DBJ Research Center on Global Warming
Discussion Paper Series No. 52 (6/2015)

On the Economic Properties of the CDM:
Does Emissions Trading Contribute to Global Warming Problem?

Morio Kuninori
Masayuki Otaki

This paper is a preliminary material in the draft form to stimulate discussion
and comments from academics and policy makers.Views expressed in thispaper are those of the author(s) and do not necessarily reflect the official
views of the Development Bank of Japan.

On the Economic Properties of the CDM:
Does Emissions Trading Contribute to Global Warming Problem?

Morio Kuninori
Hosei University
kuninori@hosei.ac.jp
Masayuki Otaki
The University of Tokyo
ohtaki@iss.u-tokyo.ac.jp

Abstract
This study examines the role of the Clean Develop Mechanism (CDM) in mitigating
global warming problems and considers its economic welfare implications of the CDM.
The CDM is a kind of offset trading scheme of carbon dioxide (CO2) emissions between
advanced and developing economies. We consider that the right to trade CO2 emissionsat an ideal price as rewards to advanced economies for investing in more CO2 saving
technologies and/or factories to developing economies. This study explains that undersome condition the CDM succeeds in suppressing CO2 emissions and can become asecond-best measure to mitigate global warming. Nevertheless, we clarify that the
carbon markets between advanced economies are generally not sustainable without thehelp of their governments. That is, the fact that carbon markets cannot support ideal
prices without the help of substantive government purchases suggests that the CDM
incurs an additional burden, such as taxes to advanced economies for preserving thescheme although the resultant transfer evidently equalizes the international income
distribution.

Keywords: Clean Development Mechanism; Global Warming Problem; Offset Trading;
Additionality; Baseline
JEL Classifications: Q51; Q54; Q58
1

1. Introduction
Whether the Clean Development Mechanism (CDM) substantially mitigates the excess
CO2 emissions is quite obscure. This is not merely because the structure of the CDM
scheme is rather complicated to understand, but also because the offset trading systemdoes not seem to reduce total CO2 emissions in reality. This study offers a simple modelof the CDM scheme that captures its important characteristics and analyzes the
economic welfare implications of this scheme.
The carbon market under the CDM scheme trades reduction credits of CO2 emissions
originating from nascent and/or prevailing emission-saving technology in developing
economies 1 . This study clarifies that the CDM contributes to mitigating excess
emissions of CO2 as long as the carbon price is set properly (i.e., modified Samuelsonrule). In addition, since the CDM presumes voluntary transactions, it is apparent thatdeveloping economies becomes better off by joining this scheme. That is, if it works, theCDM could achieve mitigation of income disparity between advanced and developing
economies.
The second concern of this study is the income redistribution effect of the CDM scheme.
There is no object that designates proper carbon price in the CDM scheme. Accordingly,
the rationing of allowable CO2 emissions to each firm is unavoidable if one considers
that the control of CO2 emissions is effective. Nevertheless, as long as the actualized
aggregate emissions of advanced economies stay within the amount of the acquired
reduction credit by the CDM, the price of carbon cannot remain at ideal levels. As such,the economic value of the tax credit is heavily impaired. This makes the CDM scheme
dysfunctional. If the governments of advanced economies intend to sustain a suitable
positive carbon price, the governments, by themselves, must intervene in the market, bypurchasing the corresponding amounts of reduction credits.
Because government expenditure is ultimately financed by tax, such purchases
redistribute incomes from tax payers unrelated to the CDM scheme to participants.
While one could encounter many difficulties in judging the fairness on income
distribution, it should be noted acutely that debt finance is undesirable because this
disturbs the income distribution of future generations who are not responsible for thestate of current economies. Thus, it is quite important where to set the baseline of the
CDM scheme that is the reference point that determines the volume of tax credit of CO2
emissions. This study also analyzes this problem.
The rest of this study is organized as follows. Section 2 constructs a static model of CO2
Typical types of CDM projects and their methodologies are explained in UNFCCC(2014).

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emissions control by the CDM scheme and shows that the CDM can enhance wellbeing
in both an advanced economy and a developing economy. Section 3 explains the income
redistribution effect associated with the CDM, and discusses the role of the carbon
finance alongside the trade of emissions rights. Section 4 provides brief concluding
remarks.

