DEPARTMENT OF ECONOMICS
TECHNOLOGICAL CHOICE UNDER
ENVIRONMENTALISTS’ PARTICIPATION IN
EMISSIONS TRADING SYSTEMS
Elias Asproudis, University of Loughborough, UK
Maria José Gil-Moltó, University of Leicester, UK
Working Paper No. 09/09
April 2009
Technological choice under environmentalists�
participation in Emissions Trading Systems
Elias Asproudis�
Dpt Economics
Loughborough University
Maria José Gil-Moltóyz
Dpt Economics
University of Leicester
April 7, 2009
Abstract
We model competition in an emissions trading system (ETS) as a
game between two �rms and environmental group. In a previous stage,
�rms endogenously choose their manufacturing technologies. Our re-
sults show that there is an inverted U-shape relationship between how
polluting the chosen technology is and the degree of the environmen-
talists�impure altruism. Firms choose a less polluting technology in
the presence of the environmentalists than in their absence only if they
are characterised by intermediate degrees of impure altruism.
Keywords: ETS; Technology Choice; Induced Technological Change;
Impure Altruism
JEL Codes: L13 Q30 O31
�[email protected]; Dpt Economics, Loughborough University, Loughborough, LE113TU (United Kingdom).
[email protected]; Dpt Economics, University of Leicester, Leicester, LE1 7RH(United Kingdom).
zBoth authors thank insightful comments by J.C. Bárcena-Ruíz, N. Georgantzís, R.Faulí-Oller and P. Zanchettin. Elias Asproudis gratefully acknowledges the �nancial sup-port received from Loughborough University where he is conducting his PhD studies.
1
1 Introduction
Emissions trading systems (ETS henceforth) are market based instru-
ments used to control pollution. The idea of the ETSs or permits markets
has its origins in Coase (1960) and Dales (1967) and relies upon the creation
of economic incentives to reduce pollution through the exchange of permits.
Following the Kyoto Protocol (1998) ETSs have become major tools in the
anti-pollution policy in a number of countries. For example, in the US, there
are ETSs in place for the reduction of SOx and NOx emissions. Also, the
European Union (EU) has implemented an ETS for the reduction of CO2.1
Interestingly, several legal frameworks opened the participation in the
Emissions Trading System not only to �rms but also to third parties, such
as citizens, consumers, environmental organizations, etc. In other words,
both polluters and victims can participate in the ETS and their interac-
tion will determine pollution levels. This right to participate is comtem-
plated, for example, in the United Nations�Framework Convention for Cli-
mate Change (Guidelines FCCP/ CP/ 2001/ 2/ Add.4) and in the EU�s
Directive 2003/87/EC. Similarly, in the US, third parties can participate in
the Sulphur Allowance Trading Program (SAT) and in the Clean Air Incen-
tives Scheme (RECLAM). Groups such as the Acid Retirement Fund or the
Clean Air Conservancy Trust are examples of NGOs who use their funds
(mainly collected through charitable donations) to purchase permits from
ETSs. By withdrawing permits from the market, this type of organisations
hope to increase the price of polluting and therefore induce �rms to invest
in technologies to reduce their emissions.2
The reasons why third parties should be allowed to participate have been
the focus of a number of theoretical contributions. For example, Smith and
1This is the largest application of ETS in geographic terms up until now (Newbery,2008).
2For example, this objective appears very clearly stated in the Acid Rain RetirementFund�s ethos.
2
Yates (2003a, 2003b) and Shrestha (1998) show that the thirds�participation
in the permits�market gives valuable information to the regulator regarding
the market equilibrium when the regulator faces uncertainty: If third parties
purchase permits, it must be that the initial number of permits was higher
than the optimum. Also regarding the regulators�uncertainty, English and
Yates (2007) show that the Kwerel�s mechanism may be e¤ective only if the
citizens take part in the ETS.3
Interestingly, the academic literature already provides empirical evidence
on the presence of the thirds in ETS and its e¤ects. For example, Schwarze
and Zapfel (2000) documents the participation of third parties in the SAT and
the RECLAIM. Joskow et al. (1998) showed that third parties o¤ered very
high prices in the auctions of SO2 permits in the 90s. Israel (2007) examines
the magnitude of the participation by third parties (mainly environmental
groups) between the years 1993 and 2006, concluding that the number of
permits withdrawn by these agents is not very high relative to the total
number of permits. According to the author the above fact could also be
interpreted as an indication that the US Environmental Protection Agency
had targets close to the social optimum.
