reported in sections 3.6 and 3.7 indicate that by introduc-
ing some quite small and not implausible changes into DICE and other

optimization models, major numerical conclusions may change dramati-
cally. We should therefore be very cautious about claims stating that 
long-term concentration limits of, e.g., 450 ppm CO	
2 are too ambitious. 
The studies in sections 3.1 and 3.3 also solve constrained optimization 
problems, where there is a limit on the atmospheric concentration of CO	
2 
or on temperature increase. These studies thus take some climate goals as 
given and calculate the optimum given these goals (see section 2.1 for a 
theoretical discussion of this type of optimization). In table 3.9 of section 
3.9 we have summarized the results from the studies for such a con-
strained optimization. The climate goal is similar across the studies. Nev-
ertheless, there are large differences in the time paths of the carbon price, 
which is an indicator of how difficult it is to achieve the goal. This table 
indicates how the results of the analyses depend heavily on details about 
the assumptions made. 
c) The costs of reducing emissions 
For a given climate goal, the costs of reducing emissions are higher 
 
 the stricter the climate goal; 
 the higher the BaU emissions; 
 the higher the mitigation costs. 
 
Many of the studies we consider report costs for stabilizing CO	
2 emis-
sions at about 450 ppm CO	
2, corresponding roughly to 500–550 CO	2-e. 
The long-term temperature increase fo r such a concentration target will 
be about 2.5–3 degrees. There are two relevant concepts of costs, namely 
absolute costs and marginal costs. The absolute costs should in principle 
be reported as a present value of all future costs. However, this way of 
reporting makes costs depend on the disc ount rate used and may therefore 
make comparisons across studies with different discount rates difficult. A 
more usual way is to report costs in a particular year, often as a percent-
age of GDP. 
Table 1 below gives such costs fo r some of our studies. We can see 
that the cost estimates vary considerab ly, in spite of the climate targets 
being similar. Some studies give costs for stabilizing emissions at or be-
low 550 ppm CO	
2-e well below 2% of GDP. Some other studies, in par-
ticular one of the OECD studies discussed in section 4.3, suggest that 
costs might be considerably higher . We suspect the reason for these high 
costs is that this study considers a mitigation path with very little mitiga-
tion in the near future, therefore making large emission reductions neces-
sary in 2050 (see also the discussion below). 
The Australian study also reports relatively high costs and we think 
the reason in this case is the high emissions under BaU here. It is also 
interesting to note that the costs of stabilization at 450 ppm CO	
2-e in this

study are not much higher than the costs of stabilization at 550 ppm CO	2-
e. We believe that there are two important reasons why the Australian 
study suggests that 450 ppm costs ar e closer to the 550 ppm costs com-
pared to the Stern Review: 
 Carbon capture and storage (CCS) technology is included, becoming 
very important and widespread, and there are developments in other 
technologies as well. In other words, the possibilities for technological 
development seem more optimistic in the Australian scenarios. 
 The 450 ppm stabilization scenario involves overshooting, so a 
majority of the costs of reaching the 450 ppm level are pushed into the 
future, where they are then more heavily discounted. 
 
The marginal cost of mitigation, often called the carbon price, tells us 
how strict climate policy must be in order to achieve the climate target. If 
there were no other distortions in the economy than the climate external-
ity, a carbon tax or a carbon quota price equal to this price would give an 
efficient outcome. The carbon price is therefore a good measure of how 
strict the climate policy must be. For a given climate target, minimizing 
the present value of mitigation costs gives a carbon price that increases at 
a rate equal to the sum of the discount rate and the depreciation rate of 
carbon in the atmosphere.	
4 If we also care about when the upper limit on 
concentration is reached (later is better), the carbon price should grow at 
a slower rate. For the two OECD studies and the IEA study “World En-
ergy Outlook”, the carbon price incr eases much faster than any reason-
able value of the discount rate (see table 1) This indicates that the as-
sumed emission path does not minimize costs of keeping GHGs under the 
concentration limits assumed. If we have understood these studies cor-
rectly, the emission paths are designed taking into account what is politi-
cally feasible, and this need not minimize discounted mitigation costs. In 
any case, the fact that the carbon price is too low at an early stage implies 
that emissions are ‘too high” at an early stage. To keep CO	
2 concentration 
under the imposed limit, emissions in 2050 must therefore be cut back 
quite sharply, implying a high carbon price in 2050 and also a high abso-
lute mitigation cost. From table 1 we can see that there are very large differences in the 
long-term carbon price (2050), even for comparable climate goals. Some 
of the differences have been explai ned above and in the discussion in 
section 3.9. In any case, the tables indicate how the results of the analyses 
depend heavily on details about the assumptions made. 
 	
 	4 The depreciation term is of th e magnitude 0.5–1%. Note that this rule for the price development 
holds only as long as the concentration level is be low the exogenous limit: see section 2.1 for further 
discussion.

Table 1: Carbon prices (US $ per ton CO	2) and costs (% of GDP) 	
Study Stabilization target Carbon price	5 
2010-2015 Carbon price	6 
2050-2055 Costs as % of 
GDP (2050) 	
Nordhaus, Dice Maximum 2	oC tempera-
ture increase 
 US $ 20 
 US $ 83 
 0.6%	7 	
Nordhaus, Dice 
420 ppm CO	2 US $ 67 
 
 US $ 189 
 1.4% 
ENTICE 
 Constant 1995 emis-
sions US $ 182 
 
 US $ 491 
 1.6% 
Grimaud et al. 
 450 ppm CO
2 	US $ 48 
 
 US $ 200 
 
WITCH 
 450 ppm CO	
2 
US $ 20 
 
 US $ 350 
 3.9% 
Stern Report 550 ppm CO
2-e 1% 
(-0.6-3.5%) 
IPCC, 2007 445-535 ppm CO	
2-e < 5.5% 
 
IPCC, 2007 535-590 ppm CO
2-e US $ 20-80 
(in 2030) US $ 30-150 
0.1-4% 
OECD, Env. Outlook 
2008 450 ppm CO	
2-e 
US $ 5 
 US $ 177 
 
 2.5% 
OECD, 2008b 550 ppm CO
2-e US $ 5 
 US $ 400 
 4.8% 
IEA, World Energy 
Outlook 550 ppm CO
2-e 
US $ 40 
(in 2020) US $ 90 
(in 2030) 
IEA, Energy Technology 
Perspectives 2008 450 ppm CO
2-e 
 US $ 200 
 
 
Australia's LPF, Garneau 550 ppm CO
2-e US $ 20 
 US $ 91 
 2.7-3.2% 
Australia's LPF, Garneau 450 ppm CO
2-e US $ 34 
 US $ 158 
 4.2-4.3% 	
 d) What types of policies should be used to reduce emissions? 
Whether an emission path is derived 
from optimization or is simply given 
as an exogenous policy target, we need to use policy instruments to 
achieve the desired emission level. It is well known that a key instrument 
is a correct price of emission, either as a carbon tax or as a price on trad-
able emission quotas. An important question is whether any policy in-
struments in addition to a correct em ission price are needed. If climate 
externality was the only externality in the economy and all markets were 
perfect, and if there were no regulatory failures, there would be no need 
for any policy instruments in addition to a price of emission. However, 
the real world is more complicated than such an ideal. Failures exist in 
most markets, including markets of particular relevance for climate is-
 	
 	5 The exact date within the period 2010–2015 varies across studies 6 The exact date within the period 2050–2055 varies across studies 7 The DICE studies give the present value of costs as percent of present value of output.

sues, such as energy markets and markets for technological development. 
There may also be regulatory failures. In particular, it is not possible for 
any government to commit to a car bon price path far into the future. 
Since many decisions in the present have long-term consequences for 
emissions, assessments of carbon price development will be important for 
current emissions. If market agents be lieve in a slower increase in the 
carbon price than policymakers intend, th is will typically lead to deci-
sions in the present that make future mitigation costs higher than they 
would be in an efficient outcome. 
In addition to a correct carbon price, policy instruments should ideally 
be designed to correct whatever market and regulatory failures exist. 
Various types of subsidies and regulat ions can be part of such a policy 
package. It is in any case important to be clear about exactly what type of 
market or regulatory failure we are trying to correct when a carbon price 
is supplemented with other policies. Future technological development will be important for the costs of 
achieving whatever emission goal we have. A correct carbon price will 
give market agents strong incentives to use resources in order develop 
new climate-friendly technologies. Howe ver, there is little doubt that the 
outcome of unregulated markets is far from perfect with respect to the 
development of new technologies. An important reason why unregulated 
markets give an inefficient outcome is that the benefits of new knowledge 
will, to a large extent, go to othe rs than those who created the new 
knowledge. This positive knowledge extern ality implies that unregulated 
markets tend to put too little effort into creating new technologies. The 
patent system to some extent addresses this issue. However, since the 
marginal cost of knowledge is clo se to zero once the knowledge has been 
created, the patent system must not be too strict if the new knowledge is 
to be used to a sufficient extent. Ev en with a patent system there will 
therefore typically be positive externalities associated with the creation of 
new knowledge. This is a key argum ent for letting public institutions 
participate in knowledge creation (typically basic research) and for giving 
various types of public support to knowledge creation in the private sec-
tor. These issues are treated in more detail in section 2.4. In several of the numerical studies in chapter 3 technological devel-
opment is endogenous and depends on both the carbon price and other 
policy instruments. Some of these studies derive only what the optimal 
R&D levels should be (s ections 3.1 and 3.2), while others discuss how 
policy instruments in addition to a carbon tax should be used in order to 
achieve the optimal outcome (sections 3.3 and 3.8). These latter studies 
show that subsidies towards R&D and the use of new technologies may 
play an important role in the design of climate policy.

e) For a given climate goal, what are the additional costs of using sub-
optimal policies? 
No matter how abatement costs (or benefits from emissions) are mod-
elled, aggregate abatement costs will depend not only on total emissions 
but also on how emissions are allocated across sources and sectors. The 
cost-minimizing allocation is often called the cost-effective allocation. 
An important output from several analyses is to compare the costs of the 
policies giving the cost-effective allo cation of emissions with other poli-
cies giving the same aggregate emissions. Deviating from cost-effective 
policies typically gives quite large cost increases. This is discussed theo-
retically in section 2.3 and is also shown in several of the numerical 
analyses in this report. 
In section 3.1 we consider two examples using the DICE model. First, 
under the Kyoto Agreement only countries accounting for about 33% of 
global emissions in 2010 are given qua ntitative commitments. The cost of 
reaching the Kyoto limits is calculate d to be 7.4 times higher than the 
costs of the same global emission reduction with full participation. The 
second example concerns an agreemen t between the USA, EU and eight 
other large countries: China, Russia, India, Brazil, Canada, Japan, Mexico 
and South Africa. Between them, they accounted for 75% of global emis-
sions in 2004. Reducing emissions in these countries, without imposing 
any restrictions on emissions from the remaining countries, gives total 
costs that are 68% higher than the costs of the same global emissions 
reduction with all countries participat ing in a cost-effective agreement. 
These numerical illustrations show very clearly how important it is to 
achieve an international climate ag reement with the broadest possible 
participation. 
The OECD and IEA studies discuss several scenarios of international 
cooperation on climate policies. The results are similar to what the analy-
sis with the DICE model indicates: costs are substantially higher with 
limited participation than with full participation. For example, the OECD 
(2008b) study shows that GHG concen tration targets below 750 ppm are 
out of reach if Annex 1 countries act alone. These studies also consider 
restrictions on the use of some ways of reducing emissions. In particular, 
one of the reasons why the costs are relatively high in the OECD (2008b) 
study is that the mitigation options of halted deforestation and reforesta-
tion as well as CCS are ruled out. The same study shows that exempting 
energy-intensive industries from po licy action increases the cost of 
achieving the 550 ppm concentration target by 50%. Likewise, not in-
cluding all GHGs, but focusing only on CO	
2, increases the cost of reach-
ing the target by almost 100%. A similar illustration is presented in section 3.4. In this analysis the 
WITCH model is run with restrictions on nuclear power (no increase 
from present capacity), not allowing CCS, and restrictions on the size of 
solar and wind energy (max. 30% of total electricity). By imposing these

restrictions, mitigation costs in 2050 are increased from 3.9% of GDP to 
more than 7%. We have already briefly discussed why it could be desirable to sup-
plement the correct carbon price with other policy instruments. In policy 
debates the view is sometimes put fo rward that other policies should be 
an alternative rather than a supplement to the correct price: i.e. ‘a carrot is 
better than a stick”. Economists are re asonably unanimous that the correct 
price is crucial in order to get an efficient outcome. There is, however, no 
guarantee that this type of policy recommendation will be followed. It is 
therefore interesting to see numerical studies indicating how large the 
efficiency loss may be if we try to achieve an emission goal with policies 
other than a suitable emission price. One example of such a study is 
Fischer and Newell (2008), which we discuss in section 3.8. Fischer and 
Newell consider a model of the US electricity sector. Due to imperfec-
tions in the markets for technological development, the optimal policy 
package is a carbon tax combined with a production subsidy for renew-
able energy and subsidies for R&D. For the same emission target, there is 
a modest efficiency loss if one uses only a carbon tax and not the other 
two policy instruments as well. The efficiency loss is considerably higher 
if one uses only a subsidy of renewa ble energy and/or an R&D subsidy 
and not a carbon tax. * * * * * 
All of these issues are considered in more detail in the subsequent chap-
ters. We start with a thorough theoretical discussion in chapter 2. While 
we believe this chapter gives a u seful background for understanding is-
sues treated in later chapters, it is also possible to skip it and move di-
rectly to chapters 3 and 4. Chapter 3 discusses numerical analyses that 
focus mainly on optimization. Most of these studies are based on rela-
tively simple aggregate models of the world economy. The studies cov-
ered in chapter 4 are mostly large ones that treat a broad range of issues 
and often consider quite complex and disaggregated models of the world 
economy. These models usually have no optimization, but instead typi-
cally identify a policy that is consistent with a specific emission target 
and then calculate the costs of such a policy. In some places we have given a brief mathematical description of key 
features of the models used. However, we believe that the main points 
will be easily understood by those not familiar with this type of formal 
model discussion. Throughout, we have presented costs in US$. We have not always 
been explicit about what year these pr ices refer to (e.g. 2005 US$ versus 
2007 US$) as the amounts can only be regarded as very crude estimates 
because of all the uncertainties involved.

2 Theoretical background 
This chapter presents a theoretical discussion of the ways in which the 
results of various types of analysis depend on the assumptions that have 
been made. 
2.1 Optimization 
The simplest possible optimization problem for the climate problem is to 
maximize the net present value of be nefits minus the costs of greenhouse 
gas emissions. If we restrict our attention to CO	
2 from burning fossil fu-
els, the benefits of emissions are simply the benefits of using fossil fuels. 
If carbon capture and storage (CCS) is a relevant alternative to CO	
2 emis-
sions, the benefits of emissions are the costs saved by not using CCS. The 
costs of CO	
2 emissions go via the stock of CO	2 in the atmosphere, which 
affects the climate. Using e(t ) and S(t ) to denote carbon emissions at time 
t and the stock of carbon in the atmosphere at time t respectively, a very 
simple representation of the present value of benefits minus costs at an 
initial date is 
(2.1) 	
 
V  e	rt	B(e (t), t)  D(S (t), t)

 
	
0
	dt
Here 	
 denotes benefits of fossil fu
el use (or costs saved by not 
using CCS) and D denotes costs from climate change. Benefits are as-
sumed to depend on carbon emissions as well as time, the latter reflecting 
factors such as increased income, which raises the demand for fossil fu-
els, and energy-specific technological development, which reduces car-
bon emissions. In this section we ma ke the simplifying assumption that 
these two effects are of the same magnitude, so that the net effect is zero. 
We thus disregard time as an argument in the benefit function, so that it 
can simply be written as B(e). 
B
(e ,t )
In several analyses the benefits of fossil fuel use are modelled in con-
siderable detail, often linked to a detailed description of the production 
technology of the economy. The term denotes costs from climate change. These costs de-
pend on the stock of carbon in the atmosphere ( S), since this stock affects 
D
(S ,t )

climate development (the exact relationship between S and the climate is 
not explicitly considered here, but it is included in most numerical analy-
ses). The costs of climate change may also depend directly on time, as a 
given climate change may have a greater monetary impact the higher the 
GDP, and the valuation of non-market effects of climate change may also 
increase as a result of higher income (see, e.g., Hoel and Sterner, 2007). 
The discount rate r is exogenous in this si mple optimization problem. 
However, in several of the analyses that derive an optimal emission path, 
the discount rate is endogenous. In th is case it will depend on exogenous 
parameters, reflecting preferences as well as technology. We will return 
to this in section 2.2. The simplest way to model the re lationship between carbon emissions 
and the stock of carbon in the atmosphere is 
(2.2) 	
() () ()
St et St		
	
where a dot over a variable denotes its derivative w.r.t. time, and 	 is 
a depreciation factor telling us how CO	
2 is gradually moved from the 
atmosphere to other sinks (in particular the ocean). In this formulation, S 
measures the concentration in the atmosphere in excess of the natural 
concentration, so that if emissions become zero S will gradually decline 
to zero. In reality, the relationshi p between emissions and the develop-
ment of the stock of carbon in the atmosphere is more complex than (2.2). 
A more realistic description of this relationship is given in many of the 
numerical analyses of these issues. 
Before discussing the solution to this dynamic optimization problem, 
it is useful to consider its static counterpart. The flow pollution prob-
lem, with similar notation as above, is to maximize B(e )	
D (e )*	. The 
optimal e	
missions and corresponding emission price 
q are given 
by 
 . 
e	*	

q	*	B'(e	*)  D'(e	*)
This optimum is illustrated in Figure	 2.1, where is the BaU level of 
emissions. e	0

23	
 
While 
 is the marginal cost of emission reductions (at the optimal 
level), total costs are given by the shaded area

C* in Figure 2.1. Obvi-
ously, 
 , 
 
 and C	
* all depend on the functions 
B and D representing 
technology and preferences. In particular, it is straightforward to see from 
Figure 2.1 that an upward shift in the marginal damage costs ( D”) will 
reduce emissions e and increase the emission price 
 and total costs 
C	
*. An upward shift in marginal abatement costs ( B”) will increase emis-
sions 
 and increase the emission price 
q. However, it is not obvious 
how total costs will be affected. If D” is sufficiently

steep, total costs C	* 
will increase, while they may decline if D” is sufficiently flat and 
 
 does 
not increase as a response to the shift in B”. 
q	
*
e*
e*	
q*
*	
q*
*	
e0	
Turning now to

our dynamic optimization problem, maximizing V 
subject to (2.2) gives the following well-known result (see the Appendix 
to this section for details): 
(2.3) B'(e(t))	
q (t) 
(2.4) 
q (t)  e
(r)( t)	
t
	DS(
S (	),)d	
The variable q(t) defined by (2. 4

) is often called the social cost of carbon. 
Equation (2.4) has a straightforward interpretation: the emission of one 
ton of carbon into the atmosphere at time t gives an addition to the carbon 
stock in the atmosphere at a future time 	
 equal to 	e	() t		. The marginal 
damage of this addition to the stock is at time 	
 equal to , so 
that the ma	
rginal damage of the one ton emitted at t is 	
S	 
at time 	 	e(DS( S (	),)	t)D (S (	),)	
, which discounted to t gives 	. The sum of 
e	 (r 	)( t)DS(S (	),)

these terms over all dates 	 t	 is the marginal cost of one ton of emis-
sions at t and is given by (2.4). 
In the optimal outcome the marginal benefits of carbon emissions (of-
ten termed the marginal costs of reducing carbon emissions) are equal to 
the social cost of carbon: see (2.3). This implies that emissions are given 
as a declining function of the carbon price q.	
8 
The optimization problem above is discussed in more detail in the 
Appendix to this chapter. Here we derive the following relatively well-
known results: 
 	
 If D is proportional to S, implying D	S is constant, q(t) will be 
constant. 	
 If D	S is rising for all 
 	t, q(t) will be rising at time t.	9 	
 Whenever 
 D	S0 , the growth rate of 
q is less than 	r. 	
 Whenever 	 
 D	S
0	 (which could be the case for low values of 	S), the 
growth rate of 	
q will be equal to	 r. 
 
It is often assumed, and seems reasona ble, that both total and marginal 
climate damage, i.e. 	
D and , is quite small for relatively small values 
of 	
S. As 	S increases, 	D and eventually increase quite rapidly. If 	
Ds
Ds	SD	ri-
ses rapidly enough, it is almost as if there is an absolute upper limit on 
S. 
In the Appendix to this chapter we therefore consider an approximation to 
this situation, by assuming that 	
 D
(S ,t )	m (t) S	 for values of 	S up to 	S*, 
and that 	
 S* is an upper limit for 	S. In a diagram where the horizontal axis 
measures 	
S and the vertical axis measures the marginal damage 	SD	, the 
curve for will be horizontal up to 	
Ds	S* and become vertical at 	S*. Mo-
reover, if 	
m(t) is increasing in 	t, the horizontal portion of this curve will 
gradually move upwards as time passes. 
An alternative interpretation of th e case described above is that the 
damage cost is simply given by 
 
 D
(S ,t )	m (t) S	, but in the optimization 
problem we add the constraint that 	
SS*. With this interpretation our 
problem is a mixture of restricted and unrestricted optimization, since 
 	
 SS*is an exogenous constraint. 
In the Appendix we derive the follo wing properties of the optimal so-
lution for the case in which the constraint is binding from some 
date 
T onwards. Prior to 	T, q(t) rises at a rate less than 	
S(t)S*	
r. The value 
 	
 	8 If benefits depend on t for a given q (cf. the discussion above) the relationship between emissions 
and the carbon price is more complicated. In this case a constant carbon price will generally not give 
constant emissions; emissions will increase or decline over time depending on whether or not the in-
crease in demand as a result of income growth exc eeds the decline in demand resulting from energy-
specific technologi cal development. 
9 There are two reasons why 	 	 might be increasing over time. First, there will be a direct effect if 	
 	. Second, if , which is often assumed, an increase in S will 	 make increase. If the 
optimal outco	
me implies that S never overshoots its long-term stationary value, will therefore 
in cr
ease over time if	
 	. 	
DS	D 0	DSS 0
D	
SS 0	
DSDS

of 	q(t) reaches a value at 	T and remains constant at this level after 	T.	q*
q*	
10 
This value is the carbon price making emissions exactly equal to 	
, so 
that carbon in the atmosphere remains constant equal to 
 after 
T (for-
mally , is defined b

y : see (2.4)). 	
S*
(
qt	
S*	
*q
S*
S*
(
qt 
))
*q	
B
'(	S*)
The time path of q(t) is illustrated in Figure 2.2. In this figure is 
the price path that would have been optim al without the constraint 
: i.e. the price path given b

y (2.8). When the constraint 
 
 is binding for some values of t, the optim
al price path q(t) lies 
above . The exact position

of the curve for q(t) in Figure 2.2 will of 
course depend on all ex

ogenous variables as well as on the function 
 
 . We will discuss the effects of changes in some important vari-
ables. 	
)	
 
 S
(t)		
S (t)		
B '(e(t	
)	
 	
Consider an increase in the m

arginal damage costs m(t). This will shift 
the initial carbon price q (0) upwards. However, it will also reduce the 
growth rate given by (2.9), so the whole price path will become flatter, 
and the new price path will at some date intersect the old price path. The 
price remains unchanged but will now be increased at a later date. 
Total abate ment costs ass

ociated with the optimal climate policy will 
increase as a consequence of the increase in m(t): i.e. the present value of 
 will go down. 
 B
(e (t))
A reduction in the limit 	
S* will imply an increase in . The whole 
path of q(t) will in this case m	
ove upwards. Just as with an increase in 
m (t), a reduction in q*	
S*	
e
(t)) will increase total abatement costs: i.e. reduce the 
present value of . 
B (

10 As shown in the Appendix, q(t) may start to increase again at a date later than T if m (t) continues 
to increase after T.