2. The Model
2.1 The Laissez Faire Economy
As a reference case, let us consider the laissez fair world economy in which there is no
regulation on CO2 emissions and emission decisions are segregated from the calculationof associated damages. It is assumed that there are n economies of type k ( k  a, d : aand d refer to advanced and developing economies, respectively). Let the economic  , where e is the volume of emissions ofbenefits of an economy be denoted by  F eikikthe i -th economy of type k .  is a parameter that represents the efficiency of the fossil  . It should be noted

fuel combustion. Figure 1 illustrates the shape of the function F eikthat it is assumed there is an upper limit of the benefits from the combustion for a given (i.e.,  F  e  ).
For simplicity, the damage function  of global warming via fossil fuel combustion isassumed to be the same linear homogenous quasi-concave, non-negative, strictlyincreasing and symmetric function denoted









 , elk , , elk' '    , elk' ' , , elk  , k , k ', l , l '.

(1)

The symmetry represented in Equation (1) implies that the damages of global warming
are not unrelated to the locations where CO2 is emitted.
Since the emissions decisions are assumed to be segregated, the maximal emissions e
are actualized in the laissez faire economy. Consequently, the resultant welfare of an
economy is F  e     e , e , , e , , e , e  .

3(2)

2.2 Economic Welfare under the CDM Scheme
This subsection examines whether economic welfare is improved by applying the CDM
scheme to a pair of one advanced and one developing economy relatively to both
economies being in laissez faire situation. This study captures the CDM scheme asfollows.
(i)  units of goods are required for capital investment in a developing country. Whichof the two economies finance the associated fund is not essential for evaluating the
economic welfare as is discussed in Section 3.
(ii) If and only if the capital investment is additional (the term additional is strictly
defined below), is the project certified.
(iii) Such a certified investment is rewarded by an emission right whose value is  e  e  .  denotes the unit carbon price that is designated by governments. e is thebaseline of emissions associated with this investment, and e represents the actual
emissions.
(iv)Whenever the carbon market falls into disequilibrium, the government of theadvanced economy bridges the gap. The necessary funds for this compensation are
financed by taxes in the advanced economy.
The sum of the gains obtained by applying the CDM scheme of the i -th pair ofadvanced and developing economies is written as F  eia    F  eid   2  e1a eia ena , e1d eid end    .

(3)Equation (3) becomes the objective function of the CDM scheme. One must note that thetransaction amount of the emissions right,   e  ei  , does not appear in Equation (3).
dThis is because the carbon market between an advanced and a developing country
functions only as an income transfer mechanism and does not relate to efficient carbon
allocation although such an amount is vital for capital investment to become additionalin the CDM scheme.
While the conditions for additionality under the CDM scheme are very complicatedand there are many requirements in reality, this study focuses on the following two
properties.

4Definition 1.

A plan to invest capital in a developing economy is additional whenever the following
two conditions are satisfied.
(i) Financially additional: the investment is feasible in that the direct benefits fromemissions trading are privately beneficial and the revenues from the trading,   e  e  ,exceeds the associated cost  . That is, the following should hold2: e  eid   (4)(ii) Socially additional: the maximized value of social welfare function (3) takes a larger

value than that in the state of laissez faire defined by Equation (2).
Condition (i) prescribes that the capital investment should be compatible with theprivate motive. Condition (ii) requires that the CDM scheme should enhance theeconomic wellbeing of the conjoining two economies in reality.
The problem to be solved in this subsection is to maximize Equation (3) on

e , e aidiunder the constraint of Equation (4). One must also ascertain whether the maximized
value satisfies the requirement of being socially additional (Condition (ii) in Definition1). For the first step, the following lemma is used.
Lemma 1.

For any fixed   e  ei  , there is a sufficiently small  that satisfies Equation (4).
dConversely, for any fixed  , there is a sufficiently large e that satisfies Equation (4).

This is a half of the notion of additionality. The other half indicates that, without theCDM project, the capital investment must not be feasible. Since most of the profitable
investment projects would be feasible even without the revenue, additionality condition
rules out these profitable projects. Although UNFCCC (United Nations Framework
Convention on Climate Change) has been trying to satisfy the additionality condition inchoosing CDM projects, issued methodological tools such as UNFCCC (2012), various
studies, including Schneider (2009), have claimed that many of CDM projects often failto pass the additionality test, thereby, losing the “environmental integrity” of the CDN
credit program. In our study, one of the sufficient conditions of additionality may be
expressed as  F(eid )   . However, hypothetically speaking, there would be other kinds ofbarriers in preventing the project when the revenue is unavailable. Some of the barriers
are discussed in UNFCCC (2012).