Despite the relevance of the issue, the literature on ETS and technology
choice has largely overlooked the implications of thirds�participation in ETSs
for �rms�technological choice. A related literature strand explores the link-
ages between the existence of policies against climate change and the degree
of technological change. For example, Newell et al. (1999) and Popp (2002)
analyze how higher energy prices induce a higher technological innovation4.
Regarding tradable permits, Fischer et al. (2003) and Requate and Unold
3Recently, Rousse (2008) also highlights the advantages of the direct participation inthe carbon emissions trading systems. Malueg and Yates (2006) also show that the citizensmay prefer to participate in the permits�market under a grandfathered system instead oflobbying the regulator to reduce the total number of allocated permits.
4See also Chakravorty et al. (1997). Also Goulder and Schneider (1999) and Goulderand Mathai (2000) examine the implications of Induced Technological Change (ITC) forCO2 abatement policy.
3
(2003) compare the propensity to technological innovation generated by sev-
eral market-based instruments and Kerr and Newell (2003) show that ETSs
provide more e¢ cient incentives for green technology adoption than taxes.
In the same spirit, Kennedy (1999) argues that the regulator can reduce the
quantity of available permits as a way to generate incentives for �rms to
adopt a greener techonology even in the presence of uncertainty about the
environmental damages. However, none of these contributions incorporates
the participation of the thirds in the ETS.
The objective of our paper is to study the interaction of �rms and envi-
ronmental groups in ETS and the implications of this for �rms�technological
choices. We introduce a duopsony that must purchase permits in an ETS.
The �rms can choose the type of production technology they will use. The
technologies available to �rms di¤er in their environmental credentials and
their set-up or adoption costs. The more polluting the production techology
is, the more permits the �rm requires per unit of output but also the lower the
adoption cost. We allow an environmental group to purchase (and therefore
withdraw) permits from the market. The price of the permits will depend on
the aggregation of the �rms�and the environmentalists�demand of permits.
It should be obvious that the higher the number of permits withdrawn by the
environmentalists, the higher the permit prices and therefore, in principle,
the more incentives �rms will have to adopt to a greener technology. Follow-
ing Hahn and Stavins (1992), we consider that the environmental group not
only cares about the level of pollution or externalities but also about total
surplus.
In the spirit of Andreoni (1989, 1990), we assume that the members of
the group gain a non-material utility from withdrawing permits.5 Andreoni
(1989, 1990) highlights that people are impurely altruistic and may obtain
some gains in utility from charitable giving. In our paper, we assume that the
5We consider members of the group not only the activists but also the donors or con-tributors to the group.
4
environmentalists feel that they do something right or fair by withdrawing
permits and this feeling increases their own utility (through self-satisfaction
or warm-glow). This "impurely altruistic" behavior introduces a distortion
in the market, as the environmentalists might be interested in withdrawing
more permits than socially optimal. Therefore, the presence on the envi-
ronmentalists in the ETS does not guarantee a �rst best solution. In the
paper we will study how the emission levels and technological choice are
a¤ected by the environmentalists�presence in the ETS and their degree of
impure altruism and study the equilibrium outcomes with and without their
participation.
Our results show that there is an inverted U-shape relationship between
how polluting the chosen technology is and the degree of the environmental-
ists�impure altruism. Moreover, �rms tend to choose a "greener" technology
in the presence of the environmentalists in the ETS than in their absence only
if the environmentalists are characterised by intermediate degrees of impure
altruism. Higher degrees of impure altruism can actually induce �rms to
adopt worse technologies but can also lead to lower emissions levels through
the reduction of output.