An increase in the interest rate r will make the path of q(t) steeper. 
Since 
 remains unchanged, the new price path will at some date inter-
sect the old pa th, and q(t

) will reach at an earlier date than before. 
q*	
q*	
Finally
,

consider the effect of the assumptions about technology. A 
more favourable technology in relation to reducing emissions means a 
lower value of for any given value of e
: i.e. the carbon price 
necessary to achieve a particular emission level is lower the better the 
technology is. Better technology will give a lower path for q(t), so that 	
*q	 will be reached at a later date. Just as in the static case described ear-
lier, it is not obvious that total costs go down if marginal abatement costs 
 go down. The reason is that the improvement in technology 
gives us a reduction in climate costs through lower emissions and a lower 
time path of the stock of carbon in the atmosphere, implying that the limit B
'(e(t))
B '(
 e
(t)
)	
S* is reached at a later date. Overall, welfare is increased by the techno-
logical improvement, but this welfare increase can come as an increase in 
abatement costs that is more than compensated for by the decrease in 
climate costs. The discussion above gives a rough picture of how various factors in-
fluence the development of the optimal carbon price in numerical optimi-
zation models. However, the detailed results of these models may differ 
slightly from the analysis above, as this was based on several simplifying 
assumptions. 	
2.2 The discount rate 
In all analyses involving some kind of optimization, the size of the dis-
count rate is important. It follows fro m the discussion in section 2.1 that 
the discount rate is important even if we have a constrained optimization 
problem where we have imposed an upper limit on CO	
2 in the atmos-
phere (or an upper limit on temperat ure change). We will therefore 
briefly discuss some of the issues related to the discount rate. The question of the ‘correct” size of the discount rate in dynamic op-
timization problems has been discussed at length for many decades in the 
economics literature. In the last five to ten years this discussion has inten-
sified because of the increased focus on the climate problem, which by its 
nature has a very long time horizon.	
11 
One of the issues in this discussi on has been the extent to which ob-
servations of market data can give us useful information for determining 
the ‘correct” discount rate. There is relatively broad agreement that ob-
served market rates of return are important for determining the discount 
rate to be used in public decision-making about projects with a time hori-
 	
 	11 Important contributions include Arrow et al. ( 1996), Cline (1992), Dasgupta (2001), Hasselmann 
(1999), Heal (1997), Horowitz (1996), Lind (1982), Nordhaus (1997), Portney and Weyant (1999), 
Schelling (1995), Shogren (2000), Weitzman (1994, 1998, 2001) and Zerbe (2004).

zon up to about 20 years. However, for projects giving costs and/or bene-
fits further in the future it is not clear that there are any good market data. A related issue is whether there are r easons why the discount rate should 
be lower for analyses involving a long time horizon (such as the climate 
problem with a horizon of more than a century) than for analyses with hori-
zons up to only a couple of decades.	
12 An example of a declining discount 
rate is given in the ‘Green Book” from HM Treasury in the UK (see HM 
Treasury, 2003), where the discount rate over time is as in Table 2.1. 	
Table 2.1 Example of a declining discount rate (from HM Treasury, 2003) 
Year 0–30 31–75 76–125 126–200 201–300 301+ 
Discount rate (%) 3.5 3.0 2.5 2.0 1.5 1.0 
 
Note that a correct interpretation of this table is not that one should use a 
constant discount rate throughout the calculation period for projects last-
ing from 31 to 75 years.	
13 What is does mean is that for a project lasting, 
say, 50 years, costs and benefits incurred during the first 30 years should 
be discounted at a rate equal to 3.5%, and that costs and benefits for the 
remaining years first should be discounted back to year 30 at the rate 3% 
per year, then to year (the initia l date) at the rate 3.5% per year. 
In economic models of dynamic optimization and cost-benefit analy-
sis, a frequently used objective function is of the type 
(2.5) 	
W	, 	 e	tN(t)	
0
T	U
(c (t)) dt	
where N(t) and c (t) denot e populati

on and per capita consumption at 
time t. The function U can be interpreted as a measure of well-being or 
utility, and T is the time horizon. The trade-offs between consumption at 
different points of time are given partly by the utility discount rate	
 and 
partly by the utility function U. The larger 	
 is, the more weight is given 
to the present relative to the future. The function U is assumed to be 
strictly concave, so that it increas es less than proportionately with con-
sumption. The more concave U is, the more weight is given to periods 
with low consumption relative to periods with high consumption. In most 
analyses it is assumed that the elasticity of the marginal utility U” is con-
stant, denoted 	
	 (where concavity of U implies 		0	). 
For issues with a time perspective of a century or longer (such as the 
climate problem), it is natural to interpret the function (2.5) as a represen-
tation of society”s preferences over distributions of consumption across 
 	
 	12 See, e.g., Weitzman (1998, 2001) and Gollier et al. (2008). 13 To see that this would be meaningless consider two projects, A and B, that are identical for the 
first 30 years, with an initial investment and then positive benefits for 30 years. In project A there are 
zero costs and benefits after the first 30 years, while B has a small closing cost at year 31. Clearly, A is 
better than B. But if one uses a 3% discount rate for B (since it lasts 31 years) and a 3.5% discount rate 
for A (since it lasts only 30 years), the present value of B will be higher than for A if the closing costs 
are sufficiently small!

generations. An assumption of 	0 means that society gives the current 
generation more weight than it gives future generations, and that society 
gives future generations lower weight the more distant they are. In the 
economics literature, there has been extensive discussion about whether a 
positive value of 	
 can be given an ethical justification. 
When the function (2.5) is interprete d as a representation of society”s 
preferences over distributions of consumption across generations, the 
concavity of U measures inequality aversion: the more concave U is – i.e. 
the higher 	
	 is – the more weight is given to generations with low con-
sumption relative to generations with high consumption. In a situation 
with economic growth (rising c(t)), the future is thus given lower weight 
the higher 	
	 is. In a situation with economic decline, however, the value 
of future consumption might even be given a higher weight than current 
consumption. We would thus have a ne gative discount rate if the rate of 
economic decline was sufficient to outweigh the effect of utility discount-
ing ρ: see equation (2.6) below. 
The appropriate interest rate r for discounting consumption when pre-
ferences are given by (2.5) is found by differentiating (2.5) w.r.t. con-
sumption and time to see how the marginal utility of consumption chan-
ges. It is well known that this give s the following ‘Ramsey equation (see, 
e.g., Dasgupta and Heal, 1979) 
 
(2.6) r
(t)	
g (t), 
 
where is the relative growth rate of consumption. If, e.g., 
 
g
(t )	
0.01 , 	 	1.5	 and 
 
 , we find 
r = 0.04:	 i.e. a discount rate 
of 4%. g
(t)0.02
Notice that this discount rate will be constant over time only if the 
growth rate of consumpt ion is constant over time. During the last 50 
years the average growth in consumption per capita has been about 2.5% 
per year (world average). This is unusually high in a long time perspec-
tive and there may be several reasons to believe that it will not be so high 
the next 100 years. If, e.g., the c onsumption growth rate gradually de-
clines towards 1% per year, this w ill give a gradually declining discount 
rate. To determine a numerical value of the discount rate r, we need values 
of the parameters 	
 and 		. A major controversy in the literature is how 
these parameters should be determined. Put very simply, there are two 
camps in this discussion: one (e.g. Cline, Stern) argues that the parame-
ters should reflect ethical considera tions regarding equity across genera-
tions; the other (e.g. Nordhaus) argues that the parameters should be set

so that historical values of r calculated from (2.6) should be (at least 
roughly) equal to historical rates of return.	14 
The interest rate given by (2.6) is usually defined as the appropriate 
discount rate to be used for investme nts for which there is no uncertainty. 
From standard economics literature we know that for a project giving a 
return that is positively (negatively) correlated with the general future 
consumption level (or, more generally, welfare level) a discount rate that 
is higher (lower) than the risk-free discount rate should be used. What 
does this mean for the discount rate to be used for analyses of the climate 
problem? The answer to this is not obvious. For example, consider the 
simple case in which we have a constraint on the accepted global average 
temperature increase (e.g. 2 degrees Celsius) and ignore climate costs for 
temperatures below this limit. The economic issue is thus to choose 
among all possible emission paths satisfying the constraint on tempera-
ture increase. Typically we thus have choices between more abatement in 
the near future (next couple of decades) versus abatement in the more 
distant future (second half of this century). The investment project of 
abating in the near future thus has a pay-off equal to the implied lower 
abatement costs in the more distant fu ture. This pay-off is uncertain, for 
at least three reasons: 
i.)	
 	uncertain total factor productivity growth; 
ii.)	
 	uncertain carbon-reducing technological progress; 
iii.)	
 	uncertain climate sensitivity. 
 
With regard to i), the higher total factor productivity growth is, the higher 
BaU emissions are. Higher total factor productivity growth therefore 
gives a higher abatement requirement in the future and thus higher mar-
ginal abatement costs in the future. Th is means that the pay-off of abating 
now instead of waiting until some time in the future has a higher pay-off 
the higher the total factor productivity growth. Since future consumption 
is higher the higher the total factor productivity growth, the returns on 
abatement in the near future are pos itively correlated with the future con-
sumption level. For this type of uncertainty, the appropriate discount rate 
should therefore be higher than the risk-free discount rate. 
With regard to ii), a favourable development of technologies for low-
carbon energy sources will imply lower marginal abatement costs in the 
future, implying a lower return on ab atement in the near future. Such a 
favourable technological development will also give a yield in terms of 
higher future consumption. Returns on abatement in the near future are 
thus in this case negatively correlated with the future consumption level. 
 	
 	14 Even if one accepts this second approach, it is not obvious what the parameters in (2.6) should be, 
since historical rates of return vary across different types of investment.

For this type of uncertainty, the appropriate discount rate should therefore 
be lower than the risk-free discount rate. With regard to iii), the long-term concentration of carbon in the at-
mosphere that is consistent with a given temperature target is lower the 
higher the climate sensitivity. This means that future abatement and 
hence future marginal abatement co sts are higher the higher the climate 
sensitivity turns out to be. The returns on abatement in the near future are 
therefore higher the higher the climate sensitivity turns out to be. More-
over, higher required future abatement implies lower future consumption. 
Also, for this type of uncertainty, the appropriate discount rate should 
therefore be lower than the risk-free discount rate. From the examples above, it is clear ly not obvious which discount rate 
to use in analyses of the climate pr oblem; the choice depends on which of 
the three sources of uncertainty is believed to be most important. 
2.3 Simulation 
As mentioned in chapter 1, many economic analyses make no attempt to 
optimize emissions. These analyses instead do simulations of various 
types. The most common type of simulation is to analyse consequences, 
including costs, of some particular policy package: e.g. some combina-
tion of carbon taxes, subsidies to R&D and/or renewable energy. A close-
ly related analysis is to identify a po licy that is consistent with a specific 
emission target and then calculate the costs of such a policy. There is no 
sharp distinction between these two type s of analysis, as in the latter case 
the policy necessary to achieve an exogenous emission target is often 
derived through an iteration process. A wide range of models may be used for analyses of this sort, from re-
latively simple and aggregated models to large-scale numerical general 
equilibrium models with a detailed se ctor disaggregation covering many 
regions of the world. In these models, the costs of climate change are not 
usually included, but the costs of reducing emissions will always play a 
crucial role. Just as with optimization analyses, the actual modelling of 
these costs may be done in several ways. The most detailed and micro-
based approach is to link CO	
2 emissions to the use of fossil fuels as in-
puts in production functions. No matter how abatement costs (or benefits from emissions) are mod-
elled, aggregate abatement costs w ill depend not only on total emissions 
but also on how emissions are allocated across sources and sectors. The 
cost-minimizing allocation is often called the cost-effective allocation. 
An important output from several analys es is to compare the costs of the 
policies giving the cost-effective allo cation of emissions with other poli-
cies giving the same aggregate emissions. Deviating from cost-effective 
policies typically gives quite large cost increases. To illustrate, consider a

case of n identical emission sources, each with a strictly convex abate-
ment cost function c(a ), where a is abatement. If total abatement is given 
by A, the cost-minimizing allocation of abatement is for abatement to be 
equal at each source, giving a total abatement cost equal to nc(A/n ). Con-
sider instead a policy that exempts half of the sources from having any 
abatement, so that abatement at the remaining sources must be 2 A/n. This 
gives a total abatement cost equal to ( n/2) c(2 A/n ), which will be higher 
than nc(A/n ) when the abatement costs are st rictly convex: i.e. when mar-
ginal abatement costs are increasing in abatement. The size of this differ-
ence will of course depend on the de tailed properties of the abatement 
cost functions. If, e.g., these are quadratic with marginal costs being zero 
at a=0, it is straightforward to verify that ( n/2) c(2 A/n ) will be exactly 
twice as large as nc(A/n ). In other words, this particular deviation from 
the cost-effective allocation of abatem ent will, in this example, make 
total abatement costs twice as high as they need to be. 
2.4 Policy instruments 
Whether an emission path is derived from an optimization or is simply 
given as an exogenous policy target, we need to use policy instruments to 
achieve the desired emission level. It is well known that a key instrument 
is a correct price of emission, either as a carbon tax or as a price on trad-
able emission quotas. An important question is whether any policy in-
struments in addition to a correct emission price is needed. If the climate 
externality were the only externality in the economy and all markets were 
perfect, and there were no regulatory failures, there would be no need for 
any policy instruments in addition to a price of emission. However, the 
real world is more complicated than such an ideal. Failures exist in most 
markets, including markets of partic ular relevance for climate issues, 
such as energy markets and markets for technological development. The-
re may also be regulatory failures. In particular, it is not possible for any 
government to commit to a carbon price path far into the future. Since 
many decisions in the present have long-term consequences for emis-
sions, assessments of carbon price development will be important for 
current emissions. If market agents be lieve in a slower increase in the 
carbon price than policymakers intend, th is will typically lead to deci-
sions in the present that make future mitigation costs higher than they 
would be in an efficient outcome. 
In addition to a correct carbon price, policy instruments should ideally 
be designed to correct whatever market and regulatory failures exist. Va-
rious types of subsidies and regulations can be part of such a policy pack-
age. It is in any case important to be clear about exactly what type of 
market or regulatory failure we are trying to correct when a carbon price 
is supplemented with other policies.

Future technological development will be important for the costs of 
achieving whatever emission goal we have. A correct carbon price will 
give market agents strong incentives to use resources in order develop 
new climate-friendly technologies. Howe ver, there is little doubt that the 
outcome of unregulated markets is far from perfect with respect to the 
development of new technologies. An important reason why unregulated 
markets give an inefficient outcome is that the benefits of new knowledge 
will, to a large extent, go to others than those who have created the new 
knowledge. This positive know ledge externality implies that unregulated 
markets tend to put too little effort into creating new technologies. The 
patent system to some extent addre sses this issue. However, since the 
marginal cost of knowledge is close to zero once the knowledge has been 
created, the patent system must not be to strict if the new knowledge is to 
be used to a sufficient extent. Even w ith a patent system there will there-
fore typically be positive externalities associated with the creation of new 
knowledge. This is a key argument for letting public institutions partici-
pate in knowledge creation (typically basic research) and for giving vari-
ous types of public support to knowledge creation in the private sector. 
It is beyond the scope of the presen t study to analyse the concrete de-
sign of policies to promote technologi cal development. We will neverthe-
less briefly discuss what role technology considerations play in the de-
termination of the optimal developmen t of the carbon price. This issue 
has been extensively discussed in the literature, both for environmental 
taxes in general and for the particular case of a carbon price.	
15 Distinc-
tions are often made between knowledge derived from experience (so-
called ‘learning by doing”, or LbD) and knowledge based explicitly on 
research and development (R&D), a lthough the distinction in practice is 
not so clear. Goulder and Mathai (2000) show that with LbD the optimal 
outcome under reasonable conditions w ill be characterized by the mar-
ginal mitigation costs exceeding the social cost of carbon: i.e. exceeding 
the carbon price given by (2.4). This does not necessarily imply that the 
appropriate carbon price should exceed the social cost of carbon. If all the 
benefits of the learning that results from the activities of a market agent 
go to this same agent, the agent will in self-interest choose its activities so 
that the optimum conditions are satisfied. It is only to the extent that the 
benefits of the learning also go to others that this type of learning is an 
argument for the carbon price to exceed the social cost of carbon: see, 
e.g., Rosendahl (2004). Goulder and Mathai also show that if there are sufficiently good pol-
icy instruments to influence R&D, the optimal carbon price should be 
equal to the social cost of carbon. However, if there are limited possibili-
ties of influencing R&D directly, it may also for the case of R&D be op-
 	
 	15 See Jaffe et al. (2002), Löschel (2002) and Requa te (2005) for general surveys of environmental 
policy instruments under endogenous technological development. The optim al rate of an environmental 
tax is explicitly analysed by, e.g., Bigl aiser and Horowitz (1995) and Parry (1995).

timal to let the carbon price exceed the social cost of carbon: see, e.g., 
Gerlagh et al. (2008) and Hart (2008). If the carbon price is set correctly – i.e. according to the principles 
discussed in section 2.1 – there is in principle no difference between the 
imperfections associated with developing climate-friendly technologies 
and the imperfections associated w ith technological development else-
where in the economy. There are therefore no good reasons for policies to 
differ in the area of climate-friendly technology development from those 
in other areas of the economy. Mark et imperfections may, however, be 
larger in the climate area than else where, in which case it could be argued 
that a correct policy design in this ar ea is more important than in other 
areas of the economy. 
A point related is that if one gi ves various forms of economic support 
to R&D in the climate area, this might crowd out other forms of R&D. If 
this occurs, the benefits of such support are weakened if other types of 
R&D are lower than what is socially optimal. This point is made by Popp 
(2004), who assumes that the social returns on climate-friendly R&D are 
four times higher than the private returns (in the absence of any subsi-
dies). This can justify subsidizing th is type of R&D. However, the in-
crease in this type of R&D following such a subsidy will partly come at 
the expense of a decline in other types of R&D, which also are assumed 
to have social returns that are four times higher than private returns. The 
social benefits of subsidizing clim ate-friendly R&D are therefore lower 
than they would have been had other R&D been unaffected by this sub-
sidy. 
2.5 Fossil Fuels as Non-renewable Resources 
The most important contribution to the climate problem is CO	2 from the 
combustion of fossil fuels. The climate problem is thus to a large extent 
caused by extracting carbon resources and transferring them to the at-
mosphere. Logically, any discussion of the climate problem therefore 
ought to be intimately linked to a discussion of the extraction of carbon 
resources. In spite of this obvious fact, surprisingly little of the literature 
makes this link. However, there are important exceptions, such as the 
early contributions by Sinclair (1992), Ulph and Ulph (1994) and Witha-
gen (1994), and more recent contributions, such as Hoel and Kverndokk 
(1996), Tahvonen (1997), Chakravorty et al. (2006), Strand (2007) and 
Sinn (2008). One of the insights from this literature is that the principles for setting 
an optimal carbon tax (or price of carbon quotas) are the same as those 
derived in section 2.1. The literature shows what such an optimal climate 
policy implies for issues such as the time path of resource extraction, the 
transition to non-carbon substitutes, and the magnitude and timing of

CCS. Some of it also discusses the consequences of non-optimal climate 
policies when we explicitly consider the link between climate policies 
and the market for fossil fuel resources. We will outline some of the main 
insights below. The conventional wisdom is that CO	
2 emissions will be lower at any 
time the higher the carbon tax. If the supply side of the markets for fossil 
fuels is taken into account this is not so obvious. To understand this, con-
sider the simplest possible case of one aggregate of fossil fuels that exists 
in a known total supply and has zero extraction costs. The Hotelling rule 
tells us that in this case the producer price of the fuel must increase at the 
rate of interest, denoted r. The price at any date t is thus 
where 	
0	
p (t)		p0ert	
p	 is the initial price. The level of this price path – i.e. – is 
determined so that total dema	
nd over th e whole future is exactly equal to 
the total available fuel resource. Without any carbon tax, the demand at 
any time is given as a declining function of : i.e. lower the lower is 	
0	
p0	
p(t)	
p	. The equilibrium 	 	 is the value of 	0	p (t)  p	0ert	p	 that makes total 
demand over the whole future exactly equal to the total available fuel 
resource. We now introduce a carbon tax . Consider first the case in 
which it increases at the rate r and that . The price to consumers is 
now 	
 
 where 
 is the producer price after the 
carbon tax h	
as been introduced (which as before must rise at the rate r 
due to the Hotelling rule). Since the c onsumer price rises at the same rate 
as without a tax, the requirement that total demand over the whole future 
is exactly equal to the total availabl e fuel resource must require the same 
initial price as before, implying 	
 and thus 
q	

)
p(
t)
p	
0
0	q0	%p (t
q
0
%	
p
(t)	q (t)	(%p0q0)ert	
%p0	%p (t)	q (t)		p (t) 
for all t. The consumer price path is thus unaffected by the carbon tax, so 
the extraction path is also unaffected. In the absence of CCS, the level of 
the carbon tax therefore has no effect on CO	
2 emissions. The only effect 
of the carbon tax is to transfer some of the resource rent from the re-
source owners to the government that sets the tax. 
In the reasoning just outlined we assu med that the carbon tax rose at a 
rate equal to the interest rate r. It is straightforward to show (along the 
lines above) that if the carbon tax rises with a rate higher than r , the pace 
of extracting the fuel will be increased compared with the case of no 
carbon tax, so that CO	
2 emissions will increase in the immediate and near 
future (in the absence of CCS). Conversely, if the carbon tax rises with a 
rate lower than r , the pace of extracting the fuel will be reduced com-
pared with the case of no carbon tax and CO	
2 emissions will therefore 
decline in the immediate and near future. 
Finally, consider the case in which the carbon tax path is so high that, 
even with a zero producer price of fuel, total demand over the whole fu-
ture is less than the total available fuel resource. Here the equilibrium 
producer price of fuel will be zero and some of the fuel will never be 
extracted. In this case the simp le conventional wisdom holds: CO	
2 emis-
sions will be lower at any time the higher the carbon tax.