2

5

Lemma 1 implies that the constraint in Equation (4) becomes redundant as long as theinvestment cost  is sufficiently small relatively to the benefits obtained from trading
emissions rights, and this is attainable by setting the baseline e to be high enough.
Since the baseline e is directly unrelated to the maximization problem in Equation (3),we can separate the maximization problem from the decision of where to set thebaseline e .
Accordingly, the necessary and sufficient condition for the maximization of the social
utility function in Equation (3) becomes F '  eia   2,  F '  eid   2 d , i
a
ei
ei

(5)

By the symmetry assumption in Equation (1), we obtain  ,eia eid e1a

i .

(6)

Substituting Equation (6) into (5), it is ascertained that

 F '  eik    F '  e*   2


,
e1a

k , i.

(7)

Since the right-hand side of Equation (7) represents the social marginal cost of CO2
emissions, the price of carbon  should be determined at this level. That is,

 2


.
e1a

(8)

Equation (8) implies that the price of carbon should be equal to the sum of the marginalnuisance of the emissions of the economies that are partners in the CDM scheme. Thisis a form of Samuelson’s (1954) rule in the sense that the price of public bads (goods)
should be determined by the sum of marginal disutility (utility) of sufferers(beneficiaries).
As discussed above, we confirm that the capital investment satisfies the condition (i)for additionality if  is small enough, and that the carbon price subdues the rule inEquation (8). Finally, what remains to check is whether the resource allocation
designated by the rule in Equation (8) is consistent with condition (ii) in Definition1.
Concerning this question, the following theorem holds.
Theorem 1.

Since F  e*     e* e* e* , e* e* e*    F  e     e e e , e e e  ,(9)the CDM scheme that satisfies Equation (6) improves economic welfare in both6

advanced and developing countries in comparison with the laissez faire state inEquation (2).
Proof. Because  F   is strictly concave and  F '  e   n|   n a |ea  e  0 ,a e1a  e
e1
e1 1

e*  e . Accordingly, (9) holds. If  is sufficiently small,  exists such that

 F  e*     e* e* e* , e* e* e*      F  e     e e e , e e e  .

(10)Equation (10) implies that economic welfare in both economies is improved by the CDM
regardless of which economy has incurred expense for the capital investment, as long as
the investment costs are not so expensive. QED.
Consequently, it has been ascertained that the CDM scheme that obeys optimal carbon
pricing rule (8) satisfies the conditions for capital investment additionality in the senseof Definition 1.

3. Determination of the Baseline and Associated Change of Income Distribution
3.1 Relationship between the Baseline and Domestic Income Distribution
The discussion about the CDM scheme in Section 2 neglects the income redistribution
effect into the domestic economy. This is because the determination of the baseline e is
not concerned with the optimal emissions allocation, and relates only to the income
redistribution in conjunction with the achievement of the CDM scheme. This section
deals with how the level of e affects income distribution within an advanced economy.
While trading in emissions rights is limited to the bilateral case, the essence of the
discussion is also applicable to the case of the international and open market in whichan economy in excess supply of the emissions rights exports its rights to economies withexcess demand for such rights.
Excess supply emerges in an economy when e is located at *  e  e*    *e* .

(11)The left-hand side of Equation (11) is the supply of the emissions right that is obtained
from the emissions-saving capital investment for a developing economy. The right-handside is the demand for the emissions right of the domestic industry. Insofar as
Inequality (11) is maintained, the emissions right market cannot sustain the carbon
price in market  at the designated price  because of the existence of excess supply,
*

7

*
*
which amounts to   e  2e  .