The rest of the paper is structured as follows: In section 2 we present
our model. In section 3 we solve the output stage. In section 4 we analyse
the technology choice by �rms when the environmentalists do not partici-
pate in the ETS. In section 4, we study the case of the environmentalists�
participation in the ETS. That is, their behavior in the ETS and �rms�tech-
nology choices. In section 5 we conduct some comparative static analysis
regarding technology choices, emissions and output levels in both settings
(with and without the environmentalists�participation in the ETS). Section
6 concludes.
5
2 The model
In our model, two monopolistic �rms act as duopsonists in the permits�mar-
ket. Each �rm faces a linear inverse demand function such as
Pi = a� qi (1)
where qi is �rm i�s level of output produced by �rm i. Prior to start produc-
ing, �rms choose their manufacturing technology from a spectrum of available
technologies which di¤er in the level of emissions derived from the production
of each unit of output. Firms must buy permits to o¤set their emissions. One
interpretation of our model is that the �rms are new entrants to the mar-
ket and they do not receive permits through grandfathering. An alternative
interpretation is that, even with grandfathering, �rms do not have enough
permits with their initial allocation. In that case, the demand of permits
would represent the extra permits needed above the initial allocation.
The choice of technology determines the number of permits required to
produce each unit of output. We denote the number of permits required per
unit of output by k and will use k to index the technologies available to �rms.
The greener (the more environmentally friendly) the technology is, the lower
its associated k. For the sake of simplicity and without loss of generality, we
assume that k 2 (0; 1]. Consequently, even if a �rm chooses a very "green"
technology (k close to 0), it still needs to purchase some permits to cover its
emissions.
The total number of emissions and, as a consequence, the total number of
permits demanded by �rm i depends on the type of technology (how polluting
the technology is) and the level of output chosen by �rm i
yi = kiqi (2)
We assume that the available technologies di¤er also in the investment
required to adopt them
6
Fi = (1� ki)2 (3)
Our modelling of the technology costs implies that adopting a greener
technology entails higher adoption costs than adopting a more polluting one.6
The innovation costs are assumed to be quadratic to re�ect the existence of
diminishing returns to investment.
For simplicity, we assume that �rms do not incur in any other production
costs than those derived from the acquisition of permits. Thus, �rms pro�ts
can be written as follows
�i = Piqi �Ryi � (1� ki)2 (4)
where R is the unit price of permits.
We assume that in the permits market there is a third player: an environ-
mental group. The environmentalists can withdraw permits from the market
by purchasing a number x of permits. This will a¤ect the equilibrium in the
permits market and subsequently, �rms� technological choice. We assume
that the price of permits, R, is an increasing function of the total number of
demanded permits
R = c+ h(yi + yj + x) (5)
The unit price of permits, R, can be interpreted in our modelling as the
equilibrium price of permits in the ETS market. In other words, we are
implicitly modelling the supply of permits.7 For the sake of simplicity, we
6The case in which cleaner technologies are also less costly to adopt is less interest-ing to study as in such case, the incentives of �rms would be aligned with those of theenvironment.
7The supply side can be thought to be constituted by either the regulator or those �rmsthat already have acceptable clean technology and excess of permits. They could be �rmsin other markets or even located in other countries with emissions levels well below thetargets. For example, there is ample evidence that in the countries from the Former SovietUnion (FSU), the total quantity of the permits is far above that of the real emissions. The
7
normalise c to 0 and h to 1. Our modelling of the price of permits di¤ers from
those contributions which assume that �rms are price-takers and also from
those contributions, such as Boyd and Conley (1997) and Conley and Smith
(2005), where �rms can buy permits at personalized prices. Our model is
suitable to represent situations in which a small number of �rms are present
in the market (say, for example, electricity companies) and therefore have
some degree of market power but they have to buy permits from a centralised
market.