This reasoning is based on the assumption that extraction costs were 
zero. However, as shown by, e.g., Long and Sinn (1985) and Sinn (2008), 
similar results hold when extraction costs are positive and rise with in-
creased extraction. The details differ, but the main message remains the 
same: it is not only the level but also the whole time profile of the carbon 
tax that is important for CO	
2 emissions. 
Another piece of conventional wisdom regarding climate policies is that 
a reduction in the price of non-carbon su bstitutes (as a result of either tech-
nological improvements or subsidies) will reduce CO	
2 emissions. This is 
not necessarily true when we take th e supply side of the market for fossil 
fuels into consideration. For instance, Jon Strand (2007) has shown that a 
technology agreement that will make carbon redundant in the future may 
increase present carbon em issions. Less dramatically, Hoel (2008) assumes 
that although technological improvement will lower the costs of renewable 
energy, carbon resources will still have lower costs than the substitute. The 
consequences of such a technological improvement are analysed for a 
situation where different countries (or groups of countries) have climate 
policies with differing levels of ambi tion, but where there is no efficient 
global climate agreement. In particular , each country is assumed to have 
some willingness to pay (WTP) for re ducing carbon emissions and sets a 
carbon tax equal to its WTP. There wi ll thus be a distribution of carbon 
taxes across countries. Moreove r, there exists a perfect substitute for fossil 
fuels, with a constant unit cost. This substitute will be adopted by countries 
for which the fuel price plus the car bon tax exceeds the cost of producing 
the substitute. However, in countries th at have a lower WTP the fuel price 
including the carbon tax will be lower than the cost of the substitute and 
these countries will not adopt the substitute. 
Consider an improvement of the technology for producing the substi-
tute, thus lowering its cost. If the fossil fuel price were unaffected, this 
cost reduction would induce some countries to switch from fossil fuels to 
the substitute, so that global carbon emissions would decline. However, 
fossil fuels are non-renewable and the competitive supply gives a price 
path of the fuel which depends on both present and future demand. When 
this ‘Hotelling feature” is taken into consideration, the whole price path 
of the fuel will shift downwards as a response to the reduced cost of the 
substitute. An implication of this is that it is no longer obvious that 
greenhouse gas emissions decline in the near future. An important policy implication of the paper”s results is that techno-
logical improvement in the production of renewable energy cannot in 
itself be trusted as a good mechanism to reduce greenhouse gases. While 
technological improvement may be a significant feature of international 
climate cooperation, it is important that this cooperation also focuses 
directly on emissions reduction.

3. Articles with a main focus on 
optimization 
This chapter presents articles containing numerical analyses that focus 
mainly on optimization. 
3.1 Analyses with the DICE Model 
In his book A Question of Balance (Nordhaus, 2008), William Nordhaus 
describes the most recent version of the integrated assessment model 
DICE (Dynamic Integrated model of Climate and the Economy),	
16 using 
this to analyse a number of key issues: 
i.)	
 	the calculation of emission path and climate change under BaU; 
ii.)	
 	the derivation of the optimal emission path and associated climate 
change; 
iii.)	
 	as ii) but with the addition of various exogenous constraints, such 
as a limit on the atmospheric concentration of carbon; 
iv.)	
 	the consequences and costs of va rious climate policies that have 
been suggested; 
v.)	
 	the consequences and costs of lim ited participation in an interna-
tional climate agreement. 
 We will start by giving a very brief description of the DICE model be-
fore going on to discuss these issues. 
DICE is an aggregate model for the world economy. Total world out-
put at any time is assumed to be given by the following output function 
(omitting time references): 
 
(3.1) Q	
	(T )1	12		F(K ,L ) 
 
In the absence of climate change costs and mitigation costs, output 
would simply be , which is a Cobb-Douglas function of capital 
F (K ,L )
 	
 	16 The first version of DICE was presented in Nordhaus (1979).

(K ) and labour ( L).	17 Technological progress is also assumed, so that F 
increases over time for given values of K and L. Climate change costs are 
given by 
 , which is declining in gl
oba	
 l mean temperature (above 
pre-industrial level), with . The term (
T )	
(0)	1 1	12		 gives the output 
loss due to mitigation of CO	
2, where 	 is the control rate of emission, 
telling us how much emissions are reduced below BaU emissions. BaU 
emissions are proportional to potential output F, but lower the higher the 
control rate 	
 is. Total emissions are thus: 
 
(3.2) 	
(1 		)

)	F
(K ,L


 E	
 
The proporti
onality

factor 	
 is assumed to decline exogenously, but 
the growth in F nevertheless implies that uncontrolled emis-
sions grow ov er tim

e. 	
 F
(K ,L )
	
In addition to
 various standard ec onom

ic equations (such as output 
equalling consumption plus investment , labour being determined by po-
pulation) the model contains equations determining the climate variable 
T. These equations give T as a lagged variable in the stock of carbon in 
the atmosphere, the development of which depends on the path of emis-
sions E. 
The choice of all parameters in the model is based on estimates taken 
from various sources. In particular, in the mitigation cost function it is 
assumed that 	
 	, implying that a doubling of the control rate (e.g. 
from 10% to 20% or from 50% to 100%) increases the output loss by a 
factor of (approximately) 7. Marginal mitigation costs increase by a fac-
tor of about 3.5 when the control rate is doubled, so that marginal mitiga-
tion cost at a control rate of 0.5 is about 30% of what it is if the control 
rate is 1. Moreover, the parameter (which is assumed to decline exo-
genously o

ver time) is set so that the marginal cost of completely elimi-
nating emissions ( 	
22.8	
1	
1) at the end of this century is approximately 
US$260 per ton of CO
2. This assumption implies that a 50% reduction in 
emissions relative to BaU – i.e. 0.5	
	 – at the end of this century will 
give a marginal m	
itigation cost of about US$75 per ton of CO	
2 (but 
higher in, e.g., 2050 since mitigation costs are assumed to decline over 
time). BaU predictions for emissions from DICE are on disaggregated num-
bers from 12 regions of the world. Total population is assumed to reach 
about 8.5 billon, while per capita consumption is assumed to have an 
average growth rate of 1.3% per year in this century (i.e., considerably 
lower than the growth rate from 1960-2000, which was 2.5% per year). 
Carbon emissions per unit of GDP fell by 1.7% per year during 1960-
2000, but due to a changing composition of output the decline is expected 
to be only 0.6% during the present century. 
 	
 	17 See section 3.5 for an explanation and discussion of types of production functions.

Under BaU the predicted temperature increase is about 3 degrees in 
the end of 2100 and more than 5 degrees in 2200. Aggregate climate 
costs for the world are assumed to be about 4.5% of world GDP for a 
temperature increase of 4 degrees, and about 10% for a temperature in-
crease of 6 degrees. The discount rate in the DICE model is reached by using the Ramsey 
equation (2.6), with parameters 	
 and 		 of 0.015% and 2 respectively. 
With a growth rate of per capita consumption of 1.3% this gives r(t) = 
0.041 – i.e. 4.1%. 
The DICE model is used to calculate the optimal climate policy. The 
objective function is an inter-temporal welfare function of the type (3.5) 
discussed in section 3.3, with the parameters given above. Consumption 
is equal to output (given by 3.1) minus investment, which is endogenous 
and chosen together with the climate policy in order to maximize social 
welfare. The full optimum is summarize d in Table 3.1. Perhaps the most 
striking result is that the optimum gives quite modest emission reduc-
tions, in particular in the near future. This implies that CO	
2 concentra-
tions will continue to rise during the next couple of hundred years to quite 
high levels, with a correspondingly high temperature increase. These 
results are closely linked to the assumptions made about the discount rate 
and the assumed costs of climate ch ange. With either a lower discount 
rate or higher estimates of climate chan ge costs, the optimal time path of 
emissions, CO	
2 concentrations and temperature increases would be lower. 
In addition to calculating the full optimum, various constrained optima 
are calculated. A particularly interes ting case is the one in which an upper 
limit of 2 degrees Celsius temperature increase is imposed on the optimi-
zation. The results of this are given in Table 3.1. Also for this case the 
optimal policy in the near future is quite modest: the carbon price in 2015 
is only US$20 per ton of CO	
2. However, it rises rapidly, by 3.6% per year 
from 2015 to 2055, so that it reaches US$83 in 2055. It also continues to 
rise after 2055 and is US$220 per ton of CO	
2 in 2105. Note that the time 
path of the carbon tax and of emissions in this case is not strongly influ-
enced by the costs of climate change. The assumed discount rate is, how-
ever, of some importance. With a lower discount rate it would be optimal 
to reduce emissions more in the near future and less towards the end of 
this century, implying a higher initial level and flatter time path in the 
price of carbon. Although the price of carbon rises rapidly in the case with the tem-
perature limit of 2 degrees Celsius, th e level of the price path is quite low 
compared with several other studies (see, e.g., chapter 4). With an upper 
limit on the acceptable temperature increase, the main factor that affects 
the level of this price path is the assumption made about present and fu-
ture technology for reducing emissions. As mentioned previously, the 
DICE model assumes that the marginal cost of completely eliminating 
emissions at the end of this century is approximately US$260 per ton of

CO	2. Compared with several other studies, this seems to be very optimis-
tic. With the higher costs of very larg e reductions of emissions (which are 
necessary to limit the temperature increase to 2 degrees Celsius), the 
whole time path of the carbon price would be shifted upwards. In section 2.3 we showed that aggregate abatement costs depend 
strongly on how a given amount of emissions is allocated across sources 
and sectors. The cost-minimizing allocation is often called the cost-
effective allocation and deviations from cost-effective policies typically 
give quite large cost increases. This is examined in chapter 6 of Nord-
haus”s book. Of the several examples given there, we will look at two 
here. First, under the Kyoto Agreement only countries accounting for 
about 33% of global emissions in 2010 are given quantitative commit-
ments. The cost of reaching the Kyoto limits is calculated to be 7.4 times 
higher than the costs of the same global emission reduction with full par-
ticipation. The second example concerns an agreement between the USA, 
EU and eight other large countries: China, Russia, India, Brazil, Canada, 
Japan, Mexico and South Africa. Be tween them, they accounted for 75% 
of global emissions in 2004. Reducing emissions in these countries, with-
out imposing any restrictions on emissions from the remaining countries, 
gives total costs that are 68% higher than the costs of the same global 
emission reduction with all countries participating in a cost-effective 
agreement. These numerical illustrati ons show very clearly how impor-
tant it is to achieve an internationa l climate agreement with the broadest 
possible participation.

Table 3.1 Major variables for three cases analysed with DICE 
 2015 2055 2105 2200 
Industrial CO	2 emissions, Gt 
carbon BaU 
Optimum 
2ºC limit 
 8.74 
7.37 
6.88 
13.47 
9.93 
6.72 19.75 
11.31 
1.64 	
Emission reduction as per-
centage of BaU emissions 
BaU 
Optimum 
2ºC limit 
 
16 
22 
27 
50 
44 
92 
Carbon price, US$ per ton CO	
2 BaU Optimum 
2ºC limit 
 
11 
20 
27 
83 
59 
220 
CO	
2 in atmosphere, ppm 
 BaU 
Optimum 
2ºC limit 
 405 
405 
405 
508 
481 
466 686 
586 
465 1183 
659 
442 
Mean global temperature 
increase, degrees Celsius BaU 
Optimum 
2ºC limit 0.96 
0.95 
0.95 1.82 
1.68 
1.61 3.06 
2.61 
2.00 5.30 
3.45 
2.00 
 	
3.2 Analyses with the ENTICE Model 
We have pointed out previously th at assumptions about future techno-
logical development are important for: 
 what the optimal emission path is; 	
 the total cost of achieving any given emission path; 	
 the carbon price needed to achieve any given emission path. 
 
During the last five to ten years there have been many economic analyses 
that explicitly incorporate endogenous technology development. This 
literature includes both purely theoretical models and numerical models 
of various types. An example of the latter is ENTICE	
18, which was de-
veloped by David Popp (2004, 2006). Th is model is very similar to the 
DICE model discussed in section 3.1, the main difference being that 
technology development is explicitly modelled instead of being exoge-
nous. Like DICE, ENTICE is an aggregate model for the world economy. It 
is an optimization model with the sa me type of objective function as DI-
CE: i.e. an inter-temporal welfare function of the type (3.5) discussed in 
section 3.3. The main difference be tween DICE and ENTICE is the mod-
elling of the production side of the economy. Below we present the ver-
sion in Popp (2006) that includes a backstop technology, i.e. a non-
carbon energy input, which has a cost that declines over time as a re-
sponse to R&D. 
 	
 	18 The DICE modell extended with Endogenous Technological change.

Instead of (3.1) and (3.2), the present model assumes that net output is 
given by	19 
 
(3.3) 
 Q	
	(
T )F (K ,L ,E )	peepn(H	n)n
 
where climate change costs are, as in DICE, given by 	
( T ). In the ab-
sence of climate change costs and mitigation costs, gross output would 
simply be , which in ENTICE is a Cobb-Douglas function of 
capital ( K), labour ( L) and an input E, which is ‘effective energy”. 
F
(K ,L, E)
Effective energy is produced by a co mposite of fossil energy, which by 
choice of units is equal to emissions e, and non-fossil energy ( n), as well 
as a technology or knowledge variable 
H	
E	
 	
(3.4) 
 
where the functions E and 	
 are CES production functions. The elasticity 
of substitution between the two inputs in E is assumed to be 1.6. Popp 
considers several alternatives for the elasticity of substitution between e 
and n. In the results presented below we restrict ourselves to what Popp 
considers to be the ‘base case”, which has an elasticity of substitution of 
2.2. To get net output we must subtract the cost of using fossil energy (p	
ee) 
and the cost of using non-fossil energy . The variable H
n is 
knowledge; the higher it is, the lower the cost of the non-carbon energy 
source. There are thus two knowledge variables, H	
E and H	n, in the EN-
TICE model. An increase in H	
E can be interpreted as increased energy 
efficiency, implying that more output can be produced for the same input 
of energy and other items. An increase in H	
n can be interpreted as im-
proved technology in the production of non-carbon energy, thus lowering 
the cost of such energy. 	
pn( H	n)n	
The knowledge variables H	E and H	n depend on knowledge creation, 
which in turn depends on R&D investments and current knowledge. In 
continuous time the relationships take the form (omitting subscripts for 
the two types of knowledge) 
(3.5) 	
bc	
HZ H
ZaIH		
	
 
 
where I is R&D. Finally, output can be used for consumption, investment 
in real capital ( K) or the two types of R&D, I	
E and I	n.20 
 	
 	19 See section 3.5 for an explanation and discussi on of types of production functions and the concept 
of the elasticity of substitution. 
20 Popp assumes that some of the I	E and I	n types of R&D crowd out other R&D that is assumed to 
have a higher return than other investments. Technica lly, this is modelled so that one unit increase in I	
E 
or I	
n, gives more than one unit reduction in investment of physical capital.

In Popp (2004, 2006) several exercises are done using the ENTICE 
model(s), many of them comparisons of different specifications of the 
model and of the sensitivity of variou s parameters. We will stick to what 
we interpret as the main version of the model: i.e. one with a backstop 
technology, endogenous R&D and the ‘base case” parameters of Popp 
(see section 3.1 in Popp, 2006). 
Three optimization exercises are of particular interest: 
 
i.)
 	BaU; 
ii.)	
 	optimal policy; 
iii.)	
 	constant emissions. 
 
In all cases, optimization is with respect to the three types of investment 
(physical capital and two types of R&D) and the two types of energy. Un-
der i) there is no concern for the clim ate and the carbon price is therefore 
zero. However, there will be investment in both types of R&D. The reason 
for this is that energy efficiency and low costs of non-carbon energy are 
socially valuable even if there is no concern for the climate. Under ii) the 
climate effects are taken into account in the optimization. Finally, iii) gives 
a constrained optimum, the constraint being that emissions (and thus the 
use of fossil energy) are held constant at their 1995 level. 
To demonstrate the importance of policy-induced R&D, the optimiza-
tion cases ii) and iii) are also undert aken holding R&D levels equal to 
what they were under BaU. 
Results for key variables are summariz ed in Table 3.2. From this we 
can see the following: 	
 The optimal climate policy is very modest, emissions continue to 
grow during all of this century and the difference from the BaU 
emissions is quite small. This result of course depends crucially on the 
assumed climate change costs, as well as on the discount rate. 	
 Given the moderate reduction of emissions under the optimal climate 
policy, it is not surprising that R&D in energy efficiency and in the 
production of non-carbon energy is only a little higher than under BaU. 	
 The carbon tax necessary to keep emissions at their 1995 level is very 
high – e.g. much higher than the DICE model gave for a limit of 2 
degrees Celsius, despite the fact th at this constraint requires lower 
emissions in the long run than the 1995 level. This result makes it 
clear how important the details of the production specification are for 
the results that are reached. 	
 When emissions are required to be constant, optimal R&D levels are 
significantly larger than they are under BaU, in particular for R&D 
aimed at improving the technology of non-carbon energy.

As mentioned above, the case with constant emissions is studied holding 
R&D levels equal to what they were under BaU: i.e. at lower R&D levels 
(see Table 3.2). Intuitively, we migh t expect that lower R&D would imply 
that the carbon price necessary to keep emissions constant would be higher. 
This is true for the version of the model without a non-carbon energy input 
(although the difference in carbon price is very small). However, in the full 
model with non-carbon energy we get the opposite result: i.e. the carbon 
price is slightly higher for the case with low R&D than for the case with 
high R&D. While this result might seem counterintuitive, the idea that 
increased energy efficiency and/or lower costs of non-carbon energy result 
in lower use of carbon energy is based on an implicit assumption that out-
put is unaffected. However, output ma y increase as a consequence of in-
creased energy efficiency and/or lo wer costs of non-carbon energy, imply-
ing that the intuition may be wrong. To illustrate this more formally, we 
insert (3.4) into (3.3) so that we may write the output as follows: 
 
 Q	
Q
(T ,K ,L ,e ,n ,H	E)peepn( H	n)n
The optimal choices of e and n are (where subscripts to Q represent par-
tial derivatives): 
 
 
 Q	
e(
T ,K ,L ,e ,n ,H	E)	pe	
 
 
 Q	n(
T ,K ,L ,e ,n ,H	E)	pn( H	n)
From standard micro theory we know that if p	
n(H	n) goes down, n will 
increase, while e will go down if the cross-derivative Q	
en is negative, but 
increase if the cross-derivative Q	
en is positive. If H	E increases, whether e 
increases or decreases will depend on the sign and size of all cross-
derivatives Q	
eHE	 , Q	nHE	 and Q	en . All of these cross-derivatives depend on 
the properties of the underlying functions F and E and on the size of the 
variables entering the functions. 	
Table 3.2 Major variables for three cases analysed by Popp (2006, tables 4 and 6) 
 2015 2055 2105 
Industrial CO	2 emissions, Gt 
carbon BaU 
Optimum 
Constant emissions 7.19 
7.66 
6.19 
 10.98 
9.81 
6.19 14.13 
11.59 
6.19 	
Emission reduction as percent-
age of BaU emissions BaU 
Optimum 
Constant emissions 
5 
23 
11 
44 
18 
56 
Carbon price, US$ per ton CO	
2 BaU Optimum 
Constant emissions 
4 
182 
10 
491 
20 
801 
Energy efficiency R&D ( I	
E) as 
percentage of BaU BaU 
Optimum 
Constant emissions 100 
101 
106 
 100 
102 
109 
100 
102 
109 
Non-carbon energy R&D ( I
n) as 
percentage of BaU BaU 
Optimum 
Constant emissions 100 
107 
133 100 
107 
161 100 
105 
177

3.3 Market Equilibria with Endogenous 
Technological Development 
Grimaud et al. (2008) have extended the ENTICE model in three 
important directions: first, carbon cap ture and storage (CCS) is added; 
secondly, the model is designed so that, in addition to the optimal 
outcome, various sub-optimal market outcomes can be studied; thirdly, 
the market for fossil fuels is modelled along the principles described in 
section 2.5. In other respects their model is roughly in line with the 
ENTICE model. However, emissions e are no longer equal to the use of 
fossil energy, denoted by F in this chapter. Instead we have 
 e	
FS, 
where S is the amount of CCS. In the net output function corresponding 
to (10.1), we must now also subtract the cost of CCS, which is 	
pS(HS,S
F)S. The unit cost of CCS, F
p	S(
H	S, S	)
, is assumed to be 
increasing in the proportion of carbon captured – i.e. S/F – and declining 
in a knowledge variable H	
S. The knowledge variable is assumed to 
develop endogenously over time, ju st like the two other knowledge 
variables in the ENTICE model (for energy efficiency and non-carbon 
energy production). The Grimaud et al. model thus has three knowledge variables. Unlike 
ENTICE, markets for knowledge – i.e. for innovations – are explicitly mod-
elled. It is assumed that only a share (with 0<	
i	i		<1) of the social value of 
an innovation of type i is paid to the innovator (in the absence of subsidies). 
The unregulated market outcome therefore gives too few innovations of all 
three types. This market imperfection can be corrected through subsidizing 
the R&D sectors, and if the subsidies are equal to 
1	i	 the market values of 
innovations will be identical to the social values. The emissions under BaU are not reported directly. However, the con-
centration of CO	
2 in the atmosphere reaches about 1000 ppm in 2105 
under BaU (see Figure 8 in the paper), which is much higher than in the 
analysis with DICE reported in section 3.1 (686 ppm). This means that 
emissions under BaU are considerably higher in this study than in the 
DICE study. There are four policy variables in the model: a carbon tax and subsidy 
rates for the three types of R&D. With appropriate time paths for these 
four policy instruments, the full social optimum is achieved. This full 
optimum is derived using a climate cost function of a similar type as in 
DICE. It is also derived when a constraint on atmospheric concentration 
of CO	
2 is added, the two constraints considered being 550 ppm and 450 
ppm CO
2. The latter is roughly in line with the limit of 2 degrees Celsius 
analysed by Nordhaus (see section 3.1). 
The carbon tax associated with the optimal outcomes is somewhat 
higher than Nordhaus”s results, in par ticular for the case of stabilization 
at 450 ppm. Here the carbon tax in 2015 is US$48 per ton CO	
2, rising to

US$200 in 2055.	21 After 2055 (which is roughly when the limit of 450 
ppm is reached) the carbon tax declines . The reason for the decline after 
2055 is the improvement of the three knowledge variables (see section 
3.1 for a general discussion of this). In the study various sub-optimal cases are considered. This is done by 
keeping some policy variables equal to their values at the full optimum 
and setting other variables equal to zero. For example, if we set the car-
bon tax equal to zero but keep the subsidy rates at their optimal values, 
there is hardly any reduction of emissions compared with the BaU case. If 
we depart from the full optimum with the 450 ppm limit by setting the 
subsidy of either CCS or non-carbon energy equal to zero, CO	
2 concen-
trations will continue to rise afte r 2050 and reach about 550 ppm at the 
end of this century. The exercise of setting one or severa l policy instruments equal to zero 
and keeping the rest at their full optimum values gives some useful in-
sights. In our opinion an alternative ex ercise would be at least as interest-
ing. This would be to set, say, the R&D subsidy rates equal to zero and 
recalculate the second-best optimal carbon tax with this constraint. Simi-
larly, we could constrain the carbon tax to not be ‘too high” – i.e. under 
some limit that may increase over time – and reoptimize with respect to 
R&D subsidies. The model seems well suited to this type of exercise, 
which would be worth pursuing in a later version of the paper. 	
3.4 Analyses with the WITCH Model 
WITCH (World Induced Technical Change Hybrid) is a model developed 
at FEEM (the Fondazione Eni Enrico Matei) in Milan and Venice. A 
hybrid, it is a global model with a ne oclassical optimal growth structure 
(top-down) and a detailed energy input component (bottom-up). The top-
down part of the model is very similar to both DICE (see section 3.1) and 
in particular ENTICE (see section 3. 2). The main difference is that 
WITCH is a multiregional model, with the world divided into 12 regions. 
Although the energy sector is similar to ENTICE in the way technology 
change is endogenized, it is modelled in much more detail than in EN-
TICE and most other integrated assessment models. 
We will start with a brief description of the main version of the model 
as described in FEEM WP 10.2007 (Bose tti et al., 2007a). In several appli-
cations the model has been slightly modi fied to cope better with the issues. 
The welfare function of each region is of the ‘standard” type described 
earlier, in particular in section 2.2: i.e. 
 
