Two Intensities Analysis of London Accord
Hiroshige TANAKA
Professor of Faculty of Economics, Chuo University, Higashinakano
742-1,Hachioji-city, Tokyo 192-0393, JAPAN.

abstractLondon Accord is constructed by the two intensities on low carbon
communities in theoretical framework. This article makes clear thecharacteristics of the two indexes approach. We analyze the property of thetwo indexes approach in the dynamical adjustment procedure andequilibrium situation. We make the first step to clarify the theoreticalframework of London Accord.

1. Introduction
Globalizing economic activities and decentralization of government
might appear commonly in many advanced countries. Many environmental
and social problems require betterment with voluntary contributions ofmany agents of government, firms, residents and NPO. Global
environmental problems seem to require the global public policy to beeffective for each stakeholder 1 . For the problems new effective methods ortechnologies are possibly developed by supporting funds and efforts of theseagents. Sustainable development of communities could be achieved by acooperation and improved or voluntary participation of multi stakeholders 2 .
By effective cooperation of stakeholders
corporations or non-profit
organizations could achieve sustainable management and contribute toimprove social welfare 3 . Since many stakeholders seek self interests,
1 Medows et all(2005) and Gleeson and Low(2001) review global sustainability systems.

2 Nyssens (2006) indicates problems on multi-goal and multi-stakeholder organizations.
3 Hirshland(2006) considers the reason why the CSR are promoted globally since 2002.

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probably contributions of many stakeholders are deficient and out ofbalanced to promote sustainability 4 . We must investigate incentives ofvoluntary contributions and devise a sustainable scheme to foster and to
facilitate them 5 .
Price mechanism in market economy is vital role in the resource allocation.
The indexes to substitute or complement the price are investigated in theexternal market economy. In this essay, we consider the mechanism which
sends stakeholders signals toward low carbon emission communities. We
consider the properties of energy intensity and carbon intensity in theframework of London Accord 2007.

2. ModelWe are obliged to convert the way of life and production system in oursociety into more energy efficient system to achieve the sustainability at a
global scale. Many new technologies or policies are developed or proposed toattain the energy efficient society. Probably each method seems to contain
merits and demerits at the same time and shows various benefits and costs
to be determined. Some innovations might proceed in a sires of progresses
and mature for long time consequently. We should take strategic approach toaccelerate the innovation process. Evaluating the relative advantage of eachmethod, we should select the best mix of the policies. It is largely possiblethat each measure or technology shows environmental advantage with thecosts of decrease of consumption and production in the economy. Sometimes
we are targeting to construct conflicting goals for the economy and theenvironment. The goals for sustainability could be guided by arranging
synthetic social indexes which satisfy some proper characteristics. London
Accord focuses on the functions of a couple of indexes the energy intensity
and the carbon intensity 6 . Considering the two indexes, we explain somenotations as follows. The quantity of energy J is measured by Joule. The
4 Marshall(2005) considers collaborative solutions for environmental management.
5 Tanaka(2004),(2005),(2007a)(2007b) develops
the theory of corporate
governance(Tirole(2001)) and formulation of Altruism(Tanaka(1998) for the decision
process in multi stakeholder communities.
6 Krapivin and Varotsos(2007) review the theoretical analysis of globalization andsustainability. Bosetii ,Garraro and Galeotti( 2006) consider dynamical properties ofcarbon and energy intensity.

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scale of national product Y is denoted by GDP. It is a desirable target forclimate change that we achieve higher Y with lower consumption of J. We
should design a clear signal challenging the climate change as pricemechanism in market economy play the role on achieving efficient resource
allocations.
We must employ more efforts or resources to increase efficiency of Y
regarding to J. The developments of new production technologies or thereform of transformation or distribution system might contribute
improvement of the combination Y and J for global environmental problems.
We indicate the level of resources invested or consumed to improve Y as e y .

e j denotes the volume of effort to improve energy efficiency J. e y and e j
are traded in markets by the price of the unit. London Accord argues theproperties of the five capitals; natural capital, human capital, social capital,
manufactured capital and financial capital 7 . Resources are invested orpoured into some capitals intensively according to relative advantage ofthem. In other words, resources are arranged among feasible targets forclimate changes. If the total resource newly available to polices forconstructing the sustainable society is given by E, the fund G to improve
environment and poverty problems is expected to enlarge resource
restriction in the area of challenging global environmental problems. The
condition is expressed byey + e j = E + G .

(1)

The new technologies to improve energy efficiency possibly increase
national products but deplete J for the economy. In some case, the newtechnologies to improve efficiency of solar energy replace a part of fossil
energy but possibly decrease J for the total energy generation. In other case,the advanced equipment in power station requires great investment but isable to generate higher level of J. Although we can suppose both possibilities,
it is appropriate to consider the former case mainly. It is assumed that Yand J are the monotone increasing and decreasing functions of e y and e j as

7 Forum for the Future(2007) pp.7-15.

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Y (e y ) and J (e j ) . It is assumed that the inequalities Y ′(e y ) > 0 an J ′(e j ) < 0are satisfied 8 . We refer this assumption as negative prospect bydistinguishing from the positive prospect. C is the total amount of carbon
emitted in a nation. The growth of Y is a main factor to increase carbon
emission. Joule consumption by burning coal or oil increases Carbon
emission largely but the renewable energy is possibly assumed to affectcarbon emission in a limited way. The relation between carbon emission andJoule depends on the energy sources determined by energy policies. Carbon
function is expressed by
C = F (Y , J ) .
(2)
The shape of the carbon function is transformed by technologies, methodsand policies for the global warming. The energy intensity is defined byEI ≡J (e j )Y (e y ). Similarly, the carbon intensity is defined by CI ≡It is assumed that the inequalities

F (Y (e y ), J (e j ))J (e j ).