We assume that the environmentalists are impurely altruists, that is their
behavior is (partly) driven by the maximisation of their own utility. The
environmentalists�maximize the sum of consumer and producers surplus (CS
and PS respectively) minus the emissions (E) and the costs of withdrawing
permits (Rx) plus the satisfaction or utility gained from withdrawing permits
(zx).8 The Objective Function therefore is:
OEG = (CS + PS)� E �Rx+ zx (6)
The last term in OEG is related to the impure altruism which characterises
the environmental group. In our model, the impure altruism is measured
by a parameter, z, which represents the utility gains experienced by the
environmentalists from withdrawing one unit of permits. More generally, the
parameter z would be the extra weight that the environmentalists give to the
reduction of emissions. This could be understood as the priority they give to
the environmental objectives over other objectives such as the maximization
excess permits -up from the real emissions to the Kyoto targets- are called �hot air�. It iswidely recognised that the FSU countries will constitute a very large part of the supplyof permits in the upcoming years (see Stevens and Rose, 2002; Bohringer and Vogt, 2003,2004; Klepper and Peterson, 2005; Bohringer et al. 2006; Bernard et al. 2007).
8We do not include the revenues generated by the selling of permits as normally envi-ronmental groups�actions are targeted to a speci�c industry and/or country. Therefore,we assume they only take into account welfare and externalities generated in a particularindustry or country. The relaxation of this assumption does not change qualitatively ourresults. We discuss this later in the paper. See footnote 19.
8
of consumer welfare and/or producer welfare.9
As standard, PS is de�ned as the aggregation of �rms�pro�ts across the
two markets
PS =
2Xi=1
�i (7)
and, given the linearity of the (inverse) demand functions, CS can be written
as
CS =2Xi=1
qi2
2(8)
We assume that there is one unit of externality produced per each unit
of emissions
E =2Xi=1
yi (9)
From now on, we will use the term "emissions" as a synonim of "exter-
nalities" or "pollution". The timing of the game is as follows: In the �rst
stage, �rms choose their production technologies.10 In the second stage, the
environmentalists purchase permits. In the last stage, �rms choose quan-
tities (implicitly determining their demand of permits).11 We assume that
�rms choose simultaneously in stages 1 and 3. We solve the game by back-
wards induction to analyse the Subgame Perfect Nash Equilibrium (SPNE).
For comparison purposes, we solve the model without the environmentalists�
9Our model is related to Ahlheim and Schneider (2002), as we also (implicitly) introducethe third parties�preferences in our model. However, our contribution di¤ers from theirsin that we consider competition for permits between the citizens and the �rms, while theyconsider the case where the thirds, households, can only sell permits.10Technology choices are long term decisions. Therefore, we assume that these decisions
take place in the stage preceeding competition in the ETS and output markets.11Reducing the second and third stages to a single stage where �rms and environmental-
ists take decisions simultaneously does not alter qualitative our results but substantiallycomplicates the calculations.
9
participation (that is x = 0 and the game is reduced to stages 1 and 3).
3 The environmentalists are not allowed to
participate in the ETS market
In this section, we �nd the equilibrium of the game when the environmental-
ists are excluded from the ETS market. In the last stage, �rms choose their
output levels in order to maximize their pro�ts. The �rst order condition
(FOC henceforth) yields:
@�i@qi
= a� 2qi � k2i qi � ki(kiqi + kjqj) = 0 (10)
Solving for qi, we obtain the reaction function of �rm i
qRi =a� kikjqj2(1 + ki)2
(11)
It is relevant to see that �rms�outputs are strategic substitutes, even in the
absence of competition in the product market. In fact, although �rms do not
compete in the �nal market, their output levels are not independent from
each other�s, given that the number of permits �rms demand is a function of
their output levels and they but permits from the same market.
Solving the system of reaction functions, we obtain the equilibrium level
of output12
q�i;NG =a(2� kikj + 2k2j )
4(1 + k2j ) + k2i (4 + 3k
2j )
(12)
It is tedious but easy to check that for any values of ki and kj between 0
and 1, the derivative of q�i;NG with respect to ki;
12Second order conditions for a maximum are ful�lled.
10
@q�i;NG@ki
=a(�kj(4(1 + k2j ) + k2i (4 + 3k2j ))� 2ki(4 + 3k2j )((2� kikj + 2k2j )))
4(1 + k2j ) + k2i (4 + 3k
2j )
;
(13)
is negative. Interestingly, the more polluting the technology used by �rms
is, the less they produce. The intuition for this is that as ki increases, �rms
require more permits to produce the same level of output. Furthermore, as a
consequence of this, the price of permits increases (due to more permits being
demanded). This increases �rm i�s marginal cost of production, leading �rm
i to decrease its output. Our �rst result is summarised in the next remark.