 W	
	et
0		N (t)u (c (t)) dt
 	
T	
 	 	21 The corresponding carbon taxes for the case of th e limit of 2 degrees Celsius analysed by Nord-
haus are US$20 and US$83 resp ectively (see Table 3.1).

where u is a utility function of per capita consumption c(t), while N(t) is 
population. For all regions u(c )	
Lnc , and	and T are identical across 
regions. T is equal to 150 years, while 	
 is not constant but starts at 3% 
and declines gradually to 2% during the 150-year period. Using 	
0.03 
and consumption growth rates from 2002 to 2032 from Table 1 of WP 
95.2007	
22 we find interest rates from (according to the Ramsey formula: 
(2.6)) for OECD and non-OECD equal to 5.1% and 7.5% respectively. Consumption is equal to total out put minus investments of various 
types, extraction or import costs of fuels, various operation costs of en-
ergy and costs associated with carbon capture and storage (CCS). Total 
output for each region depends on ex ogenous total factor productivity 
growth and the development of labo ur, capital and energy services in a 
similar way to ENTICE. Total output fo r each region is also assumed to 
be affected by future climate change in the same way as described in 
section 3.1 for DICE. 
The gross output function corresponding to in ENTICE 
(3.3) is a constant returns to scale nested CES (constant elasticity of sub-
stitution) function. As in ENTICE, the elasticity of substitution between 
K and L is assumed to be 1. While the substitution of elasticity between 
energy services and a composite of labour and capital was assumed to be 
1 in ENTICE, the elasticity is assumed to be only 0.5 in WITCH. F
(K ,L ,E )	
23 
Energy services in each region are modelled in a similar way to that 
described in section 3.2 for ENTICE: i.e. 
 
E	
s( E	n,H )
where E	
n is energy and H is knowledge. The function is a CES function 
 w
ith an elasticity of substitution of 0.4: i.e. much lower 
than in ENTI
 CE, where this elasticity is assumed to be 1.6. 
E	s(
E	n,H )
The knowledge variable H depends on knowledge creation, which in 
turn depends on R&D investments and current knowledge, and is mod-
elled as described by (10.3). Howeve r, unlike the case with ENTICE, the 
costs of producing various types of energy cannot be affected through 
directed R&D in the version of WITCH outlined here. Energy E
n is a CES function of electric and non-electric energy, with an 
elasticity of substitution equal to 0.5. Finally, both electric and non-eclectic 
energy can be made in several different ways, formally modelled as CES 
production functions with the different fuels and/or technologies as inputs. 
Elasticities of substitution are larger than 1 for all types of electricity. For 
non-electric energy the el asticity of substitution between gas, oil and bio-
fuel is assumed to be equal to 0.5. For wind and solar electric energy there 
 	
 	22 We actually use growth rates of GD P per capita for the case in which CO	2 concentrations are sta-
bilized at 450 ppm. 	
23 The results reported in Chapter 3.5 indicate that WITCH elasticity seems more realistic than EN-
TICE elasticity.

is endogenous technological development through learning by doing; costs 
in each region are lower the higher the worldwide capacity. The model”s solution concept is an open-loop Nash equilibrium: each 
country chooses its own policy variable s, taking policies of other countries 
as given. Even when the climate exte rnality is ignored, the model gives an 
outcome that is not Pareto efficient, as there are various imperfections in 
the market. Among these ar e differences between countries in marginal 
productivities of capital and non-in ternalized technology spillovers. 
The model has been used for several exercises related to climate pol-
icy. Among these are the consequences of introducing limits on the con-
centration of CO	
2 in the atmosphere and finding the most cost-effective 
way to achieve this. Such an exercise gives a particular time path for total 
emissions and allocates these emissions across countries so the price of 
carbon emissions (carbon tax or quota price) is equalized across coun-
tries. Results for this exercise ar e reported in FEEM WP 95.2007 (Bosetti 
et al., 2007b). Two stabilization goals are considered, 450 ppm CO	
2, cor-
responding to roughly 550 ppm CO	
2-e, and a less ambitious stabilization 
goal of 550 ppm CO	
2, corresponding to roughly 650 ppm CO	2-e. Below 
we give the results for the most ambitious stabilization goal. 	
Table 3.4: Results from FEEM WP 95.2007 (Figures 1, 6 and 9 and Tables 1 and 2) 
 2012 2032 2052 2102 
Industrial CO	2 emissions, 
BaU, Gt carbon World 
 
 8 12 16 21 	
Emission reduction as per-
centage of BaU emissions 
World 
OECD 
Non-OECD 
 12 
 56 
52 
58 72 
 86 
Reduction in energy/GDP as 
percentage of BaU World 
OECD 
Non-OECD 
 34 
26 
38 
Reduction in CO	
2 per unit of 
energy as percentage of BaU World 
OECD 
Non-OECD 
 33 
34 
31 
Energy R&D increase as 
percentage of BaU (approx.) World 
OECD 
Non-OECD 
 50 130 175 330 
Approx. carbon price, US$ per 
ton CO	
2 20 
 80 
 350 
 	
 
Not surprisingly, emissions must be cut dramatically in order to achieve 
the stabilization goal of 450 ppm CO	
2. Compared with BaU, the cuts are 
not very different for OECD countries and non-OECD countries. How-
ever, since BaU emissions increase more rapidly for non-OECD countries 
than for other countries, emission reductions compared with 2002 levels 
are largest for OECD countries: OECD emissions decline by 31% from 
2002 to 2032, while non-OECD emissions grow by 5% during the same 
period.

For both OECD and non-OECD countries, energy saving and in-
creased non-carbon energy give about the same contribution to overall 
emission reductions (at least till 2032). We also see that energy-related 
R&D will increase significantly in the stabilization path compared with 
the BaU path. The carbon tax necessary to achieve emission reductions starts at a 
modest level, but becomes very high in 2050. The growth is more than 
7% per year, which seems high compared with the assumed interest rates 
(cf. the discussion in section 3.1). We suspect this has to do with the way 
the optimization is done, maximizing th e sum of the welfare functions of 
all countries. Since poorer countries have higher marginal utilities of 
consumption we want to transfer consumption to these countries. This 
cannot be done directly in the model, but since poorer countries have 
higher interest rates, we can help them be postponing emission reductions 
more than we would have done had we had other possibilities of transfer-
ring consumption to the poorer countries. R&D is endogenously determined in the model, with each country 
choosing R&D expenditure to maximi ze its own welfare given the re-
striction the country has on its emissions. From Table 3.4 it might be 
tempting to conclude that R&D plays an important part in the mitigation 
effort and that costs of reaching the stabilization target would be much 
higher had we not had this option. However, according to FEEM WP 
14.2009 (Bosetti et al., 2009), this is not the case. In this study the same 
stabilization target is achieved under the constraints that countries cannot 
expand their energy R&D investments beyond the BaU levels and that 
there are no learning by doing effects in the production of wind and solar 
energy. Compared with the unconstrained case, the world mitigation costs 
as a percentage of GDP increase only from 3.9% to 4.15% in 2050. The 
study argues that ‘costs can be reduced to a greater extent by widening 
the range of technological options available at competitive prices than 
through improvements in existing technologies”. To illustrate this, the 
model is run with restrictions on nuclear power (no increase from present 
capacity), not allowing CCS, and restrictions on the size of solar and 
wind energy (max. 30% of total electricity). By imposing these restric-
tions, mitigation costs in 2050 are increased from 3.9% of GDP to more 
than 7% of GDP. The study continues with a modification of the model which, if we 
have understood it correctly, allows for R&D to significantly reduce the 
costs of non-carbon types of energy (cf. ENTICE). With the modified 
version of the model, total mitiga tion costs in 2050 are reduced from 
3.9% of GDP to less than 2%. For further applications of the WITCH model, and also for short pol-
icy papers referring to studies using the WITCH model, see http:// 
www.feem-web.it/witch/.

3.5 Production Functions for Climate Policy Modelling 
In many economic models treating climate policy issues the production 
side of the economy (either for the whole economy or for a particular 
sector) is modelled by a production function with energy (E) and other 
inputs as arguments. Consider first the case with only one other input ( v), 
so that output is . Typically, it is assumed that when both (or 
more generally all) inputs increas e by1%, output also increases by 1%. 
An important characteristic of such a production function is the elasticity 
of substitution. Denote this by s: It tells us how the cost-minimizing ratio 
between E and v change as the price of E increases relative to the price of 
v . More precisely (and in obvious notation): If increases by 1%, 
E/v will decline by
 s %

. A high value of s means that it is easy to substi-
tute one input for the other, while the opposite is true is s is small. 
F
(E ,v )
p	E/p	v	
For a so-called Constant Elastic ity of Substitution (CES) production 
function, t

he elasticity s is constant, i.e. independe nt of E and v. A special 
case is , which describes a Cobb Douglas (CD) function: 	
1
s 
1	Ev
(,)
FE	v				. 
Several studies use a production function of the type 
where K, L and E stand for capital, labour and so
me

measure of energy 
input respectively. In some studies, su ch as in the ones discussed in sec-
tions 3.2 and 3.3, the F -function is a Cobb-Douglas function: i.e. the elas-
ticity of substitution is 1 between all three inputs. In other studies, some 
type of nested CES function is used: e.g. 	(,,)
FKLE
((,),) KL E
(,,)
FK	
LE			. 
This is called a (KL)E nesting structure and is the one used in the 
WITCH models (see section 3.4). For such a structure, there will be one 
elasticity of substitution between K and L, and another one between ( KL) 
and E. In the WITCH models the 	
	-function is a Cobb-Douglas func-
tion: i.e. the elasticity of substitution between K and L is 1. The elasticity 
of substitution between ( KL) and E in the WITCH models is assumed to 
be 0.5: i.e. lower than that assumed in ENTICE and the model used by 
Grimaud et al. Other nesting structures are also possible: i.e. (KE)L and 
(LE)K. The combination of the nesting structure and the assumed elastic-
ities of substitution describe how easy it is to reduce the use of fossil 
energy sources. It is therefore important to study what data can reveal 
about these issues. Edwin van der Werf (2007) has undertaken a thorough empirical ana-
lysis. Production functions are estimated both for different industries and 
for different countries. He has tested which types of nesting structure and 
what magnitudes of elasticity are suppor ted by the data. He has five main 
conclusions:

 The (KL)E nesting structure seem to fit the data best. 	
 For several countries and industries, the non-nested structure KLE 
seems to be as good as the (KL)E nesting structure.	
 	
 The size of the elasticities varies considerably over both countries and 
industries.	
 	
 The Cobb-Douglas production function is rejected by the data for all 
countries and industries.	
 	
 For the (KL)E nesting structure, the elasticity of substitution between 
( KL ) and E ranges from 0.1 to 0.6, while the elasticity of substitution 
between K and L ranges from 0.2 to 0.6.	
 	
 
The models we have considered in sections 3.2-3.4 use either a non-
nested KLE structure or a (KL)E structure. Those in sections 3.2 and 3.3 
use a Cobb-Douglas production function: i.e. assume elasticities of sub-
stitution equal to 1. Such high elastic ities are, according to van der Werf, 
rejected by the data. Also the WITCH model (see section 3.4), which has 
a (KL)E nesting structure, assumes an elasticity of substitution between 
( KL ) and E that is at the higher end of the range suggested by the data. 
Assuming an elasticity of substitution between ( KL) and E higher than 
it actually is will give an overly optimistic result regarding how easy it is 
to substitute away from fossil energy. The costs, and the necessary carbon 
price, associated with a particular emission goal may therefore be biased 
downwards compared with the true va lues. Moreover, if it is easy to mo-
ve away from fossil energy with existing technologies, the importance of 
developing new technologies will be underestimated. 
3.6 Future Climate Change Costs 
As shown in section 2.1, the optimal carbon price, and thus the optimal 
emission path, depends crucially on the size of climate change costs. In 
the studies we have considered so far, these costs have been treated as a 
reduction in consumption compared w ith the consumption level in the 
absence of climate change. However, by ‘translating” all negative climate 
effects into reduced consumption, it is easy to underestimate the true 
future costs. This is because some costs of climate change will come in 
the form of reductions in non-market goods, such as loss of biodiversity, 
effects on human well-being (health, amenities), various forms of ex-
treme weather events, risk of conflicts etc. Non-market goods of this type 
grow only slowly over time, or might even decline. If the number of pro-
duced market goods increases rapidly at the same time, we should expect 
an increased marginal valuation of non-market goods as time passes. 
Formally, assume that overall well-be ing is given by a utility function 
of the type u(c , E) where c is traditional consumption and E is a non-

market environmental good. The willingness to pay for one unit more of 
the environmental good in terms of the traditional consumption good is 
given by the ratio of marginal utilities u	
E/uc, which typically will increase 
if c/E increases. In most studies of climate change effects far into the 
future, traditional consumption is assumed to grow significantly. For 
instance, in both the Stern Review (see section 4.2) and Nordhaus”s ana-
lysis (see section 3.1) per capita consum ption is assumed to grow at a rate 
of 1.3% per year if climate change is ignored. This makes per capita con-
sumption about 12 times higher in 2200 than it is today. Even with the 
worst climate outcomes considered by Stern (giving an output loss of 
about 35%) consumption in 2200 will be about eight times higher than 
today. At the same time, some non-market goods (often defined in terms 
of quality) will be about as today, or might even decline. With such large 
changes in c/E, there is good reason to expect willingness to pay for in-
creased E (or to avoid a deterioration of E) to be much higher than today. 
Exactly how much higher will depend on the elasticity of substitution 
between the two goods. Hoel and Sterner (2007) have made a formal analysis of these issues 
using a CES utility function. This has been followed up by Sterner and 
Person (2008), who have incorporated them into a model that in other 
respects is practically identical to Nordhaus”s DICE model. They assume 
that about half the climate effects are in non-market goods and that the 
elasticity of substitution between tr aditional consumption and such non-
market goods is equal to 0.5. With this modification of the DICE model, 
the optimal climate policy is much stri cter than what Nordhaus suggests. 
Even with the high discount rate us ed by Nordhaus (4.1%) optimal emis-
sions decline sharply in the second half of this century, implying that 
CO	
2-concentrations reach about 450 ppm in 2100 and then decline. This 
is a very similar result to what we found in the analysis with DICE in 
section 3.1 when the 2 degree limit was added: see table 3.1. 
The exact numbers derived from Sterner and Person should not be ta-
ken too literarily, as our knowledge about future preferences over tradi-
tional consumption goods and non-mark et environmental goods is obvi-
ously quite limited. But the analysis shows that by introducing some quite 
small and not implausible changes into the DICE model, major numerical 
conclusions may change dramatically. 	
3.7 Handling Uncertainty 
There are many uncertainties relating to almost all aspects of climate 
policy and climate change. In particular:

 The development of future climate policies and climate agreements is 
uncertain. 	
 For given policies, their cost and impact on emissions are uncertain. 	
 For a given emission path, the climate development is uncertain. 	
 For a given climate development, the impact on nature is uncertain. 	
 For a given impact on nature, the economic impact (including 
valuation: see section 3.6) is uncertain. 
 
While these uncertainties are frequently mentioned in the economics lit-
erature, very few studies provide an explicit formal treatment of them. 
Typically, some sensitivity analysis is undertaken, but the main analysis 
uses point estimates of central variables and parameters as if there were 
no major uncertainty associated with them. Perhaps the largest area of uncertainty relates to the impact of emis-
sions on the climate. There are two as pects to the uncertainty: first, the 
relationship between anthropogenic increases in CO	
2 and other green-
house gases and the ultimate increas e in GHG concentrations, including 
heat-induced feedbacks (such as CH	
4 from permafrost) and the weaken-
ing of carbon sinks; second, the relationship between GHG concentra-
tions and the climate. The latter relationship is often characterized by the 
so-called climate sensitivity, which tells us by how much the global aver-
age temperature will ultim ately increase as a response to a doubling of 
the atmospheric concentration of CO
2-e. 
According to IPCC (2007), climate sensitivity is ‘likely to be in the 
range 2	
oC to 4.5	oC with a best estimate of 3	oC, and is very unlikely to be 
less than 1.5	oC. Values substantially higher than 4.5	oC cannot be ex-
cluded, but agreement of models with observations is not as good for 
those values.” In an important recent contribution, Martin Weitzman 
(2009) focuses on the possibility of ‘values substantially higher than 
4.5	
oC”. Based on the scientific literature on this topic, he argues that there 
is a 5% probability of climate sensitivity higher than 7 degrees	 Celsius 
and a 1% probability of climate sens itivity higher than 10 degrees Cel-
sius. He combines this with a model in which climate costs become very 
high for large temperature increases. Moreover, the probability distribu-
tion of temperature increases is ‘fat-tailed” in the sense that as we move 
towards higher temperature increases, the probabilities decline less rap-
idly than the damages increase. As a consequence, he finds that expected 
climate costs will be ‘infinitely high”. This is of course not meant liter-
ally, but it implies that actual expect ed climate costs will be very sensi-
tive to both details of the probability distribution of the climate sensitivity 
and the exact costs of very large temperature increases. Weitzman argues 
that most analyses of optimal climate policy (such as the studies dis-
cussed previously in this chapter) ignore this important feature and may 
therefore give very misleading results. A similar argument has recently

also been made by Nævdal and Vislie (2008), based on a formal analysis 
resembling Weitzman”s. They conclude that ‘if cost-benefit calculations 
are done within a model that encompasses the type of catastrophic risk 
that…scientists worry about, the resu lting stabilization target will only be 
slightly influenced by the discount rate”. 
3.8 Alternative Policies for Achieving Emission Goals 
Policy instruments for achieving emi ssions goals were discussed theoreti-
cally in section 2.4, where an important conclusion was that the correct 
carbon price is a crucial element in an optimal policy package. However, 
we also briefly discussed some reas ons why it could be desirable to sup-
plement the correct carbon price with other policy instruments. In policy 
debates the view is sometimes put forward that other policies should be 
an alternative rather than a supplement to the correct price: i.e. ‘a carrot is 
better than a stick”. Economists are re asonably unanimous that the correct 
price is crucial in order to get an efficient outcome. There is, however, no 
guarantee that this type of policy recommendation will be followed. It is 
therefore interesting to see numerical studies indicating how large the 
efficiency loss may be if we try to achieve an emission goal with policies 
other than a suitable emission price. One example of such a study is Fi-
scher and Newell (2008). Fischer and Newell start by presenting a simple two-period model of 
the electricity sector of the economy. There are three ways to produce 
electricity: by coal, natural gas and a renewable source. The first two lead 
to CO	
2 emissions. The cost function of renewable energy is assumed to 
develop endogenously depending on th e growth of ‘knowledge capital”. 
The growth in knowledge depends partly on how much electricity is pro-
duced by renewables in the first period – learning by doing (LbD) – and 
partly by how much is spent on R&D directed at renewable energy in the 
first period. For both types of knowledge creation, it is assumed that only 
part of the social value of knowledge creation is appropriated by the 
agent causing the knowledge increase: i.e. the producer of renewable 
electricity for LbD and the research sector for knowledge resulting from 
R&D. This part of the model is therefore quite similar to the model de-
scribed in section 3.3 (Grimaud et al., 2008). In addition to the supply 
side of the electricity market, the demand side is modelled in a traditional 
manner and the market equilibrium can be calculated. The equilibrium 
will depend on the specification of policies. Six policy instruments are 
explicitly analysed:

i.) 	CO	2 emission price; 
ii.)	
 	tax on fossil-fuelled energy; 
iii.)	
 	tradable emissions performance standard; 
iv.)	
 	portfolio standard for renewable energy; 
v.)	
 	production subsidy for renewable energy; 
vi.)	
 	subsidies for R&D. 
 
The paper presents a theoretical discussion of the effects of each policy. 
Note that in order to reach the full social optimum, this model requires 
the use of three policy instruments: i.e. i), v) and vi). The carbon price is 
needed to correct for climate extern ality. The subsidy for renewable en-
ergy is needed to compensate for the f act that only part of the benefits of 
learning from a particular producer of renewable energy goes to this pro-
ducer. The subsidy for R&D is needed b ecause the research sector is able 
to appropriate only part of the social value of the innovations it creates. 
After the theoretical discussion, th e paper gives a numerical analysis 
of the US electricity sector based on this model. Obviously, such a simple 
model can only give a very rough description of such a complex sector as 
the US electricity sector. The numbers derived should therefore be looked 
upon only as very crude estimates of the true values. The paper first con-
siders the effect of a constant carbon tax of $7 per ton of CO	
2. This mod-
est carbon tax reduces CO	
2 emissions by 4.8%. The paper then considers 
each of the alternative policies in turn , used so that they give the same 
emissions reduction as the carbon tax. As theory would predict, all the 
alternative policies have higher costs. This is particularly true for the 
three subsidy policies, iv),
24 v) and vi). Policies iv) and v) give costs be-
tween two and three times higher than the costs of a carbon tax, while a 
pure R&D subsidy has a cost that is more than ten times as high as the 
cost of using a carbon tax. As mentioned above, the policy instruments i), v) and vi) must all be 
used in order to reach the full social optimum. In this model the full op-
timum is socially beneficial compared with the benchmark case of no 
policy even if the benefits of emissions reduction are ignored. The reason 
for this is that even in the absence of a climate externality, there will be 
some use of renewables and correcting for the market failure in knowl-
edge creation for such production more than outweighs the negative ef-
fect (when climate costs are ignored) of the carbon tax. 
 	