Such an amount of emissions right is purchased by the government to sustain theequilibrium market price at  . Because the government expenditure is financed by***taxation,   e  2e  amounts of income, which corresponds to the subsidy paid forparticipating in the CDM scheme, are transferred from unrelated (taxed) individuals tothe participants of the CDM scheme within the advanced economy. Thus, the baseline,

e , acutely affects the income distribution within the advanced economy. While
employers are encouraged to participate into the CDM scheme by an increase in thebaseline, e , the associated costs are burdens for other taxpayers.
Thus, the evaluation of income redistribution is quite a difficult problem. There is, atleast, one thing of which to be cautious. Since CO2 emissions remain in the atmosphere
over time and aggravate the standard of living of our descendants, the associated costs
for encouraging the CDM scheme should be levied not from future generations but fromthe present generation. This is because only direct taxation from the present generation
could warn a legitimate price for which they should pay for their own emissions. In thissense, debt finance for the subsidy is prohibitive since this procedure is accompanied byno pain to the present generation.
3.2 Carbon Financing and Government Intervention
In this subsection, the function of carbon finance is formatted and reveals the necessity
for the government intervention analyzed in the subsection 3.1. Carbon finance in thisstudy is regarded as a type of finance in which money is lent to a developing economy fora capital investment in emissions-saving technology and/or factories in exchange for the
trade in those emissions savings.
Accordingly, the first condition for the capital investment being additional, that is,
Inequality (4), is equivalent to the viability condition of such finance. Thus, to makefinancial intermediaries confident in the result of carbon financing, the confidence inthe government’s intervention to equilibrate the carbon market at the designated price * must be acutely decisive. As such, carbon finance is a fragile concern without
government help, as depicted by Lovins and Cohen (2011: P.227).

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4. Concluding Remarks
This study designates the CDM as an acquisition mechanism of carbon tax credits for
returns from emissions-saving capital investments in developing economies, which areconditional on additionality. The requirements for a project to be additional are defined
clearly.
It should be noted that our theory is also applicable to the case in which a developing
country constructs an emissions-saving facility and sells the acquired tax credits to anadvanced economy.
This is because the difference between the former and the latter case is only thedifference to who owns the property rights of the emissions-saving capital andassociated tax credits. In the former case, these property rights belong to the advanced
economy, and the converse is true in the latter. By the Coase theorem (Coase, 1960), theefficient allocation of public goods (bads) through a bargaining process is achievable
without conferring the location of property rights. Therefore, our model is also
applicable to the case in which a developing economy directly accesses the CDM
scheme3.
This study finds that the optimal carbon price, which should be designated in the
carbon market, is the sum of the marginal disutility of the two economies derived fromCO2 emissions. This is a variant of Samuelson rule concerning the allocation of public
goods (bads).
Finally, the role of the baseline is discussed in conjunction with the role of thegovernment intervention to equilibrate the carbon market under the designated price.
Whenever the baseline is set above the equilibrium transaction volume, an excess
supply of tax credits appears, and the government purchases such residues in order tosustain the designated price. Such purchases subsidize and enhance the CDM projects
but ultimately becomes burdens of taxpayers who are unrelated directly to the CDM
projects. Thus, we find that the location of the baseline from the viewpoint of economics
strongly related to the income redistribution problem provoked by CDM projects.

See Mas-Colell, Whinston, and Green (1995: pp. 356–357) for a concise explanation
about the Coase theorem.

39

References
R. Coase (1960). “The Problem of Social Cost,” Journal of Law and Economics 1: pp.
1-44.
L. H. Lovins and B. Cohen (2011). Climate Capitalism: Capitalism in the Age of Climate

Change, New York: Hill and Wang.
A Mas-Colell, M.D. Whinston and J.R. Green (1995). Microeconomic Theory, Oxford:
Oxford University Press.
P. A. Samuelson (1954). “A Pure Theory of Public Expenditure.’’ Review of Economic

Statistics 36: pp. 387-389.
L. Schneider (2009) “Assessing the Additionality of CDM Projects: Practical Experiencesand Lessons Learned,” Climate Policy 9, pp. 242-254.
UNFCCC (2012) “TOOL01, Methodological Tool: Tools for the Demonstration andAssessment of Additionality,” Version 07.0.0.

https://cdm.unfccc.int/methodologies/

PAmethodologies/tools/am-tool-01-v7.0.0.pdf. Accessed 28 May 2015.
UNFCCC (2014) CDM Methodology Booklet, Sixth Edition, Information Updated as of
EB 79, November.

https://cdm.unfccc.int/methodologies/documentation/1411/Meth_

Booklet_2014_Named.pdf. Accessed May 28 2015.

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