Remark 1 Firms produce more, the less polluting their production technol-ogy is.
Substituting q�i;NG and q�j;NG into �rms�pro�t maximising and rearranging
yields
�i(q�i;NG) = (1 + k
2i )(q
�i;NG)
2 � (1� ki)2 (14)
In the �rst stage, �rms choose ki to maximise their pro�ts. The �rst order
condition yields
@�i@ki
= 2ki(q�i;NG)
2 + 2(q�i;NG)@q�i;NG@ki
(1 + k2i ) + 2 (1� ki) = 0 (15)
In this paper, we focus on the symmetric solution ki = kj = k. The FOC
evaluated in symmetry are given by13
13We must reassure the reader that we have imposed ki = kj = k only after having cal-culated the derivative. That is, �rst, we have calculated @�i
@kiand only after calculating this
derivative, we have evaluated it in symmetry. Imposing ki = kj = k prior to calculatingthe derivative would yield the cooperative solution.
11
@�i@ki
=�2( (2 + 3k2)3(�2 + 2k � k2 + k3) + a2k(6 + 11k2 � 6k4)
(2 + k2)(2 + 3k2)3= 0 (16)
It can be easily checked that the SOC for a maximum14 holds for any
k 2 (0; 1) for > 0:08601a2. From now on, we assume that and a take
values that ful�ll this inequality so that to guarantee the existence of interior
solutions.
Condition 1: and a take values such that > 0:08601a2.
Using the implicit function theorem we can characterise the relationship
between the equilibrium k in symmetry, k�NG, and the parameters of the
model, a and : Furthermore, k�NG will be unique in the relevant range k 2(0; 1): Our �nding is the following15
Remark 2 k�NG(a; ) is increasing in and decreasing in a.
In other words, the higher and the lower a, the more polluting �rms�
technology will be in the absence of the environmentalists from the ETS. The
intuition behind our result follows: The parameters a and are related to the
pro�tability of the investment in a technology. Although the parameter is
invariant with the technology choice, it magni�es the di¤erences between the
costs of adopting a clean or a polluting technology. Essentially scales up
the di¤erences in the technology costs. As a consequence, the higher , the
more expensive "cleaner" technologies (lower ki) relative to "more polluting"
ones (higher ki).
The market conditions are also important to explain the technology adop-
tion. The parameter a is related to the size of the market. Higher a indicates
larger market sizes and therefore, higher pro�tability (other things being
14 @2�i@k2i
= �(2 + 2a2(16�44k2�168k4�183k6�72k8)(2+k2)2(2+3k2)4 ) < 0
15The proof is in the appendix.
12
equal) of investing in a "greener" technology. Higher market sizes will lead
to higher output levels (other things being equal). This, in turn, will lead
to higher demand of permits and therefore higher permit prices. Given this,
�rms have a stronger incentive to invest in a "greener" technology in larger
markets. Figure 1 despicts the equilibrium k, k�NG, against the ratio =a2.
The reader can easily see that the equilibrium technology choice is more
polluting (higher k), the higher the ratio =a2.
It is also interesting to study the type of strategic interaction between
�rms. Are the technological choices made by �rms strategic substitutesor complements? We focus our analysis on the relationship between �rms�choices in the area close to the equilibrium (that is, around k�NG). We can
characterise the sign of the derivative @ki=@kj using the implicit function
theorem.16 The sign of the derivative is positive for k < 0:816497 and neg-
ative for k > 0:816497. This implies that (in symmetry) the technological
choices made by �rms are strategic complements for k < 0:816497 and strate-
gic substitutes for k > 0:816497. Given that k�NG(a; ) is increasing in and
decreasing in a, we can therefore say that �rms�technological choices will
tend to be strategic substitutes large values of and small market sizes and
strategic complements if the opposite holds.
4 The environmentalists are allowed to par-
ticipate in the ETS market.