 	24 A portfolio standard for renewable energy is e quivalent to a subsidy for renewable energy fi-
nanced by a tax on fossil-fuel-based electric ity: see, e.g. Amundsen and Mortensen (2001)

3.9 Summary / discussion of articles 
with a main focus on optimization 
The preceding sections have considered the assumptions made and results 
for several optimization studies. They differ both in methodology (in 
particular, how technology and technological development are modelled) 
and in assumptions about exogenous va riables. Not all the assumptions 
are reported, making comparison between the studies quite difficult. 
The DICE model (section 3.1) differs from the other studies by having 
a very simple mitigation cost function, while the other studies (except the 
one in 3.6, which uses the DICE m odel) have production functions with 
fossil and non-fossil energy as inputs along with other inputs. Clearly, the 
latter type of analysis is ‘better” in the sense that it shows more funda-
mentally exactly how we can reduce carbon emissions. However, the 
mitigation cost function used in the DICE model has the advantage of 
being very transparent, so it is rela tively easy to see how the results of the 
analysis depend on the assumptions made about mitigation costs. As 
mentioned in section 3.1, it is assumed in this study that the marginal cost 
of completely eliminating emissions at the end of this century will be 
approximately US$260 per ton of CO	
2. Compared with the results of 
several other studies in this chapter, that estimate seems to be very low. 
The estimate is particularly importa nt for determining the appropriate 
carbon price path to attain ambitious c limate targets, such as the 2-degree 
limit. This price path is lower than carbon price paths for similar climate 
targets from the other studies: see Table 3.9. With a higher cost of com-
pletely eliminating emissions, the whole time path of the carbon price 
would be moved upwards. Analyses using a production function with various types of energy as 
inputs show exactly how carbon emissions can be reduced. However, 
their reliability depends crucially on parameters such as elasticities of 
substitution between different inputs and on how technological progress \
is modelled. Our knowledge of such parameters and function forms is 
based on historical data, which may give misleading estimates for a low-
carbon future. The study in section 3.5 shows that many analyses assume 
elasticities of substitution between ener gy and other inputs that are higher 
than the data suggest. This may give results that are too optimistic, in the 
sense that reduced emi ssions with current technologies can seem less 
costly than they will actually turn out to be. The importance of techno-
logical development can therefore also be underestimated. Of the studies 
reported in this chapter, it is the WITCH model that has a value for this 
elasticity that seems to be ‘best”, according to the study in section 3.5. 
In addition to the elasticity of substitution between energy and other 
inputs, the studies in this chapter have elasticities between knowledge and 
energy and between carbon and non-carbon energy. It is difficult to have

a firm opinion about the scale of these elasticities, but this is obviously of 
crucial importance for the results. The analyses discussed in sections 3.1-3.4 all use a model with a simi-
lar structure. However, there are also important differences. In particular, 
the possibility of CCS (carbon capture and storage) is included in the 
studies in sections 3.3 and 3.4, but not in those in section 3.2. 
In many of the studies an optimal emission path is derived. Most of 
these suggest that mitigation efforts should be quite moderate, implying 
optimal temperature increases beyond 3 degrees in the next century. It is 
important to bear in mind that thes e results depend crucially on what is 
assumed about the relationship betw een emissions and climate change, 
and how climate change will be valued in the future. Our current knowl-
edge of these factors is fairly limited, but the studies reported in sections 
3.6 and 3.7 indicate that by introducing some quite small and not implau-
sible changes into DICE and other optimization models, major numerical 
conclusions may change dramatically. We should therefore be very cau-
tious about claims that long-term concentration limits of, for example, 
450 ppm CO	
2 are too ambitious. 
Many of the studies also solve constrained optimization problems, 
where there is a limit on the atmospheric concentration of CO	
2 or on tem-
perature increase. These studies thus take a climate goal as given and 
calculate the optimum given this goa l (see section 2.1 for a theoretical 
discussion of this type of optimization). In Table 3.9 we have summa-
rized the results from the studies for such a constrained optimization. The 
climate goal is similar across the studies. Nevertheless, there are large 
differences in the time paths of the carbon price, which is an indicator of 
how difficult it is to achieve the goal. 
One of the most striking features of the table is the very large differ-
ence in carbon price, despite the climate goal being roughly the same. 
One might believe that this is due to large differences in BaU emissions. 
However, from Table 3.1 it is clear that the study with ENTICE has much 
lower BaU emissions than the other studies, which should tend to make 
the carbon price low, while this study actually gives a much higher car-
bon price than other studies do. It is not obvious to us why the analysis 
with ENTICE gives such a high carbon price compared to the analyses in 
the other two studies with similar production functions (Grimaud et al. 
and WITCH), but we suspect the reason is that CCS is not an option in 
the study with ENTICE. In any case, th e table indicates how the results of 
the analyses depend heavily on details of the assumptions made.

Table 3.9: Carbon prices for different studies 
 Concentration of 
CO	2 in 2100 (ppm) Temperature 
increase in 2100 
(degrees Celsius) Carbon price 2015 
(US$ per ton CO	2) 
Carbon price 2055 
(US$ per ton CO	2) 	
DICE 
2-degree limit 
 465 2 20 83 
ENTICE 
Constant 1995 
emissions 
 2 182 491 
Grimaud et al. 
450-ppm limit 
 450 48 200 
WITCH 
450-ppm limit 
 450 20 350 
 
Most of the studies discussed in this chapter say little about policy in-
struments to achieve emissions goals. Most of them report the carbon 
price associated with the derived 
emission path. Without any other mar-
ket or regulatory failures, this carbon price (as a carbon tax or a quota 
price) would be sufficient to achieve the desired outcome (see the discus-
sion in section 2.4). The studies in s ections 3.3 and 3.8 explicitly address 
market failures linked to technological development. These studies show 
how the carbon tax must be supplemente d with some subsidies related to 
technological development in order to achieve the desired outcome. The 
study in section 3.8 suggests that th e welfare loss may be very large if 
one tries to use subsidies as an alte rnative rather than a complement to 
carbon price.

4. Articles with a main 
focus on simulations 
This chapter presents large studies that treat a broad range of issues, and 
often consider quite complex and disaggregated models of the world 
economy. These models typically identify a policy that is consistent with 
a specific emission target and then calcu late the costs of such a policy. 
4.1 The Fourth IPCC Assessment Report 
The IPCC is a scientific intergovernmental body set up by the World 
Meteorological Organization (WMO) and by the United Nations Envi-
ronment Programme (UNEP). 
The IPCC was established to provide the decision-makers and others 
interested in climate change with an objective source of information 
about climate change. The main activity of the IPCC is to provide in re-
gular intervals Assessment Reports of the state of knowledge on climate 
change. The latest one is "Cli m

ate Change 2007", the Fourth IPCC As-
sessment Report. The Fourth IPCC Assessment Report was prepared by 
three working groups, each of which produced its own report: 	
 Working Group I, ‘The Physical Science Bases”, 	
 Working Group II, ‘Impacts, Adaptation and Vulnerability”, and 	
 Working Group III, ‘Mitigation”. 
 
In addition, the IPCC published a ‘S ynthesis Report” summarizing the 
work of all three groups. The IPCC does not try to estimate the economic cost of climate chan-
ge. Instead, Working Group II”s report includes a descriptive analysis of 
the likely impact on natural and human systems of an increase in the glo-
bal temperature and its associated changes. Working Group III”s report is of most relevance for this study. The 
summary for policymakers, released on 4 May 2007, is organized into 
five sections:

i.) 	Greenhouse gas (GHG) emission trends; 	 
ii.) 	
Mitigation in the short and medium terms across different economic 
sectors (until 2030); 	
 
iii.) 	
Mitigation in the long term (beyond 2030); 	 
iv.) 	
Policies, measures and instruments to mitigate climate change; 	 
v.) 	
Sustainable development and climate change mitigation. 	 	
 
The emission trends are based on a set of scenarios developed by the 
IPCC in a ‘Special Report on Emission Scenarios” (SRES). These assume 
no explicit climate policy such as, for instance, the Kyoto Protocol, so 
they should be interpreted as business-as-usual (BaU) scenarios. Basi-
cally there are four main families of scenario, A1, A2, B1 and B2, each 
with a group of sub-scenarios. The scenarios differ in four parameters: 
 	
 the size of economic growth, 	
 regional difference in economic growth, 	
 degree of global technology diffusion and 	
 success of less polluting technology. 
 
Together they cover a range of possible emission time paths which, ac-
cording to the IPCC, will lead to a concentration of GHG emissions in the 
atmosphere in the year 2100 of between 855 and 1,130 ppm CO	
2-e. 
Clearly, the chosen BaU scenario is important when considering both the 
physical need for emission reductions and the cost of emission reduc-
tions. Other key findings of the report are as follows: 
 	
 GHG emissions have increased since pre-industrial times, with an 
increase of 70% between 1970 and 2004. The largest increase in global 
GHG emissions between 1970 and 2004 came from the energy supply 
sector (145%). The increase in di rect emissions from transport was 
120%, from industry 65%, and from land use change and forestry 40%. 	
 The effect on global emissions of the decrease in global energy intensity 
(-33%) from 1970 to 2004 was smaller than the combined effect of 
global income growth (77%) and global population growth (69%), both 
drivers of increasing energy-related CO	
2 emissions. The long-term trend 
of declining carbon intensity in energy supply reversed after 2000. 
Differences in terms of per capita income, per capita emissions and 
energy intensity among countries remain significant. 	
 With current climate change mitigation policies and related sustainable 
development practices, global GHG emissi ons will continue to grow over

the next few decades . The SRES project an increase of baseline global 
GHG emissions by a range of 9.7 GtCO	
2-e to 36.7 GtCO	2-e (25%–90%) 
between 2000 and 2030. In these scenarios, fossil fuels are projected to 
maintain their dominant position in the global energy mix to 2030 and 
beyond. Hence CO	
2 emissions between 2000 and 2030 from energy use 
are projected to grow between 45% and 110% over that period. Two-
thirds to three-quarters of this increase in energy CO	
2 emissions is 
projected to come from non-Annex I countries, with their average per 
capita energy CO	
2 emissions being projected to remain substantially 
lower (2.8–5.1 tCO
2/cap) than those in Annex I countries (9.6–15.1 
tCO	
2/cap) by 2030. According to SRES , Annex I countries are projected 
to have a lower energy use per unit of GDP (6.2–9.9 MJ/US $ GDP) than 
that of non-Annex I countries (11.0–21.6 MJ/US$ GDP). 	
 In 2050 global average macroeconomic costs for multi-gas mitigation 
towards stabilization between 710 and 445 ppm CO	
2-e are between a 
1% gain and a 5.5% decrease of global GDP. For specific countries 
and sectors, costs vary considerably from the global average. 	
 Modelling studies show carbon prices rising to US$20–80/tCO	2-e by 
2030 and US$30–155/tCO	
2-e by 2050 are consistent with stabilization 
at around 550 ppm CO	
2-e by 2100. For the same stabilization level, 
studies since The Third Assessment Report (TAR, 2001)	
 that take into 
account induced technological change lower these price ranges to 
US$5–65/tCO	
2eq in 2030 and US$15–130/tCO	2-e in 2050. 
 
Most top-down, as well as some 2050 bottom-up assessments, suggest 
that real or implicit carbon prices of US$20–50/tCO	
2-e, sustained or in-
creased over decades, could lead to a power generation sector with low-
GHG emissions by 2050 and make many mitigation options in the end-
use sectors economically attractive. According to IPCC policies that pro-
vide a real or implicit price of carbon could create incentives for produc-
ers and consumers to significantly invest in low-GHG products, tech-
nologies and processes. Such policies could include economic instru-
ments, government funding and regulation. The cost of mitigation presented in Working Group III”s report is based 
on many different models and many different model runs. In 2030 macro-
economic costs for multi-gas mitigation, consistent with emissions trajecto-
ries towards stabilization between 445 and 710 ppm CO
2-e, are estimated at 
between a 3% decrease of global GDP and a small increase, compared to 
the baseline. However, regional costs may differ significantly from global 
averages. It is pointed out that new energy infrastructure investments in 
developing countries, upgrades of energy infrastructure in industrialized 
countries and policies that promote en ergy security can, in many cases,

create opportunities to achieve GHG emission reductions compared to 
baseline scenarios. Addi tional co-benefits are country-specific but often 
include air pollution abatement, balance of trade improvement, provision of 
modern energy services to rural areas and employment. Future energy infrastructure invest ment decisions, expected to total 
over US$20 trillion between now and 2 030, will have long-term impacts 
on GHG emissions, because of the long lifetime of energy plants and 
other infrastructure capital stock. The widespread diffusion of low-carb\
on 
technologies may take many decades, even if early investments in these 
technologies are made attractive. In itial estimates show that returning 
global energy-related CO	
2 emissions to 2005 levels by 2030 would re-
quire a large shift in the pattern of investment, although the net additional 
investment required ranges from negligible to 5%–10%. Baseline emissions scenarios published since SRES are comparable in 
range to those presented in the IPCC ‘Special Report on Emission Sce-
narios” (25–135 GtCO	
2-e/yr in 2100) Studies since SRES used lower 
values for some drivers for emissions, notably population projections. 
However, for those studies incorporating these new population projec-
tions, changes in other drivers, such as economic growth, resulted in little 
change in overall emission levels. Economic growth projections for Af-
rica, Latin America and the Middle East to 2030 in post-SRES baseline 
scenarios are lower than in SRES, but this has only minor effects on 
global economic growth and overall em issions. Representation of aerosol 
and aerosol precursor emissions, including sulphur dioxide, black carbon 
and organic carbon, which have a ne t cooling effect, has improved. Gen-
erally, these are projected to be lower than reported in SRES. 	
4.2 The Stern Review 
The Stern Review , which was published in 2007, runs to almost 700 pa-
ges and covers a broad range of issues relating to climate change. We will 
restrict our attention here to the main economic analyses and results, 
which have been widely discussed in the literature since its publication. 
The review looks closely at projec tions of greenhouse gas emissions 
under BaU. Based on these, it calculates economic (market and non-
market) climate costs associated with a particular projection. The projec-
tion used gives a fairly rapid growth in CO	
2-e: on average 1.4% per year 
during the first half of the present decade. Moreover, emissions are as-
sumed to continue to grow at a fairly high rate for the whole period cov-
ered in the analysis (which goes to 2200). Behind this projection is an 
assumption of average population growth until 2200 of 0.6% per year, 
implying that the world population will be 20 billion in 2200. In addition, 
world GDP per capita is assumed to have an annual growth rate during 
the period equal to 1.3% (before subtracting the costs of climate change).

This implies that before correcting for the negative impact of climate 
change, per capita income will be about 12 times higher than today. 
Under the BaU projection, there will be dramatic climate change dur-
ing the next couple of decades. The co sts of such change are considered 
at length in the Stern Review. In economic terms, there is great uncer-
tainty about what these costs will act ually be, even if the uncertainty 
about what the climate will be like is ignored. The Review considers sev-
eral scenarios, which differ both with respect to what the climate changes 
will be and what types of costs are included. In all cases costs will rise 
over time, both in absolute terms and as a percent of GDP. Monte Carlo simulations are used to illustrate some of the uncertainty, 
presenting climate change costs at the end of the next century under BaU 
as a range from about 3% to about 35% of GDP, with a mean of 13.8% 
(see Table 6.5c in the Stern Review, which describes the case with highest 
costs). 
The Review ”translates” these ri sing costs into “balanced growth 
equivalents”: These are constant percentage losses of consumption, based 
on a welfare function of the type (2.5): The reduction in W caused by 
climate change is translated into a constant percentage reduction in con-
sumption (relative to the case with no climate change) from the present to 
the infinite future that gives the same reduction in W as the increasing 
cost. With the costs above this give s an expected consumption loss of 
14.4% (with an interval from 2.7% to 32.6%, see Table 6.1 in the Re-
view). It is important to note that it is the consequences in the far future 
that are most important for the values of the hypothetical constant per-
centage consumption reduction. While the actual losses described in Fig-
ure 6.5 of the Review are independent of the parameters of the function 
(2.5), the “balanced growth equivalents” depend strongly on the parame-
ters of this function. With paramete rs implying a higher discount rate, the 
“balanced growth equivalents” would be lower. 
The Stern Review does not give a formal optimization in order to find 
an optimal emission path (as described in section 2.1). However, it dis-
cusses the costs of stabilizing greenhouse gases at levels between 500 and 
550 ppm CO	
2-e: i.e. at the high end about twice the pre-industrial level. 
Due to very high costs of adopting a target below 500 ppm, the Review 
recommends a target between 500 and 550 ppm. 
Given a climate sensitivity of 3 (the ‘best guess” of the IPCC), this 
would limit the global mean temperature increase to 3 degrees Celsius 
(while it would increase to 7–9 degrees by 2200 under the BaU scenario). 
The review goes into great detail about how such a stabilization might be 
achieved. Based on several sources, it also gives estimates of the costs 
involved. In particular, a study by De nnis Anderson (2006) is reported in 
section 9.8. Here it is argued that mitigation costs might be about 0.3% of 
GDP in the near future, increasing to about 1% in 2050. However, these 
numbers are uncertain and the range for 2050 is from -0.6% (i.e. a small

gain) to 3.5% of GDP. These costs are compared with the costs of climate 
change under BaU and it is (informally ) argued that the reduction of cli-
mate costs resulting from mitigation efforts more than outweigh mitiga-
tion costs. The review is rather vague regarding the marginal costs of mitigation 
in the near future under the stabilizat ion scenario. This is an important 
variable, since it tells us what the price of carbon emissions must be in a 
market economy. Table 9.2 in the Review gives numbers for average 
costs of mitigation, which are reported to be US$61 per ton of CO	
2 in 
2015, declining to US$22 in 2050. Ther e are two interesting features of 
this table. First, average costs are a ssumed to decline over time in spite of 
strongly increased mitigation. This s uggests a very rapid improvement in 
mitigation technologies. Second, marginal costs are higher than average 
costs. If the ratio between marginal a nd average costs is the same in 2050 
as in 2015, this table implies that marginal costs will decline over time. 
As explained in section 2.1, an optim al policy will typically have increas-
ing marginal costs. A declining marg inal cost suggests that too much 
mitigation is assumed in the near futu re, instead of mitigating more at a 
later date, when technology is assu med to have improved significantly. 
Note, however, that if the assumed technological development requires 
early mitigation as a result of learning by doing (see section 2.4), it may 
be best to make significant mitigation ef forts at an early stage, even if the 
marginal mitigation costs are higher at this early stage than they will 
eventually become after the technology has improved. 
The social cost of carbon – i.e. th e variable given by (2.4) – is dis-
cussed in section 13.2 of the Stern Review (see in particular boxes 13.1 
and 13.3). This variable depends on the time path of carbon in the atmos-
phere (since D	
S in (2.4) depends on S) and thus on the time path of emis-
sions. The review shows that there is a wide range of estimates in the 
literature under BaU scenarios. This is partly due to different estimates of 
what emissions will be under BaU, but the uncertainty regarding the size 
of climate costs is probably a more important reason for the wide range of 
estimates of the social cost of car bon. For the climate change costs and 
BaU scenarios used in the review, the estimate of the social cost of car-
bon is US$85 per ton CO	
2. As mentioned above, climate change costs 
could be more than twice the point estimate; the same is therefore also 
true for the social cost of carbon. Since marginal climate change costs 
will be lower under a stabilization scenario, so will the social cost of car-
bon. In the review the social cost of carbon is estimated to be US$30 per 
ton CO	
2 for an emission path giving stabilization at 550 ppm CO	2-e, whi-
le it is estimated to be US$25 per ton CO	
2 for an emission path giving 
stabilization at 450 ppm CO	
2-e. Due to the uncertainty regarding climate 
costs, these estimates are very vague. Ignoring uncertainty, we have the following numbers in the case of 
stabilization at 550 ppm CO
2-e: the present (and near-future) social cost

of carbon is about US$30 per ton CO	2, while the marginal mitigation cost 
is more than US$61 per ton (which was the average cost in 2015: see 
above). From chapter 2 we know that in an optimal outcome the marginal 
mitigation cost should equal the social cost of carbon. The fact that the 
marginal mitigation cost exceeds the so cial cost of carbon for an emission 
path giving stabilization at 550 ppm CO
2-e indicates that such a stabiliza-
tion target might be too ambitious. However, bearing in mind the uncer-
tainty relating to all these numbers, and also some issues relating to en-
dogenous technological development, we should be cautious before draw-
ing such a conclusion.	
25 
Several studies of the Stern Review have criticized its estimates of 
climate change costs (see, e.g., Me ndelsohn, 2008) and mitigation costs 
(see, e.g., Weyant, 2008). However, most of the focus has been on the 
review”s way of comparing climate change costs and mitigation costs. 
The major part of climate costs will occur in the next century, with hardly 
any costs before 2050. Mitigation co sts, on the other hand, will be con-
siderable even in the first half of this century. The discount rate used in 
the comparison of these time-dependent costs is therefore of crucial im-
portance for the result obtained. The Stern Review uses a discount rate 
based on the Ramsey equation (2.6). The annual per capita consumption 
growth rate is assumed to be 1.3%: i.e. g(t)=0.013. The parameters 	
 
and 	
	 are assumed to be 0.001% and 1 respectively. This gives 
r (t) = 0.014: i.e. 1.4%. This is very low compared with what is usually 
assumed and with a higher discount rate the case for stabilizing green-
house gas concentrations at 550 ppm CO	
2-e compared with a less ambi-
tious goal would be weakened. We will not attempt to summarize the 
lengthy debate on the discount rate that has followed the Stern Review , 
but a couple of important references are Nordhaus (2008; see section 3.1) 
and Dasgupta (2008), as well as the references found in these studies. 	
4.3 Studies by the OECD 
The OECD studies we present are based on the OECD”s own Environ-
mental Linkages Model, which is a general equilibrium model of the 
world economy, with many different sectors and several geographical 
regions. All the six major GHG gases are included in the model. The OECD “Environmental Outlook to 2030” (2008) covers a wide 
range of environmental problems, from climate change to waste and mate-
rial flows. Many of the results from the chapter on climate change are 
modified in a later public ation, see Burniaux (2008) . For instance, the ‘En-
vironmental Outlook” includes stabilization at 450 ppm CO	
2-e scenario, 
while the later publication considers only a target of 550 ppm CO
2-e. 
 	
 	25 The average mitigation cost is assumed to fall rapidly and be only US$22 dollars in 2050. In this 
year, therefore, the marginal mitigation cost may be roughly equal to the social cost of carbon.

We will first comment briefly on the ‘OECD Environmental Outlook 
to 2030”. This analyses a range of climate policy scenarios, among them: 
i.)
 	a global CO	2 tax of US$25 from 2008, increasing yearly by 2.4% 
in real terms; 
ii.)	
 	an OECD CO	2 tax of US$25 from 2008, followed by BRIC	26 in 
2020 and ROW	
27 in 2030; and 
iii.)	
 	the above-mentioned stabilization at 450 ppm CO	2-e, starting in 
2008. 
 
Note that already none of these scen arios accord with reality. For in-
stance, at the time of writing there is no economy-wide CO
2 tax of US$25 
in the OECD and no global abatement of CO	
2 in all sectors. Moreover, 
the 450 ppm CO	
2-e stabilization target is arrived at partly by assuming 
that halting deforestation and reforesta tion happen at no cost. Finally, the 
effect of CCS is not modelled explicitly, but emission reductions from 
CCS are still factored in, but in a wa y that, according to the OECD, likely 
leads to an underestimation of the costs of CCS. 
Below we present some of the ke y results from the phased-in action 
scenario ii) and the 450 ppm scenario iii): 	
Table 4.3.1 Selected results from the phased-in action scenario ii) and the 450 ppm 
scenario. Source: ‘Environmental Outlook to 2030”, OECD (2008) 
 	 	2005 	2030 	2050 	2100 	
BaU Gt/year (CO	2-e) 46.9 64.1 71.4 	
Phased-in action 21% 41% 
Emission reduction as 
percentage of BaU 
emissions (world) 
450 ppm CO	2-e 	 39% 64% BaU 
 
Phased-in action $25 
(OECD only) $59 $67 
 
Carbon price, 2001 
US$ per ton CO	
2-e 	
450 ppm CO	2-e 	 <$2.4 48 155 BaU 380 
465 543 1,000 
Phased-in action 455 501 ~650 
CO	
2 in atmosphere, 
ppm 	
450 ppm CO	2-e 	 455 443 463 450 BaU 
1.2–1.6 1.7–2.4 
Phased-in action 1.1–1.4 1.5–2.0 	
Mean global tem-
perature increase, 
degrees Celsius, 
compared to pre-
industrial level 	
450 ppm CO	2-e 0.6 1.1–1.4 1.3–1.8 	
 
Note that emission tax in the 450 ppm s cenario increases very sharply: It 
increases from $2.4 in 2010 to $48 in 2030, and from $48 in 2030 to $155 
 	
 	26 Brazil, Russia, India and China. 27 Rest of the world.

in 2050. This corresponds to a growth rate of 16% per year in the first 20 
years, and a growth rate of 6% the next 20 years. We do not fully under-
stand the assumptions and/or mechanisms in the OECD study that is driv-
ing this steep emission tax path, however, a part of the explanation may 
be that the initial tax rate is fixed exogenously, and that the study does 
not allow jumps in the emission tax rate. Hence, the emission tax path has 
to be steep in order to secure that the concentration target is reached. 
Note also that the long-term temp erature increases beyond 2050 will 
be higher than the above reported values as they incorporate only short- 
and medium-term effects. The expected temperature increase in 2100 is 
not reported, but according to other re ports, such as ‘World Energy Out-
look 2008”, temperature increases coul d be as high as 6 degrees Celsius 
under BaU. Note also that it is very hard to stabilize GHG concentration 
levels to below 550 ppm if global actio n is delayed. We will elaborate on 
this further in our review of the ne xt report on climate change mitigation 
by the OECD, see Burniaux et al. (2008). The OECD measures mitigation costs as reductions in GDP compared 
to the BaU scenario. The cost of the most ambitious target above is re-
ported by the OECD to be 2.5% lower GDP by 2050 than what it would 
have been without any measures (BaU ). However, as already mentioned, 
the OECD arrives at another result in their later report, where they do not 
consider the 450 ppm CO	
2-e target (Burniaux et al., 2008)). Burniaux et 
al. report that the cost of reaching a 550 ppm CO	
2-e target to be 4.8% 
lower world GDP by 2050. Thus, the cost of reaching the 550 ppm target 
in the OECD's later report, is seemi ngly nearly twice as high as the cost 
of reaching the 450 ppm target in the 'Environmental Outlook 2030'. On 
the other hand, their BaU scenario has also changed, incorporating higher 
emissions and so making the need for abatement greater. For instance, the 
assumed growth in GHG emissions in the BaU scenario in the ‘Environ-
mental Outlook” in the period 2005–50 is below 1%, while in the later 
report it is 1.4% due partly to updated estimates of the emission growth in 
the BRIC countries. Moreover, while GHG abatement was taken to begin in 2008 in the 
‘Environmental Outlook”, the later repor t gives 2013 as the starting date. 
Instead of incorporating halted deforestation and reforestation at no cost, 
and including CCS in an unsatisfactory way, it has simply disregarded 
these three options (OECD, 2008b). The following table shows some of the key numbers.