∂F∂F> 0 and> 0 are satisfied.
∂Y∂J

3. Methods of indication for minimizing carbon emission
In this section, we consider implications of index approach in climatechange by employing a model analysis. The policies for minimizing carbon
emission are derived by solving the first order conditions of the following
Lagrange function (3). λ is a Lagrange multiplier. Differentiating

F (Y , J ) + λ (e y + e j − E − G )(3)with regard to e y and e j , we derive the following conditions∂F dY+ λ = 0,
∂Y de y∂F dJ+λ =0.
∂J de jIt is certain that the inequality
8 This assumption is reflected by negative prospect. Some technologies intend toincrease J by additional investment of e j . The positive prospect J ′(e j ) > 0 is

discussed later.
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dJ
dJ de j−=<0dYdYde y(4)holds. Considering (4), we can suppose that J and Y satisfy a positive
correlation 9 . That is, (4) expresses the increment of J required by one unit
enlargement of Y in the most efficient carbon emission. In order to construct
low carbon emission communities, the depletion of energy efficiency is
obtained by a expense of decreasing GDP. (4 ) implies that the depletion of J
required by the growth of GDP to achieve low carbon communities decreasesdJor higher marginal
to lower in lower marginal depletion effect of energy
de jnational productdY. That is, the economic or shadow price should bede ydetermined by the rate of the two marginal effects of energy and product.
The rate will be set up as a targeting index for market oriented solution forclimate change. In this essay, policies based on (4) is named by direct orsingle index approach.
London Accord adopts two indexes expected to arrange investments formany fields of depleting carbon effectively and efficiently. We assume thatthe most efficient social system with carbon emission is attained in thecondition satisfies the highest level of carbon intensity. To solve thesolution the Lagrange function is described as follows.
F (Y (e y ), J (e j ))Y (e y )+ μ (e j + e y − E − G )(5)

μ is a Lagrange multiplier. Differentiating (5) with e j and e y , the firstorder conditions of low carbon communities is written by∂F dJ∂J de jY+ μ = 0,

9 In the case of positive prospect for energy technologies

J ′(e j ) > 0 , (4) is positive. If

our society construct by these technologies, the growth of Y can be achieved by depletingJ. In this condition, we could attain the growth of Y and depletion of J at the sametime. So we could easily find the way to low carbon society.
5dY∂F dY−Fde y∂Y de yY2+ μ = 0.

By arranging the above tow expressions, we ensure that the growth rate ofJoule and GDP satisfy∂FdJF( ∂Y − ) deYY = j .
dY∂Fde y∂J(6)Although we must develop some more investigation, the following result isobtained by comparing (5) and (6). Considering the left side of (6) istransformed intoFdJ 1 Y−−dY Y ∂F∂J(7)For the relatively small economy Y<1, (6) is assumed to be larger thannegative value of (4). Index approach seems to target greater substation rate
between the energy J and the product Y.
Finally. We consider the energy intensity. Employing the following
Lagrange function
J (e j )Y (e y )+ α (e j + e y − E − G ) .

(8)

α is a Lagrange multiplier. The first order conditions of the energy intensity
are exhibited bydJ
de j+α = 0 ,YJ dY− 2+α = 0.
Y de yThe above expressions are arranged bydJ
de jJ+dY
de yY= 0.

(9)6

Consequently, the intensity of energy implies the depletion rate of J andgrowth rate of Y of the two efforts e j and e y equilibrate each other in thelow carbon communities. (9) is rewritten by (10). In other words, the rate
between J and Y should be equal to rate of marginal effect of twoefforts e j and e y . Considering the intensity of energy employs average
rateJdJ
instead of marginalin the case (4), this intensity sends moreYdYcautious signal to deplete J than the single index approach.
dJde jJ(10)=−> 0.
dYYde yNoticing that (7) is rewritten by−F
1 dJ+()∂FY dY∂J(11)

two intensities approach adopted by London Accord indicate the larger
economy Y more effort to deplete J.
Finally, two intensities approach more sophisticate valuation for policies
for climate change in dynamic arrangement process. In a equilibrium, twoindexes (7) and (10) turn into the identical value. To simply the expression
the elasticity of energy to carbon emission∂F J
is denoted by ε . Making∂J F(10) equal to (11),dJ
1= J (1 − )εdY(12)is derived. J depletion accompanied by decrease of production Y becomeslarger as J or ε increases. That is, the economic or market value of energy
depends on the elasticity of energy to carbon emission.

4. Remarks
To achieve low carbon emission we should target to combine the economicor market value to resource allocation between production and energy

7efficiency improvements in the direct one index approach. On the other,London Accord is constructed by the two intensities on low carbon
communities in theoretical framework. This article makes clear thecharacteristics of the two indexes approach. Two main results are confirmed.
First, the two indexes approach makes many effective signals to moving
communities into low carbon system of society in the dynamical adjustment
procedure. Second, in the goal the economic or market determine theresource allocation between economy and environment value depend onenergy J and the elasticity of energy to carbon emission.
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Acknowledgments
I acknowledge Mr. Simon Mills, Sustainable Development Coordinator in
the City of London, and Professor Michael Mainelli for offering current
materials of sustainability program developed by the City of London .

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