Table 4.3.2. Key numbers from the OECD 2008 b. Source: Burniaux et al. (2008) 
 	 	2005 	2025 	2050 	
BaU Gt/year (CO	2-e) 	 46.9 73.3 87.7 	
Emission reduction as percent-
age of BaU emissions (world) 
 	550 ppm CO	2-e 	(450 ppm CO	2-e, Env. 	Outlook to 2030) 19.1% 
(39%) 62.5% 
(64%) 
Carbon price, 2001 US$ per 
ton CO	
2-e 	
550 ppm CO	2-e $75 
(2030) 
 $400 	
 
The emission reduction levels from 
the ‘Environmental Outlook to 2030” 
are in parentheses in Table 4.3.2. Note that because of the above-
mentioned factors (later start, higher BaU emissions etc.), the need for 
reductions in year 2050 in the 550 ppm scenario is comparable to the 
need for reductions in the 450 ppm scenario. The emission tax rate in the 
Burniaux et al. 550 ppm scenario starts low in 2013, reaches US$75 in 
2030 and becomes US$400 in 2050. The inclusion of CCS in the model 
would probably significantly lower this later figure. Moreover, the 
growth in the tax rate is again very high; from 2030 to 2050 it is about 
9% per year. We believe a part of th e reason to be an exogenously fixed 
initial tax rate, and constraint that jumps cannot occur. 
There are a number of other interesting results in Burniaux et al. 
(2008): 
 Exempting energy-intensive industries from policy action increases 
the cost of achieving the 550 ppm all gases concentration target by 
50%. Likewise, not including all GHG gases, but only focusing on 
CO	
2, increases the cost of reaching the target by almost 100%. Finally, 
the cost of incomplete country c overage appears to be high. For 
example, GHG concentration targets below 750 ppm are out of reach 
if Annex 1 countries act alone. 	
 Climate policy is implemented through a tax on emissions. The 
revenues from the tax amount to 6% of world GDP in 2050. Probably, 
the cost of achieving the 550 ppm target could be lower if these 
revenues were used to lower distorting taxes, such as the pay-roll tax. 
In the current model runs they are recycled back to the consumer as a 
lump-sum payment. On the other hand, under a cap and trade scheme 
with grandfathered permits, costs c ould exceed the above estimates. 	
 If the European Union acts alone, carbon leakage could be significant. 
As an illustration, the report considers a 50% reduction in 2050 
relative to 2005 levels by the EU. This increases emissions outside the 
EU such that 20% of the achieve d emission reductions are off-set. 
However, if the EU acts together w ith the other Annex I countries, the 
carbon leakage effect is drastically reduced.

4.4 Studies by the IEA 
Since 1993 the IEA has presented medium- to long-term energy projec-
tions based on the World Energy Model (WEM). This is designed to rep-
licate how energy markets function and is used to generate sector-by-
sector and region-by region projections for both the reference scenario 
and alternative policy scenarios. The mathematical model is made up of six main modules: 
 
 final energy demand; 	
 power generation; 	
 refinery and other transformations; 	
 fossil-fuel supply; 	
 CO	2 emissions; 	
 investment. 
 
The main exogenous assumptions are: 
 	
 economic growth; 	
 demographics; 	
 international fossil-fuel prices; 	
 technology. 
 
Electricity consumption and electricity prices link the final energy de-
mand and power generation modules. The refinery model projects 
throughput and capacity requirements based on global oil demand. Pri-
mary demand for fossil fuels serves as input for the supply modules. 
Complete energy balances are compiled at a regional level and the CO	
2 	
emissions of each region are then calculated using derived carbon factors. WEM requires access to large quantities of historical data on eco-
nomic and energy variables, of which most are obtained from the IEA”s 
own databases of energy and economic statistics. 
A number of new features were added to the previous version of 
WEM for use in ‘World Energy Outlook 2008”: 
 The integration of the WEM into a general equilibrium model was 
further developed, in order to mode l more precisely the feedback links 
between energy markets and the macro economy. 	
 The oil and gas production and trade models were expanded to take 
better account of economic variables and to reflect the recent surge in 
cost inflation and the fall in the value of the dollar against most other 
currencies.

 Oilfield decline rates were analysed in detail on a field-by-field basis 
in order to assess the prospects for future decline rates. 	
 Energy-related CO	2 emissions were combined with greenhouse gas 
(GHG) emissions from all sources to explain the relationship between 
the level of annual emissions and th e long-term concentration of GHG 
in the atmosphere, which will determine the increase in the future 
global average temperature. 	
 A study was undertaken of how ove rall emissions limitation levels 
would translate back into an atmospheric concentration of CO	
2-e gases 
and what means might be used to achieve stabilization of that 
concentration. Energy and emissions are modelled in two scenarios: 
the 550 policy scenario, in which GHG concentration is stabilized at 
550 parts per million of CO	
2-e, and a 450 policy scenario, in which 
concentration is limited to 450 ppm CO	
2-e. 	
 Power-generation capital and operating costs were assessed in detail 
and the cost assumptions in the WEM were revised to take account of 
recent cost inflation. 
 
The quantitative implications of these changes, and their influence on 
direct comparisons between World Energy Outlook 2007 and World En-
ergy Outlook 2008 are not described explicitly. It is important to keep in 
mind that this affects not only comp arisons between the two last World 
Energy Outlook”s, but also comparisons between World Energy Outlook 
2008 and its companion “Energy Tec hnology Perspectives 2008” – which 
builds on World Energy Outlook 2007. The current WEM is the 12th 
version of the model. It covers 21 regions (modelled separately) and is 
designed to analyse: 	
 Global energy prospects: trends in demand, supply availability and 
constraints, international trade and energy balances by sector and by 
fuel to 2030. 	
 Environmental impact of energy use: CO	2 emissions are derived from 
the detailed projections of energy consumption. 	
 Effects of policy actions and technological changes: alternative policy 
scenarios analyse the impact of policy actions and technological 
developments on energy demand, supply, trade, investments and 
emissions (a policies and measures database, with over 3,600 policies 
in OECD and non-OECD countries, was compiled to support the 
analysis). 	
 Investment in the energy sector: the model evaluates investment 
requirements in the fuel supply chain needed to satisfy projected

energy demand to 2030 and also demand-side investment 
requirements in the alternative policy scenarios. 
Technical aspects and key assumptions in ‘World Energy Outlook 2008” 
Demand-side modules 
The parameters of the equations of the demand-side modules are esti-
mated econometrically, usually usin g data for the period 1971–2006. 
The reference and alternative policy scenarios 
The reference scenario takes account of government policies and meas-
ures that have been enacted or adopted by mid-2008. The same macro-
economic and population assumptions ar e used in the reference and alter-
native policy scenarios. The projections are based on the average retail 
prices of each fuel used in final uses, power generation and other trans-
formation sectors. These end-use prices are derived from assumptions 
about the international prices of fo ssil fuels. The price assumptions in 
‘World Energy Outlook 2008” are significantly higher than assumed in 
the last edition of the ‘Outlook”. 
Population assumptions 
Rates of population growth for each region are based on the most recent 
projections contained in the United Nations” Population Division report, 
‘World Population Prospects: The 2006 Revision”. In ‘World Energy 
Outlook 2008” world population is projected to grow by 1% per year on 
average, from 6.5 billion in 2006 to over 8.2 billion in 2030. Population 
growth slows over the projection period, in line with trends of the last 
three decades: from 1.1% per year in 2006–15 to 0.9% in 2015–30. 
 
Macroeconomic assumptions 
Economic growth assumptions for the short to medium term are based 
largely on those prepared by the OECD, the IMF and the World Bank. 
Over the long term, growth in each region is assumed to converge to an 
annual long-term rate. Th is is dependent on demographic and productiv-
ity trends, macroeconomic conditions and the pace of technological chan-
ge. In ‘World Energy Outlook 2008”, world GDP is expected to grow on 
average by 3.3% per year over the projection period. Growth is assumed 
to drop from 4.2% in 2006–15 to 2.8% in 2015–30. India and China are 
expected to continue to grow faster than all other regions, followed by the 
Middle East and Africa. The economies of many regions are expected to 
shift away from energy-intensive heavy manufacturing towards lighter 
industries and services, though the pace of this process, which is well 
advanced in the OECD and some em erging economies, varies. Industrial 
production continues to grow in volume terms.

Technological development 
Energy intensity is assumed to decline by 1.7% per year, mainly because 
of a shift towards service economies in many countries. Technological 
development in the WEM is mainly based on exogenous assumptions. 
Emmisions in the two policy scenarios 
World Energy Outlook 2008 considers two climate-policy scenarios cor-
responding to long-term stabilization of greenhouse-gas concentration at 
550 and 450 parts per million of CO	
2 equivalent. 
In the 550 ppm scenario fossil fuels lose market shares to renewables 
and nuclear power. Large oil savings occur in the transport sector in 
OECD countries and other major economies, as a result of sectoral 
agreements to reduce emissions from light-duty vehicles and aviation. 
The 550 ppm scenario involves a plateauing of greenhouse-gas emis-
sions by 2020 and reductions soon after. The emissions in the energy 
sector are reduced from approximately 41 Gt in the reference scenario, 
approximately 33 Gt in the 550-scenario. The distribution of the reduc-
tions are shown in figure 4.4.1, while further reductions in the 450-
scenario are shown in figure 4.4.2. 	
 
 
 
 
 
 
 
 
 
 
 
 
 
 	
 
Figure 4.4.1 Distribution of emission reductions in the 550-scenario. Based on figure 18.4 in World Energy Outlook 2008.

Figure 4.4.2 Distribution of emission reductions in the 450-scenario. Based on figure 18.4 in World Energy Outlook 2008. 
 
The 450 ppm scenario involves stronger and broader policy action from 
2020 onwards. Global energy-related CO	
2 emissions follow broadly the 
same trajectory as in the 550 Policy Scenario until 2020, and then fall to 
25.7 in 2030. Participation in an international cap-and-trade system is 
more comprehensive than in the 550 Policy Scenario, comprising all ma-
jor emitting countries from 2020. Overall costs have not been calculate d, but direct investment costs in 
the energy sector have been calculated for both policy scenarios – and for 
the reference scenario. The consequences of climate change are discussed in the report, but 
‘World Energy Outlook 2008” contains only indicative calculations of 
NPV of the additional investments in the energy sector – and no calcula-
tions of expected costs of climate change. There are no feedback mecha-
nisms between climate change and population growth/GDP. 	
About the outcome of the energy demand scenario in ‘World Energy 
Outlook 2008” 
Energy demand is an important determinant for emissions – and for in-
vestments in the energy sector. The reference scenario suggests an in-
crease in energy consumption of 45 % by 2030, a growth extrapolated 
from present investment trends and governmental policies to the year 
2030. This result follows quite directly from: 
 
 energy prices; 	
 GDP growth; 	
 energy intensity.

Of these, energy prices are derived from a new iterative model of supply 
and demand that has been introduced in ‘World Energy Outlook 2008”, 
calculating the costs of energy based upon interactions between supply 
and demand. The others are straightforward e xogenous assumptions: GDP is taken 
from the OECD, the IMF and the World Bank, while energy intensity is 
assumed to decline by 1.7% per year, meaning primary energy demand 
per unit of real GDP is expected to decline by 1.7% a year (0.6% faster 
than the average in the past three de cades). Some of the most relevant 
results with regard to emissions are summarized in table 4.4.1 
Table 4.4.1 Selected results from World Energy Outlook 2008. 
. 	 	2005 	2020 	2030 	2100 	
BaU Gt/year (CO	2-e) 44 55 60 	
550 ppm 
0 14,5 20 
 
 
 
 
Emission reduction as percentage 
of BaU emissions 
 
450 ppm 
0 
 41 
 34,5 
 
 
BaU 
 
550 ppm* 40 90 
Carbon price, 2007 US$ per ton 
CO	2-e 
* Price in OECD+. 
** Price in OECD+ and other 
major economies. 
 	
450 ppm** 180 
BaU 385 (455) 700 
(1,000) 
550 ppm 385 (455) (550) 
CO	
2 (CO	2-e) in atmosphere, ppm 	
450 ppm 
385 (455) (450) BaU 
 6 
550 ppm 3 	
Mean global temperature in-
crease, degrees Celsius 	
450 ppm 2 	
 
The 450 ppm CO	
2-e scenario involves modest overshooting: i.e. concentra-
tions exceed 450 for some time. Theref ore GHG emissions in the second 
half of the century have to be lower than the natural uptake of GHG gasses. 
The Outlook stresses the need for promoting abatement in all coun-
tries. In particular, large emission re ductions must also take place in non-
OECD countries, whose emissions in the BaU scenario in 2030 exceed 
the global emissions in the 450 ppm CO	
2-e scenario. 	
‘Energy Technology Perspectives 2008” 
‘Energy Technology Perspectives 2008” draws on modeling work within 
the IEA Secretariat and expertise from the IEA”s international energy tech-
nology collaboration network. ‘Energy T echnology Perspectives 2008” is a 
companion to ‘World Energy Outlook 2007 (not the newer version from 
2008, presented in 7.1 above), taking the same baseline scenario to 2030 
and extending it to 2050. The present study carries forward the analysis

contained in ‘Energy Technology Perspectives 2006” in the light of the 
IPCC 4th Assessment Report, released in November 2007. The IEA En-
ergy Technology Perspectives model (ET P model) have been used to ana-
lyse the ACT and BLUE scenarios for the period 2005 to 2050.	
28 
The ETP model belongs to the MARKAL family of bottom up model-
ling tools, and comprises representation of technology options of about 
1000 individual technologies. Even though Energy Technology Perspec-
tives 2008 draws on results from the Worl d Energy Model, this is another 
version than the one used in World Energy Outlook 2008, and many of 
the assumptions also differ. Therefore, the results cannot easily be com-
pared between the two reports. 
Scenarios 
Several different scenarios are presented: The set of ACT Scenarios 
shows how global CO	
2 emissions could be brought back to current levels 
by 2050. The set of BLUE Scenarios targets a 50% reduction (compared 
to 2008) in CO	
2 emissions by 2050. ‘Energy Technology Perspectives 
2008” also presents global road maps of 17 prioritized technologies. In 
the main, what distinguishes this report from the IEA”s ‘World Energy 
Outlook 2008 is that ‘Energy Technology Perspectives 2008”: 
 	
 is less focused on fossil-fuel resources and markets; 	
 has a stronger focus on technology-specific issues; 	
 is based on an ‘older” set of assumptions regarding population and 
GDP-development; 	
 has a longer time-span (2050 as opposed to 2030). 	
 An earlier version of the IEA World Energy Model has been used. 
 
The baseline in ‘Energy Technology Perspectives 2008” uses the same 
population projections as ‘World Energy Outlook 2008”, but the struc-
tural composition is slightly different (GDP projections are slightly lower 
for the OECD countries). The oil price is significantly higher in the 
‘World Energy Outlook 2008” baseline, which is probably part of the 
reason why oil demand in 2030 is 10% lower than in the ‘Energy Tech-
nology Perspectives 2008” baseline. Different assumptions, combined 
with different modes of presentation in figures and tables, partly prevent 
useful comparisons between ‘World Energy Outlook 2008” and ‘Energy 
Technology Perspectives 2008”. The ‘Energy Technology Perspectives 2008” BaU scenario builds on 
the ‘World Energy Outlook 2007”, which predicts lower world emissions 
than ‘World Energy Outlook 2008”. While emissions of CO	
2-e reaches 
62.5 Gt/year in 2050 in the ‘Energy Technology Perspectives 2008” BaU, 
they reach 59.6 Gt/year already in 2030 in ‘World Energy Outlook 2008”. 
 	
 	28 These scenarios are explained in the next section.

The ‘Energy Technology Perspectives 2008” analyses a series of 
GHG-reduction scenarios, which are divided into two main groups: the 
ACT Map scenarios and the BLUE Map scenarios. The main differences 
between the two concern the concentration target and the technology in 
the transport sector. The ACT Map does not set up a concentration target. 
Instead emissions are stabilized and brought back to the 2005 level in the 
year 2050. The BLUE Map scenario aims at a maximum temperature 
increase of 2–3 degrees Celsius. Moreover, in the ACT Map scenar io neither electric cars nor hydro-
gen/fuel-cell cars become available. Therefore emission reductions in the 
transport sector are modest, relying on a limited supply of biofuels. In the 
BLUE Map scenario either hydrogen/fuel-cell cars or electric cars enter 
the market. However, the price is fa irly high, possibly reaching US$ 500 
per ton CO	
2 in the more pessimistic scenarios. In table 4.4.2 below, some 
of the results are shown. 	
Table 4.4.2 Selected results from IEA Energy Technology Perspectives 2008. 
 	 	2005 	2030 	2050 	2100 	
BaU* Gt/year 27 44 62.5 
ACT Map 56.5% 
Emission reduction as 
percentage of BaU emis-
sions. * Includes only 
emissions in the energy-
sector 
 
BLUE Map (450 ppm) 
 78.5% 
BaU 
ACT Map $ 50 
 
 
 
Carbon price, 2007 US$ 
per ton CO	
2-e 
 	
BLUE Map (450 ppm) $ 200 
BaU 385 
(455) 700 
(1,000) 
ACT Map 386 (455) – 
CO	
2 (CO	2-e) in atmos-
phere, ppm 	
BLUE Map (450 ppm) 387 (455) (450) BaU 
 6 
ACT Map – 
Mean global temperature 
increase, degrees Celsius 
BLUE Map (450 ppm) 
 2 	
 
Note the rise in carbon tax from the ‘Energy Technology Perspectives 
2008” scenarios to ‘World Energy Outlook 2008”. In the latter carbon tax 
has already reached $180 in 2030, while in the former it is $200 in 2050. 
This not only shows the effect of in creased BaU emissions but may also 
indicate that the estimated costs of the different abatement technologies 
have increased greatly. 
4.5 Australia”s Low Pollution Future 
The Australian Treasury has conducted a large and complex economic 
modelling project that investigates the potential economic impact of re-
ducing greenhouse gas (GHG) emission s over the medium and long term.

The assumptions and results of the analysis are published in a compre-
hensive report of almost 300 pages that contains detailed modelling of the 
costs and opportunities of acting decisively to meet the challenge of cli-
mate change. The report examines four scenarios in which Australia and the world 
follow pathways to a low-polluting fu ture. The analysis focuses on the 
economic impact of policies to reduce GHG emissions. The report posi-
tions Australia within the context of global action to reduce GHG emis-
sions and stabilize concentrations at 450–550 ppm CO	
2-e around 2100 
The modelling framework is based on a suite of economic models: 
global, national, sectoral and househol d. The analysis centres on three 
top-down computable general equilibrium (CGE) models developed in 
Australia: 	
 	
 the GTEM (Global Trade and E nvironment Model; also called 
GTEM-ABARE), 	
 G-Cubed and 	
 MMRF (Monash Multi-Regional Forecasting) models. 
 
Because no single existing model adequately captures the global, na-
tional, sectoral and household dimensi ons or focuses on all relevant as-
pects of climate change policy in Australia the framework are based on a 
suite of different models that together span global, national, sectoral and 
household scales to simultaneously explore these four dimensions. A 
suite of models approach provides, according to report, a natural hedge 
against the inherent uncertainty in economic modelling. GTEM is a 
backward-looking model where consumers in the model only learn about 
the emission price at the start of each year. In contrast, some businesses 
and consumers in G-Cubed know the future of the emission price with 
perfect foresight. In G-Cubed, consum ers and businesses first learn about 
the emission trading scheme in 2007. They can then respond immedi-
ately, even though the emission price is not introduced until 2010 or 
2013. However, not all consumers are forward looking. G-Cubed as-
sumes most consumers are myopic (70 per cent), looking only at their 
current income. 
The models do not capture well the short-term economic adjustment 
costs; instead, they explore long-term multi-sector impacts. To different 
degrees, the CGE models approximate short-term adjustment paths. At 
one end of the spectrum, GTEM assumes that labour and capital are per-
fectly mobile across industries, at a ll times and at no cost. Thus, GTEM 
does not capture any short-term adjustment costs. At the other end of the 
spectrum, G-Cubed assumes immobility of capital, slow adjustments to 
wages and liquidity constraints, a nd includes partial forward-looking 
behaviour.

MMRF, a model of the Australian economy with rich industry-sector 
detail, draws on international assumptions from GTEM and is augmented 
with disaggregated bottom-up modell ing for three emission-intensive 
sectors: electricity, transport and fore stry. The results of these three mod-
els are drawn together into an integrated set of projections. 	
 	
We will start by giving a descrip tion of the GTEM model and a brief 
introduction to the other CGE models used in the report. We will then 
restrict our discussion to the global approach of various analyses and 
projections from the Australian studies. 
GTEM 
GTEM is a dynamic general equilibrium model developed at the Austra-
lian Bureau of Agricultural and Resource Economics (ABARE). It devel-
oped out of the MEGABARE model (ABARE, 1996) and the static Glo-
bal Trade Analysis Project (GTAP; Hertel, 1997). GTEM presents a future path for economic growth, population levels, 
energy consumption and GHG emissions in a world without climate 
change. The model consists of three modules: economic, population and 
environment. There is a two-way feedback between the population and 
economic modules. Economic growth a ffects fertility and mortality pat-
terns and thus brings changes in population structure and labour supply 
which affect economic growth. The economic and environment modules 
have only a one-way relationship. The model does not include risks aris-
ing from climate change itself. Even if there is no direct feedback from 
the environment module to the economic module, emission restriction 
policies will have an impact on the economic module and so, in this sen-
se, there is a strong link between the economic and environment modules. For the purposes of GTEM the global economy is represented by 13 
regions, 19 industry sectors and a typical household. The model disag-
gregates three energy-intensive sectors into specific technologies: elec-
tricity generation, transport and iron and steel. GTEM is a Solow-Swan growth mode l, with exogenus sector-specific 
technical change. The household demand for private goods responds to 
changes in income and relative prices and is modelled as a constant dif-
ference in elasticity of substitution demand function. The price and in-
come elasticity depends on budget share and is therefore variable over 
time. The public consumption expenditure shows the optimal allocation 
of commodities by maximizing a Cobb-Douglas utility function. 
On the production side, GTEM specifies four factors of production: 
land, labour, capital, natural resources and material inputs, of which land 
and labour are perfectly mobile acro ss sectors. Labour supply is exoge-
nously given and there is an unlimited supply of natural resources at a 
given real price.

Three key energy-intensive sectors that employ multiple technologies 
to produce output are identified. These sectors are defined as technology 
bundle sectors, and include electricity generation, transport, and iron and 
steel. The sectors use the output of the respective technology bundle, and 
other commodities, in fixed proportions to distribute to the users. As a 
default, input substitutions within a technology are not allowed — each 
technology uses its inputs in fixed proportions — while substitution be-
tween technologies is allowed. Output s from each of the technologies are 
chosen to minimise the cost of producing a CRESH (constant ratio of 
elasticities of substitution, homothetic) aggregate of the outputs of all 
technologies. 	
 	
Demand and supply of electricity is modelled using 12 established and 
emerging technologies. Non-technology bundle industries can, through 
substitution between four energy commodities, produce energy compos-
ites. The inter-fuel and inter-factor substitutions, as well as substitution 
between fuels and primary factors, occur using a nested CES approach 
(seeSection 3.5). Given the right market incentives, the model allows for the transport 
and electricity sectors to be gradua lly emission-free. This is achieved 
through endogenous productivity growth via learning by doing, a detailed 
technology portfolio including a suite of zero or near-zero emission tech-
nologies and substitution across technologies. By gaining the right rela-
tive prices, households will switch to electricity generated by zero-
emission technologies. The model does not allow for substitution be-
tween non-energy intermediate inputs in response to relative prices, but 
allows for energy-efficiency improvements if there is bias in the region-
specific exogenous productivity growth. This holds for all inputs and 
sectors. Markets clear each year, but this is not necessarily an equilibrium 
condition, as capital and debt accumula tion may continue year after year. 
The parameters used in the social-accounting matrix are currently ba-
sed on GTAP”s version 6 database, ba se year 2001. GTEM specifies the 
greenhouse gases used. The emission da tabase was developed at ABARE 
and contains six anthropogenic greenhouse gasses: combustion and non-
combustion carbon dioxide, methane, nitrous oxide, HFCs, PFCs and SF, 
all of them Kyoto gases. GTEM includes purpose-built carbon capture and storage (CCS) op-
erations and has a single technology for coal and gas. It takes CCS to be 
available as a generation option fro m 2020. Nuclear is modelled without 
specific constraints by assuming that resources and technology will be 
able to meet demand for nuclear electricity. 
G-Cubed, MMRF and bottom-up sector specific models 
G-Cubed, a forward-looking global m odel with macrodynamics, is de-
signed for climate policy mitigation cost analysis (McKibbin and Wilco-

xen, 1998). The version used for the report represents the global economy 
through nine regions and 12 industry sectors (including coal, oil, gas, 
agriculture and manufacturing). The model has limited technological 
detail. In order to play a part in linking the models, G-Cubed is broadly 
calibrated to GTEM BaU and provides comparative cost estimates for 
policy scenarios. 
The MMRF model is a detailed model of the Australian economy (58 
industrial sectors and all eight Austra lian states and territories) developed 
by the Centre of Policy Studies at Monash University (Adams et al., 
2008). The CGE models are complemented by a series of bottom-up sec-
tor-specific models for electricity generation, transport, land use change 
and forestry. Some of the models do make some allowance for learning to 
reduce the cost of some technologies. 
BaU 
BaU (the reference scenario) presents a development pathway for Austra-
lian and world economics up to 2100. The report contains a wide-ranging 
discussion of assumptions and projec tions under BaU. Assumptions used 
in BaU are, when possible, consiste nt across the suite of CGE and sec-
toral models. BaU has no new policy to reduce emissions and no impact 
on climate change. The pattern and rate of GDP are functions of the as-
sumptions regarding movements in po pulation, change in participation 
rates and growth in productivity. Productivity growth drives the global 
economy, with per capita GDP projected to increase by a factor of almost 
10 from 2005 to 2100, i.e., an avarage yearly growth rate of 2.4%. Note 
that this is a much bigger increase than was assumed in, e.g., the Stern 
Review or in the analysis with DICE discussed in section 3.1. Under BaU 
the global economy (GWP) rises from $54 trillion in 2005 to $268 trillion 
in 2050. Developed economies accelerat e towards, but do not reach, the 
productivity levels of developed eco nomies. World population is ex-
pected to peak at 9.5 billion in 2075, then fall to 9.3 billion in 2100. The 
annual increases in per capita GDP are higher than in, e.g., the Stern Re-
view (before subtracting the costs of climate change). Despite considerable falls in the emission-intensity of growth, annual 
GHG emissions increase between 2005 and 2050, from 39 Gt of CO	
2-e to 
just over 102 Gt in 2050. By 2100 annual emissions are projected to be at 
161 Gt. The annual rate of growth of emissions is expected to slow from 
around 2% now to less than 1% by 2100. The concentration of GHG in 
the atmosphere rises sharply to 1,560 ppm CO	
2-e by 2100. 
BaU predictions for global emissions are higher than those in other re-
cent studies and similar to the highest-emission scenario in the IPCC”s 
‘Special Report on Emissions Scenario” (IPCC, 2000). This results from 
a combination of higher-trend econom ic growth assumptions, as men-
tioned above, and slightly higher emission intensity in the area of growth.

In particular, the emission intensity in the area of development in the 
Asian region has been far above that expected in the IPCC SRES scenar-
ios, due to, among other things, the unexpected growth of brown coal use 
in China. Over the longer term it is assumed that developing countries 
will develop towards the productivity fro ntier of the US (countries do not 
get anywhere near the frontier in 100 years, but they do move towards it). 
Economic growth in the OECD BaU is also considerably lower than the 
BaU in the Australian analysis. 
Global emissions price and pathway 
A ‘Hotelling rule” is used (see sec tion 2.5) to construct a global emis-
sions pathway for each scenario within the global models. The emission 
price grows from a specified starting level at the real interest rate, as-
sumed to be 4% per year, which represents the rate of increase in compa-
rable financial assets. The ability to bank permits in the early years of the 
scheme for use later leads to actua l global emissions and emission alloca-
tions being different. Banking of permits ensures that the global price 
path satisfies the inter-temporal arbitrage condition. Initially, actual global emissions are lower than the allocations in all 
four policy scenarios, resulting in 5%–20% of permits being banked in 
the first ten years. Banking occurs initially to maintain the Hotelling price 
path and is accentuated by the step-down in global emissions after emis-
sions pricing is introduced. To achieve the desired greenhouse ga s concentration stabilisation lev-
el, the policy scenarios use different starting emission prices, which then 
grow at around 4 per cent per year The lower the stabilisation level, the 
higher the starting emission price. Th e required starting price to achieve a 
550 ppm stabilisation level is around US$23 in 2010 and US$27 if the 
starting year is 2013, in nominal terms. A slightly higher starting price of 
US$32 in 2010 achieves 510 ppm stabilisation and US$47 in 2013 
achieves 450 ppm stabilisation, in nominal terms. 	
 	
GTEM and the G-Cubed model have di fferent structures and data sets 
and use a different emissions price pa th to meet environmental and permit 
banking constraints. The global emissions price path is considerably lo-
wer under the G-Cubed projections th an under GTEM. The price of emis-
sion (or expectations of the global price path) is an important variable in 
calculating abatement costs and identifying wherever there would be no 
need for any policy instruments in addition to a price of emissions. Lower 
emission prices give higher per dollar mitigation costs. 
The discount rate 
The analysis focuses on the costs of mitigation, not the benefits, so the 
debate about discount rate is not important for the results. In the report it

is pointed out that if the results were used to judge the importance of 
future costs from today”s perspective, this would require a consideration 
of discount rates. 
Policy scenarios 
The report treats four different scenarios: CPRS-5 and CPRS-15, which 
differ only with regard to the con centration target, and Garnaut-10 and 
Garnaut-25, which also differ only with regard to the concentration tar-
get. However, while the Garnaut scenarios assumes global action (among 
other things, global cap and trade) from 2013, the CPRS scenarios as-
sume phased-in action from developing countries with complete coverage 
from 2025. Garnaut-10 and Garnaut-25 are consis tent with stabilizations of at-
mospheric concentrations at 550 and 450 ppm CO	
2-e by around 2100 
respectively. Further, CPRS-5 and CPRS-15 are consistent with stabiliza-
tions of atmospheric concentr ations at 550 and 510 ppm CO	
2-e by around 
2100 respectively. 
To achieve the desired GHG concentr ation stabilization level, the pol-
icy scenarios use different starting em ission prices, which then grow at 
around 4% per year. The required starting price to achieve a 550 ppm 
stabilization level is around US$23 in 2010 and US$27 if the starting year 
is 2013, in nominal terms. A slightly higher starting price of US$32 in 
2010 achieves 510 ppm stabilization and US$47 in 2013 achieves 450 
ppm stabilization, in nominal terms. As mentioned, Garnaut-10 and Garnaut-25 assume an ‘optimal” inter-
national emissions trading scheme, covering all emission sources and all 
economies, from 2013. These scenarios assume united global action, with 
all countries taking on emission-reduction obligations from 2013. This 
represents an optimal post-2012 agreement. National contributions are 
based on a contraction and convergen ce approach, whereby the allocation 
of emission rights among countries converges from current levels to 
equal per capita rights by 2050. 
The other two scenarios, CPRS-10 and CPRS-25, assume that interna-
tional emissions trading gradually expands, with developed economies 
participating from 2010, developing economies joining over time and 
global participation by 2025. Moreover, sectors exposed to trade are ex-
empted until 2020. The costs of climate change are not included. The global features of 
scenarios are given in Table 4.5.1.

Table 4.5.1 Globale features of scenarios 
 Reference CPRS-5 CPRS-15 Garnaut-10 Garnaut-25 
GHG 
stabilization 
goal, ppm CO	
2-e 
 1,560 550 510 550 450 	
Temperature 
change at 
stabilization 
 8ºC or 
more 3ºC 2.6ºC 3ºC 2ºC 
Global emission 
in 2050 (Gt of 
CO	
2-e) 
 102 35 27 36 22 
Global mitigation 
action none Multi-stage from 2010 Unified from 2013 	
Source: Australian Government, ‘Treasury from MAGICC and GTEM” 
 
The global economy growth in the mitigation scenarios slows slightly 
relative to BaU. The two global models indicate similar costs of mitiga-
tion policy, but the time profiles differ. G-Cubed is a forward-looking 
model and includes capital adjustment cost. When consumers and busi-
nesses plan for higher emission prices, their reactions raise the initia\
l 
adjustment cost earlier. The GWP changes from BaU are given in Table 
4.5.2. 
Table 4.5.2 GWP changes from BaU (Source: Australian Government, ‘Australia”s 
Low Pollution Future”, Table 5.6) 
 2020 
2030 2040 2050 
 GTEM G-
Cubed GTEM G-
Cubed GTEM G-
Cubed GTEM G-
Cubed 
CPRS-5 (550 
ppm) -0.7 -2.3 -1.4 -3.1 
-2.0 -3.2 -2.8 -3.3 
CPRS-5 (510 
ppm) -0.9 -2.8 -1.8 -3.6 
-2.6 -3.7 -3.5 -3.8 
Garnaut-10 
(550 ppm) -0.7 -2.2 -1.3 -2.5 
-1.9 -3.0 -2.7 -3.2 
Garnaut-25 
(450 ppm) -1.3 -3.3 -2.1 -3.6 
-3.2 -4.0 -4.3 -4.2 
 
Mitigation costs vary depending of the global stabilization target. The 
global environmental objective is the key determinant of emission prices 
and aggregate global costs. Lower stabilizations generally increase miti-
gation costs. Restrictions on international permit trade raise the overall 
economic cost of the CPRS scenarios for some economies. If the limits 
on international permit trade are lifted, the fall in GWP in 2019 is re-
duced from 2.9% to 2.5%. 
Delaying mitigation action in the global economy is examined. Ignor-
ing climate change risks, locking in more emission-intensive industry and 
infrastructure, and deferring cost reductions in low-emission technologies 
will increase the cost of achieving environmental goals. The costs of de-
laying global mitigation action by seven years but still stabilizing at 550 
ppm CO	
2-e by 2100 is calculated to be about 10% higher in 2050 and to 
remain high up to 2100. These higher costs come from the need for

greater emissions reductions in less time to achieve the same environ-
mental outcome and the high cost of low-emission technology options 
that have not benefited from reductions in capital costs. The initial bene-
fits of delay come about when emissions are not priced. Note that in the Australian studies the cost of reaching a 450 ppm 
CO	
2-e target is just about 1% of world GDP in 2050 higher than reaching 
a 550 ppm target. This is very different from the Stern Review , in which 
costs increase dramatically for a 450 ppm concentration target as com-
pared with a 550 ppm target. Others reports (see, e.g., OECD, 2008) con-
sider the 450 ppm concentration target unreachable. Careful reading of the Australian report suggests several reasons why 
the 450 ppm costs are closer to the 550 ppm costs compared to Stern: 
 	
 CCS technology is included, becoming very important and 
widespread, and there are developments in other technologies as well. 
In other words, the possibilities for technological development seem 
more optimistic in the Australian scenarios. 	
 The 450 ppm stabilization scenario involves overshooting, so a 
majority of the costs of reaching the 450 ppm level are pushed into the 
future, where they are then more heavily discounted. 	
4.6 Summary / discussion of studies with a main focus on 
simulations 
This chapter has looked at several di fferent studies to do with the eco-
nomics of climate change. One common denominator has been that they 
are all based on large and complex computable models of the world 
economy. Furthermore, none of the st udies has conducted a full benefit-
cost analysis. The IPCC fourth assessme nt report is careful not to present 
figures for the cost of climate change and focuses mainly on describing 
the physical effects of climate change. The Stern Review bolder in this 
respect and presents different cost es timates that range from a 2.7% to a 
32.7% reduction in consumption now and forever. However, Stern does 
not calculate the optimal mitigation effort to avoid costs from climate 
change in which way that, for instance, Nordhaus does in his DICE stud-
ies. More recently, the OECD studies, the IEA studies and the Australian 
studies have all restricted themselves to looking at the cost of reaching 
different targets for the atmospheric concentration of GHG gases. All the studies include an analysis of mitigation costs. The IPCC 
fourth assessment report and the Stern Review assess other studies and 
present summary figures for them. Neither of them analyses the individ-
ual studies in detail, but instead focuses on the mitigation cost estimates 
and the corresponding carbon price implied by different targets. The

OECD studies, the IEA studies and the Australian studies are all based on 
runs on specific models and therefore include a much more detailed de-
scription of the methodology behind the study. The different approaches 
taken on the one hand by the IPCC and Stern and on the other by the 
OECD, the IEA and Australia should be borne in mind when comparing 
the different results from the studies. Finally, the IEA studies differ fro m the OECD and the Australian stu-
dies in one important respect. While the OECD and the Australian studies 
are based on a top-down general equ ilibrium model of the world econ-
omy, the IEA study is based mainly on a bottom-up model of the world 
energy system. These two methodological approaches differ in a number 
of ways. In a general equilibrium framework all prices are endogenous 
and determined by supply and demand, while in a bottom-up model some 
prices must be determin ed exogenously: for example, prices for important 
inputs such as oil prices and wage s for skilled and unskilled labour. To 
the extent that climate policy changes these prices, bottom-up models 
may yield biased results. On the other hand, since a general equilibrium model aims to cover all 
parts of the economy, the degree of detail is much lower. This implies 
that new technologies such as, for instance, CCS are not modelled explic-
itly, as they are in the bottom-up models. Instead general equilibrium 
models rely largely on elasticities of substitution between inputs and/or 
products with different em ission intensity. To the extent that the resulting 
input and/or product mix induced by the required emission reductions are 
outside the empirical sample used to estimate the elasticities of substitu-
tion, general equilibrium models may also yield biased results. The two 
modelling approaches must therefore be considered as complementary. 
The Australian studies have sought to combine the methods. The choice of a bottom-up model is also the reason why the IEA does 
not present a mitigation cost figure in the same way as the other reports. 
The IEA model can measure the social cost of putting emission con-
straints on the energy system, but not the effect on world GDP. In any 
case, the IEA has chosen to focus solely on the CO	
2 emission price. 
In the table below we have summarized the main findings from the 
studies. First, we note that there are some discrepancies between the BaU 
emission GHG concentrations, in particular between the Australian study 
and the other studies. The reasons for the higher Australian figure are 
both higher trend economic growth assu mptions and slightly higher emis-
sion intensity of growth. In particular, the emission intensity of develop-
ment in the Asian region has been far above that expected in the IPCC 
SRES emission scenarios. Costs of mitigation are measured as reductions in world GDP by 2050 
compared to world GDP in the BaU scenario. Note that the OECD and 
Australia expect much higher costs of stabilizing GHG concentrations at 
about 500 ppm in the atmosphere than Stern expects. For Australia the

reason seems to be the higher BaU emissions, while for the OECD it 
seems to be that global policy action is halted until later in the century. 
The assumptions about the success of new technologies like CCS also 
differ between the studies. Halted action plays a role when determining the global CO	
2 emission 
tax path as well. If one constrains the path by saying that the tax cannot 
exceed a certain level before some y ears into the future, one will most 
likely end up with a much steeper path that also has a higher end value. 	
Table 4.6: Comparison of the studies covered by Chapter 4 
Study 
GHG target 
concentration 
(CO	
2-e) GHG BaU 
concentration 
2100 (CO	2-e) 
Initial carbon 
price 
 Carbon price 
2050 
Costs as % of 
GDP (2050) 	
Stern Report 
550 ppm > 843 ppm 1% 
(-0.6-3.5%) 
 
IPCC, 2007 445-535 ppm 855–1130 ppm < 5.5% 
 
IPCC, 2007 535-590 ppm 855–1130 ppm US $ 20-80 
(in 2030) 
 US $ 30-150 
0.1-4% 
OECD, Env. Out-
look 2008 450 ppm 
>900 ppm US $ 5 
(in 2010) 
 US $ 177 
 
2.5% 
OECD, 2008b 550 ppm >900 ppm US $ 5 
(in 2013) 
 US $ 400 
 
4.8% 
IEA, World Energy 
Outlook 550 ppm 
1000 ppm US $ 40 
(in 2020) 
 US $ 90 
(in 2030) 
 
IEA, Energy Tech-
nology Perspectives 
2008 
 450 ppm 
1000 ppm US $ 200 
 
Australia's LPF, 
Garneau 550 ppm 
1560 ppm US $ 20 
(in 2010) 
 US $ 91 
 
2.7-3.2% 
Australia's LPF, 
Garneau 450 ppm 
1560 ppm US $ 34 
(in 2010) 
 US $ 158 
 
4.2-4.3% 
 
Note that all the figures in the table assume a global CO	
2 emission price 
after some year between 2020 and 2030, and that both the OECD 450 
ppm scenario and the Australian 450 p pm scenario assume overshooting. 
Overshooting occurs when atmospheric concentrations initially exceed 
and then return to the target level. Overshooting is inherently more risky 
than approaching stabilization levels from below (Pearman, 2008). If 
reductions in atmospheric concentrati ons are not possible, which is de-
batable, the 550 ppm scenario could turn out to be the only realistic sce-
nario. This report is being written in 2009. Many people would agree that we 
are still a long way away from a global price for CO	
2 and other GHG 
emissions, facilitated by an international climate treaty in which all major 
emitting countries have a ccepted emission ceilings. Moreover, the current 
price in the countries that have taken on emission targets – that is, most of

the Annex 1 countries, but not the USA – is below the price suggested in 
some of the other studies discussed in this and the previous chapter. This 
means that the OECD and the Australian studies could be closer to the 
actual, unknown future mitigation costs. However, although between 3% 
and 5% GDP loss is a high figure, it is still small compared to the large 
increases in world GDP that w ould result from expected economic 
growth in this century. For instance, the OECD in their latest study ex-
pects world economic growth to be slightly above 3% per year in the 
period. Taking on the maximum 550 ppm GHG concentration target im-
plies a drop in growth rate of just above -0.1% per year. Finally, both the OECD studies and the Australian studies stress the 
need for a global price on CO	
2 and other GHG emissions, and an interna-
tional climate treaty in which all major emitting countries have commit-
ted to emission cutbacks. With an incomplete treaty or an incomplete 
coverage of GHG gases, reaching ambitious targets becomes a lot more 
costly. Furthermore, if only the Annex 1 countries take action (alone), the 
550 ppm target becomes out of reach.

89	
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Norsk sammendrag: 
Klimapolitikk: Kostnader 
og utforming 
Det finnes en stor og voksende litteratur om økonomiske problemstilling-
er knyttet til klimaendringer, klima tiltak og klimapolitikk. I denne rappor-
ten presenteres og vurderes noen av de nyere studiene på området. Opp-
merksomheten er hovedsakelig rettet mot numeriske analyser, ikke mot 
de rent teoretiske studiene.	
29 	
 	
Blant de viktige temaene som behandles, er følgende: 	
 	
a) Hvordan forventes utslippene av klimagasser å utvikle seg, og hvilke 
klimaendringer vil dette resultere i dersom ikke ny politikk settes ut i 
livet? 
b)
 Hva kan økonomiske analyser fortelle om klimapolitiske mål? 
c)
 Hva koster det å redusere utslippene? 
d)
 Hvilke tiltak og politiske virkemidler bør benyttes? 
e)
 Hva blir merkostnaden for å nå klimapolitiske mål dersom en benyt-
ter sub-optimale virkemidler? 
 	
I hver enkelt av studiene i rapporten, bl ir ett eller flere av disse temaene 
behandlet. 
a) Utslipp for “Business as usual” (BaU) 
Fremskrivninger av klimagass-utslippene og klimaendringene dersom 
ingen nye tiltak setes ut i livet kalles ofte ‘business as usual” (BaU) frem-
skrivninger. De vil være sterkt påvirket av forutsetninger om befolk-
ningsvekst og økonomisk utvikling (B NP per capita). Ettersom disse 
forutsetningene er svært usikre fo r de lange tidsperspektivene som er 
aktuelle for studier av klimaendringer (100 år +), benyttes ofte flere alter-
native sett av forutsetninger. 
 	
 	29 Vi ser altså på analyser som beregner ta llanslag for viktige økonomiske størrelser.

Utslipp av klimagasser kan fordeles på tre hovedkategorier; energire-
laterte CO	
2-utslipp (fra forbrenning av olje, kull og gass til energiformål), 
andre CO
2-utslipp (f eks fra avskoging) og øvrige klimagasser. Ved tall-
festing av samlede utslipp oppgis ofte mengdene som CO	
2-ekvivalenter 
(CO	
2-e). Den viktigste hovedkategorien (ca 60 %) er energirelaterte CO	2-
utslipp, som inkluderer all forbrenning av fossile energibærere samt pro-
sessutslipp fra industrien. Disse utsli ppene blir ofte modellert som endo-
gene størrelser, mens de andre to utslippskategoriene (andre CO	
2-utslipp 
og øvrige klimagasser) vanligvis blir angitt som eksogene størrelser.30 
Ulike fremskrivninger av CO	
2-utslipp gir tilsvarende forskjeller for 
fremtidige konsentrasjonsnivåer av klimagasser i atmosfæren - og for 
tilhørende temperaturendringer. I de siste IPCC-rapportene er ut-
slippstrendene basert på et sett av scenarier som er presentert i IPCC”s 
rapport ‘Special Report on Emission Scenarios”. Disse scenariene bør 
forstås som BaU scenarier, og gir re sultater som peker mot en konsentra-
sjon av drivhusgasser i atmosfæren mellom 855 ppm og 1.130 ppm CO	
2-
e i år 2100. De fleste av studiene som er behandlet her gir konsentra-
sjonsnivåer innenfor det samme området. 
Forventede klimaendringer i BaU avhenger selvsagt av de fremskriv-
ningene en benytter for konsentrasj onene av klimagasser i atmosfæren. 
Forholdet mellom konsentrasjon og klimaendring beskrives gjerne som 
”klimasensitivitet”, og angir hvor mye den globale gjennomsnittstempe-
raturen vil øke på lang sikt (i for hold til før-industrielt nivå) ved en dob-
ling av atmosfærisk konsentrasjon av CO	
2-e. I henhold til IPCC (2007) 
vil denne koeffisienten ligge innenfor området 2	oC til 4.5	oC, med 3	oC 
som den mest sannsynlige verdien, og med svært liten sannsynlighet for 
verdier under 1.5	
oC. Verdier høyere enn 4.5	oC kan ikke utelukkes, men i 
dette området er det mindre sams var mellom observasjoner og modellre-
sultater. 	
b) Optimale utslippsforløp 
Dersom vi unnlater å forebygge klimaendringer kan de fremtidige kost-
nadene bli store, særlig i neste år hundre. Utslippsreduksjoner nå gir 
umiddelbare kostnader, og en fornuf tig klimapolitikk bør ha en god ba-
lanse mellom tiltakskostnader og kostn adene forbundet med de fremtidi-
ge klimaendringene. Ideelt sett er det ønskelig å minimere nåverdien av 
fremtidige kostnader	
31 – summen av tiltakskostnader og kostnader vi 
påføres av klimaendringene. I tillegg til å gi et optimalt utslippsforløp vil 
en slik tilnærming gi marginale tiltakskostnader over tid, dvs. karbonpri-
sen. Dette prisnivået vil til enhver tid gi en øvre grense for tiltakskostna-
 	
 	30 Eksogene størrelser er gitt utenfra modellen (f ra andre kilder) mens endogense størrelser er be-
regnet i modellen. 
31 Nåverdien av fremtidige kostnader er en veiet sum av alle fremtidige kostnader, hvor kostnadene 
får lavere vekt jo lengre frem i tid de kommer. Fremdtidige kostnader blir lavere jo høyere diskonte-
ringsrenten er.

der; ethvert tiltak som koster

mindre, bør gjennomføres. Karbonprisen vil 
typisk vokse over tid, med en vekstrate som er mindre enn diskonterings-
renten.	
32 
Utslippsforløpene og karbonprisene slike analyser gir vil være av-
hengige av tre faktorer: (i) tiltakskos tnader, (ii) klimaendringenes kostna-
der og (iii) diskonteringsrenten (for å kunne sammenligne kostnader og 
inntekter på ulike tidspunkter). Resultate ne fra mange av de studier vi har 
gjennomgått indikerer at det er optimalt å ha et moderat ambisjonsnivå. 
Optimalisering med Nordhaus”s modell DICE tilsier f eks at det er opti-
malt å la CO	
2-konsentrasjonen øke til 659 ppm i slutten av neste århund-
re, hvilket tilsier en temperaturøkning på 3.5	oC. Disse studiene benytter, 
grovt sett, de samme kostnadene fo r klimaendringer i fremtiden: For 
DICE er kostnadene for 3, 4 og 6	
oC henholdsvis 2.5%, 4.5% og 10% av 
verdens samlede BNP. Det er vanskelig å vurdere om disse estimatene er 
”høye” eller ”lave”, men antatt kostnad for en økning på 4	
oC er godt in-
nenfor det kostnadsområdet som er anslått av IPCC. Antatt diskonteringsrente er viktig for utfallet av en optimalisering av 
typen over, ettersom de største kl imaendringene vil komme i fjern frem-
tid. Mange optimaliseringsstudier beny tter diskonteringsrenter i området 
4 – 5%. I Stern Review argumenteres det for en mye lavere diskonte-
ringsrente, og 1,4% er benyttet i ra pportens egne beregninger. Med ut-
gangspunkt i tentative, mindre formal iserte optimaliseringsberegninger, 
anbefaler Stern Review et kons entrasjonsmål mellom 500 og 550 ppm 
CO	
2-e. Med en klimasensitivitet på 3 (IPCC”s beste anslag) vil dette be-
grense global temperaturøkning til 3	oC (mens den ville øke 7–9	oC i 2200 
i det BaU-scenariet som benyttes i Stern Review). Mye av debatten om optimale klimam ål i litteraturen er rettet mot dis-
konteringsrenten. Hva som er ”korrekt” diskonteringsrente i dynamiske 
optimaliseringsanalyser har vært drøftet i stort omfang i mange år i øko-
nomisk litteratur, bl.a. spørsmål kny ttet til verdien av observerte mar-
kedsdata. Det er relativt stor enighe t om at observerte markedsrenter kan 
benyttes i tidsperspektiver inntil ca 20 år, men det er ikke åpenbart at 
samme type data kan benyttes for an alyser av lengre tidsperspektiver. 
Diskonteringsrenten er ikke den eneste viktige faktoren i optimalise-
ringsanalyser. Noen av klimaendringenes kostnader vil komme i form av 
redusert biologisk mangfold, redusert helse, ekstremvær, økt konfliktnivå 
og lignende. Slike goder, som ikke omsettes på noen markeder, vil typisk 
vokse sakte over tid eller til og med avta. Hvis mengden av produserte 
markedsgoder samtidig øker sterkt, vil vi vente en økt verdsetting av 
godene som vokser langsomt eller avtar. Dette trekker i retning av at kli-
maendringene kan bli mye mer kostbar e enn hva som er forutsatt i de 
fleste analyser. En av studiene vi behandler tar opp denne problemstil-
 	
 	32 Strengt tatt skal denne vekstraten være mindr e enn summen av diskonteringsrenten og den raten 
karbon fjernes fra atmosfæren med. Sistnevnte rate er imidlertid lav - mindre enn 1% av karbonet i 
atmosfæren fjernes hvert år.

lingen og beh

andler den i en modell som for øvrig er nesten identisk med 
Nordhaus”s DICE-modell. Denne endri ngen gir et optimalt utslippsforløp 
som er betydelig mer restriktivt enn det som beskrives av Nordhaus. 
Som nevnt over er det knyttet betyde lig usikkerhet til beregningene av 
klimasensitivitet. Et ferskt bidr ag i denne sammenheng kommer fra Mar-
tin Weitzman (2009), som fokuserer på mulighetene for at klimasensitivi-
teten er ”betydelig høyere enn 4,5	
oC”. Med utgangspunkt i tilgjengelig 
vitenskapelig litteratur på området mener han det er 5% sannsynlighet for 
en klimasensitivitet høyere enn 7
oC og en sannsynlighet på 1% for en 
sensitivitet høyere enn 10	oC. Han benytter disse forutsetningene i en mo-
dell der kostnadene for klimaendringer forutsettes å være høye for store 
temperaturendringer. Han viser at forventede klimakostnader vil være 
svært følsomme overfor både sannsynlighetsfordelingen for klimasensiti-
vitet og sammenhengen mellom kostnader og store temperaturøkninger. 
Weitzman påpeker at de fleste analys er av optimal klimapolitikk ikke tar 
hensyn til disse forholdene, og at de derfor kan gi misvisende resultater. Mange studier ser også på optimalisering under beskrankninger, der 
beskrankningen består av en øvre grense for atmosfærisk konsentrasjon 
av klimagasser eller temperaturøkning. På denne måten tar studiene kli-
mamålene for gitt, og beregner optimal utvikling med disse betingelsene 
som utgangspunkt. I mange av studiene som er oppsummert i tabellen 
nedenfor, er utslippsforløp og karbonpriser beregnet med slike forutset-
ninger. 	
c) Kostnadene for utslippsreduksjoner 
Kostnadene for utslippsreduksjoner vil være høyere desto: 
 
 mer ambisiøst klimamål; 	
 høyere BaU-utslipp; 	
 høyere tiltakskostnader. 
 
Mange av studiene vi ser på rapporte rer kostnader av å stabilisere atmo-
sfærisk CO	
2 –nivå på ca	 450 ppm CO	2, tilsvarende 500-550 ppm CO	2-e. 
Den langsiktige temperaturendringen for dette konsentrasjonsmålet antas 
å være ca 2.5 - 3	
oC. Det er to relevante former for kostnader, nemlig to-
tal kostnader og marginalkostnader. 
Tabellen nedenfor inneholder slike kostnadstall for noen av studiene, 
og vi ser at estimatene varierer betydelig. For omtrent like klimamål har 
Stern Review og DICE-analysene samme nlignbare anslag for totale kost-
nader, tilnærmet 1-1.5% av BNP. Andre studier, særlig en av OECD-
studiene, anslår at kostnadene kan bli betydelig høyere. Det er grunn til å 
tro at årsaken til at OECD-studien ha r betydelig høyere kostnadene i 2050 
enn andre studier skyldes en utslipps bane med små tiltak i nær fremtid – 
og tilhørende behov for omfatte nde tiltak senere (i 2050).

Den marginale tiltakskostnaden, karbonprisen, er et uttrykk for hvor

streng klimapolitikken må være for å nå et gitt mål. Nivået på karbonpri-
sen vil til enhver tid gi en øvre grense for tiltakskostnader: Ethvert tiltak 
som koster mindre enn karbonprisen, bør gjennomføres. Karbonprisen er 
derfor et godt mål på ambisjonsnivået i klimapolitikken. For et gitt kli-
mamål vil en minimering av tiltakskos tnadene gi en karbonpris som vok-
ser med en rate som tilsvarer diskonteringsrenten + den raten som CO
2 	
fjernes fra atmosfæren med (se fotnote 4). Hvis vi også legger vekt på 
når en øvre konsentrasjonsgrense nås (desto senere, jo bedre), vil karbon-
prisen vokse med en lavere rate. For de to studiene fra OECD og en av 
IEA-studiene vokser den beregnede karbonprisen raskere enn diskonte-
ringsrenten. Dette indikerer at den ut slippsbanen som er lagt til grunn i 
disse rapportene ikke gir minimale ne ddiskonterte kostnader for å nå de 
konsentrasjonsgrenser som er benyttet. Det faktum at karbonprisen er for 
lav i en tidlig fase betyr at utslippene er for høye i denne fasen. For å 
holde CO	
2–konsentrasjonen under de angitte grenser, må derfor utslippe-
ne kuttes dramatisk i 2050. Dette v il medføre høye karbonpriser og høye 
tiltakskostnader i 2050. 
I tabellen nedenfor ser vi at det er store forskjeller i den langsiktige 
(2050) karbonprisen, også for sammen lignbare klimamål. Tabellen viser 
at analyseresultatene er sterkt avhe ngige av de forutsetninger og antagel-
ser som er lagt til grunn. 	
d) Hvilke virkemidler bør bli brukt for å redusere utslippene? 
Uansett om en ønsket utslippsbane er resultatet av en optimalisering eller 
en tilpasning til klimamål som er gitt utenfra, må det tas i bruk virkemid-
ler for å oppnå de ønskede utslippsreduksjoner. Et sentralt virkemiddel vil 
være korrekt prising av utslipp, enten i form av karbonavgifter eller kvo-
tepriser. Et viktig spørsmål er hvorvidt det er nødvendig med andre vir-
kemidler. Hvis markedene fungerte perfekt og klimaendringene var den 
eneste eksternaliteten som skulle håndte res, ville det ikke være nødvendig 
med andre virkemidler enn en korrekt prising av utslippene. Imidlertid 
finnes det en rekke imperfeksjoner i økonomien, inkludert områder som 
er særlig relevante for klimapoliti kken, f eks energisektoren og teknolo-
giutviklingen. Reguleringssvikt kan også forekomme, og det er f eks 
umulig for myndighetene å forplikte seg til en bestemt karbonpris i fjern 
fremtid. Mange beslutninger i nåtid v il ha konsekvenser for utslippene på 
lang sikt, samtidig som nåtidens utslipp vil være påvirket av forventning-
ene til fremtidige karbonpriser. Hvis markedsaktørene forventer mindre 
vekst i karbonprisene enn myndigheten e har tilsiktet, vil dette lede til 
beslutninger som gir høyere fremtidig e tiltakskostnader enn det som ville 
vært optimalt. I tillegg til en korrekt karbonprising bør politikken og virkemiddel-
bruken utformes slik at den korrigere r for andre typer imperfeksjoner av

relevans for klimautviklingen. Ulik

e typer subsidier og reguleringer kan 
inngå i en slik pakke, men der et viktig at virkemiddelbruken er gjennom-
tenkt og målrettet, slik at det er klart hvilke imperfeksjoner de ulike vir-
kemidlene er ment å korrigere for. Fremtidig teknologiutvikling vil være viktig for kostnadsutviklingen 
uansett hvilke utslippsmål som settes . En korrekt karbonpris vil gi mar-
kedsaktørene sterke insentiver til å utvikle klimavennlige teknologier. Det 
er likevel liten tvil om at uregulerte markeder vil gi utilstrekkelige insenti-
ver for slik teknologiutvikling. En viktig årsak til dette er at gevinstene ved 
ny kunnskap i stor grad vil tilflyte andre enn dem som utvikler den nye 
kunnskapen. Dette er hovedårsaken til at offentlig sektor delta i kunn-
skapsutvikling (typisk gjennom offentlig finansiert grunnforskning) og for 
å gi ulike typer offentlig støtte til kunnskapsutvikling i privat sektor. 	
e) For et gitt klimamål – hva blir tilleggskostnadene for å benytte 
sub-optimale virkemidler? 	
Uansett hvordan tiltakskostnader (e ller fordelene ved utslippsreduk-
sjoner) modelleres, vil de totale kos tnadene være påvirket av hvordan 
tiltakene (og utslippene) fordeles på sektorer og utslippskilder. En kost-
nadsminimerende alloke ring betegnes ofte som kostnadseffektiv. Mange 
analyser sammenligner ofte kostnadene for et sett av virkemidler med et 
annet sett av virkemidler som er de signet for å gi de samme samlede ut-
slippene. Avvik fra de mest kostnad seffektive virkemidlene gir typisk 
store kostnadsøkninger. Dette illustreres blant annet gje nnom analyser med DICE-modellen, 
der en har antatt at det etableres en avtale mellom USA, EU og åtte andre, 
store land. Til sammen representerte avtalepartene 75% av de globale 
utslippene i 2004. For en gitt, saml et utslippsreduksjon i disse landene 
ville kostnadene være 68% høyere e nn ved å fordele de samme reduksjo-
nene på alle land på en kostnadseffektiv måte. 
OECD- og IEA-studiene behandler flere scenarier for internasjonalt 
samarbeid om klimapolitikken. Resu ltatene peker i samme retning som 
de analyser som er utført ved hjelp av DICE-modellen: kostnaden er ve-
sentlig høyere ved begren set deltagelse enn ved full deltagelse. En av 
OECD-studiene viser for eksempel at et mål om 750 ppm CO	
2-e er uopp-
nåelig hvis Annex 1 landene alene sk al sørge for utslippsreduksjonene. 
Den samme studien viser at omfattende unntak for energiintensiv industri 
vil øke kostnadene for å nå et 550 ppm mål med 50%. Tilsvarende vil en 
få betydelig høyere kostnader (100%) for et gitt mål, dersom bare CO	
2 tas 
med i en avtale, mens andre drivhusgasser holdes utenfor. Lignende illustrasjoner fremkommer i analyser med WITCH-modellen 
når den kjøres med restriksjoner for bruk av kjernekraft, CCS, solenergi og 
vindkraft. Disse restriksjonene gir kostnader som er 7% av BNP i 2050 – 
sammenlignet med 3,9% uten restriksjoner.

Vi har

allerede behandlet årsaken til at det kan være ønskelig å supplere 
en karbonpris med andre virkemidler og tiltak. I debatter om dette temaet 
fremkommer det regelmessig påstander om at det vil være gunstig å erstat-
te karbonpriser med andre virkemidler – snarere enn å supplere dem; ” det 
må være bedre med gulrot enn pisk”. Økonomer er samstemte om at en 
prising av utslipp er helt nødvendig dersom en skal unngå vesentlig høyere 
kostnader enn nødvendig. Det foreligger imidlertid ingen garantier for at 
disse synspunktene får gjennomslag. De t er derfor interessant å se på nu-
meriske studier som beregner kostnadsøkningen av å velge andre virkemid-
ler enn en riktig karbonpris for å nå et bestemt klimamål. En av studiene 
viser at for et gitt utslippsmål vil det oppstå et moderat effektivitetstap om 
en utelukkende benytter karbonprising som virkemiddel, mens tapet blir 
betraktelig større dersom en unnlater å benytte karbonprising – og kun tar i 
bruk subsidiering av fornybare energikilder og/eller FoU. 	
* * * * * * * * * * * * 	
Tabellen nedenfor oppsummerer noen av resultatene i studiene vi har sett 
på. Selv om stabiliseringsmålene varier er, er de relativt like i forhold til 
forventet temperaturendring: 2.5 - 3	
oC. Som nevnt tidligere er det store 
forskjeller i nødvendig karbonpris for å nå dette målet. De fleste av studi-
ene anslår en karbonpris på 100-400 US $ per tonn CO	
2 i 2050.

Utslipp og karbonpriser (US $ per tonn CO	2) 	
Studie Stabiliseringsmål Karbonpris	33 
2010-2015 Karbonpris	34 
2050-2055 Kostnader 
som % av 
BNP (2050) 	
Nordhaus, Dice 
Mål om max 2	oC tem-
peraturøkning 
 US $ 20 
 
US $ 83 
 0.6%	35 	
Nordhaus, Dice 
420 ppm CO	2 US $ 67 
 US $ 189 
 1.4% 
ENTICE 
 Konstante 1995 utslipp 
US $ 182 
 US $ 491 
 1.6% 
Grimaud et al. 
 450 ppm CO
2 	US $ 48 
 US $ 200 
 
WITCH 
 450 ppm CO	
2 
US $ 20 
 US $ 350 
 3.9% 
Stern Report 550 ppm CO
2-e US $ 40 
(i 2005) 
 US $ 98 
 
1% 
IPCC, 2007 445-535 ppm CO	
2-e 
 < 5.5% 
IPCC, 2007 535-590 ppm CO
2-e US $ 20-80 
(i 2030) 
 US $ 30-150 
0.1-4% 
OECD, Env. Outlook 2008 450 ppm CO	
2-e US $ 5 
 US $ 177 
 2.5% 
OECD, 2008b 550 ppm CO
2-e US $ 5 
 US $ 400 
 4.8% 
IEA, World Energy Outlook 550 ppm CO
2-e US $ 40 
(i 2020) US $ 90 
(i 2030) 
 
IEA, Energy Technology Per-
spectives 2008 
 450 ppm CO
2-e 
 US $ 200 
 
Australia's LPF, Garneau 550 ppm CO
2-e US $ 20 
 US $ 91 
 2.7-3.2% 
Australia's LPF, Garneau 450 ppm CO
2-e US $ 34 
 US $ 158 
 4.2-4.3%

Appendices 
Appendix to Section 2.1 
The problem of maximizing (2.1) subject to (2.2) with a constraint is solved using optimal contro l theory. The present-value Ha-
miltonian is (written so all sh	
 adow prices are non-negative) *	()
St S 	
 	
		( () ( (), ) () () () () ()
H Bet D S t t qt et S t t S t		  	 
The optimal solution satisfies the fo llowing equations (for an interior 
solution: i.e. for e(t)>0 for all t): 
(2A.1) 	
0
H
e				 
(2A.2) 	
() () H
qt rqt
S					
 
(2A.3) 	
() t		 and 	*	()( ()) tS St			 
(2A.4) 	
lim ( ) 0	rt
t	eqt
		 
Equation (2A.1) gives us (2.3) – i.e. 	
'( ( )) ( )B	et qt		 – while (2A.2) im-
plies 
(2A.5) 	
() ( ) () ( (), ) ()	S	qt r qt D S t t t				 
	 
Solving this differential equati on and using (2A.4) gives us 
(2A.6) 	
	()()	() ( ( ), ) ()	rt
S
t	qt e D S t d				
  
	
 
Consider first the case in which the constraint 	
*	()
St S		 is never binding 
so that 	
() t		 for all t. If 	(,) (
DSt mSt )		, where m is a constant pa-
rameter, it immediately follows from (2A.6) that 
(2A.7) 	
()m
qt
r			

102 	 
More generally, it follows from (2A.6) that q(t) will be rising at a time t if 
 is rising for all 	
SD t		. 
 
When 	
() t		 it follows from (2A.5) that 
(2A.8) 	
((),)
()
()
() ()SDStt
qt
r
qt qt		 		
 
We see from (2A.8) that as long as , the growth rate of q is less 
than 	
0	SD 	
r		. For the special case of 	0	SD		 (which could be the case for 
low values of S), the growth rate of q will be equal to	
r		. 
Consider the special case in which D(S ,t)= m(t) S. Here (2A.6) can be 
written as 
(2A.9) 	
()() ()()	()() ()	rt rt
tt	qt e m d e d	 			

   
		
 
If the constraint is binding for some t, 	
*	()
St S 	()t	 will be positive 
for these values of t. Assume that this is the case and that the optimal S(t) 
reaches at some date T. 
In this case 	
*S	()t	 is positive immediately 
after T. This implies that the second integral in (2A.9) is positive, so the 
path of q(t) must be higher than the price path when the constraint 
 is never binding: i.e. the price path given by the first term in 
(2A.9). It is useful to first consider the situation

during which *S
()
St 	*	()
St S		. 
When this holds it follows from (2.2) that 	*S
()
et
*S	
 is constant, so that 
our assumption implies that q(t) is constant. This constant value, 
denoted , follows from (2.3) with 	
0	etB	*q ()
et		 inserted. The value of 	
() t	 is determined by (2A.9) and 	*q
()
qt	 for all t when 	*	()
St S		 
holds. If m (t) eventually becomes sufficiently large, the first term in 
(2A.9) will eventually reach . From this time onwards 	
*q	() 0t		 and 	
()
et (
S t )		, so that S(t) will decline and the constraint 	*	() S
St		 will 
no longer be binding.

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Metadata Found
Author
hanne
CreationDate
2009-07-20T14:00:55+02:00
ModDate
2013-12-15T22:55:59+01:00
Producer
Acrobat Distiller 9.0.0 (Windows)
Pages
102