In this section, we �nd the equilibrium of the game when the environmental-
ists can participate in the ETS. In the last stage, �rms choose their output
levels in order to maximize their pro�ts. The �rst order condition (FOC
henceforth) yields:
16See proof in the appendix.
13
@�i@qi
= a� 2qi � k2i qi � ki(kiqi + kjqj + x) = 0 (17)
Solving for qi, we obtain the reaction function of �rm i
qRi =a� kikjqj � kix2(1 + ki)2
(18)
As in the case without the environmentalists�participation in the ETS, �rms�
outputs are strategic substitutes, even in the absence of competition in the
product market. Furthermore, �rm i�s output and the number of permits
withdrawn by the environmentalists are also strategic substitutes.
Solving the system of reaction functions, we obtain the equilibrium level
of output17
q�i;G =a(2� kikj + 2k2j )� ki(2 + k2j )x
4(1 + k2j ) + k2i (4 + 3k
2j )
(19)
Substituting q�i;G into the environmentalists�objective function and rear-
ranging yields
OEG =2Xi=1
(1=2)(q�i;G)2+
2Xi=1
[(1+k2i )(q�i;G)
2� (1�ki)2]�2Xi=1
(kiq�i;G)�Rx+zx
(20)
The environmentalists choose the number of permits to buy, x, in order
to maximise their objective function, OEG. This maximisation problem has
a solution x�(ki; kj) which in symmetry, (ki = kj = k) is18
x�G;S =�10a(k + k3) + (2 + 3k2)(2z + k2(2 + 3z))
2(4 + 5k2 + k4)(21)
17Second order conditions for a maximum are ful�lled.18The expression for x�G;S outside the symmetric path is available from the authors upon
request.
14
Several interesting observations can be made from the above result. First,
it can easily be seen that@x�;G;S@a
< 0. This means that the optimal number of
withdrawn permits is decreasing in the size of market. Although this result
might sound counterintuitive, it can be easily understood if one takes into
account the pro�tability of the investment in innovation. As discussed above,
the higher a is, the more pro�table investing on a less polluting technology
is. Therefore, the higher a, the less necessary it is to induce �rms to adopt
"greener" technologies by making permits more scarce.19
Moreover, the number of permits withdrawn by the environmentalists
is increasing in their degree of impure altruism (@x�G;S@z
> 0). In addition,
the higher k (the less clean the chosen technologies are) the more rapidly
the number of withdrawn permits, x, increase with the degree of the envi-
ronmentalists�impure altruism. (@x�G;S@z@k
> 0) In other words, the less green
the technology chosen by �rms are, the more the behavior of the impurely
altruistic environmentalists is reinforced.
Furthermore, for relatively large values of a and/or relatively low values
of z, the environmentalists would not participate in the ETS, as x�G;S would
be negative or zero.20 A negative x�G indicates that the environmentalists
would have incentive to increase the supply of permits. However, this is not
a possibility in our modelling. Therefore, for relatively large a and/or rela-
tively low values of z, we �nd a corner solution where the environmentalists
choose not to withdraw any permits. This could constitute another expla-
nation for Israel (2007)�s observation that the environmentalists have not
been participating very intensively in ETSs: Non-participation might have
19If the objective function included also the revenues from selling permits, x�G would behigher, as there would be an additional incentive of withdrawing permits: By withdrawingpermits, their would increase and as a cosequence the revenues from selling permits. Thiswould be equivalent to having a larger z. Therefore including the revenues in the objectivefunction of the environmentalists would not change qualitatively the results regarding�rms�technology choices.20In other words, there is a critical value of a, acv = 2k2
10(k+k3)+(2+3k2)2z10(k+k3) , below which the
environmentalists do not take part in the ETS. It can be easily seen that acv is increasingin z.
15
been the result of their optimization problem and a voluntary decision by
the environmentalists of excluding themselves from the ETS.
Subsitituting x�(ki; kj) into the pro�t function and applying the FOC
yields
@�i;G@ki
= 2ki(q�i;G)
2 + 2(q�i;G)@q�i;G@ki
(1 + k2i ) + 2 (1� ki) = 0 (22)
Again, we focus on the symmetric solution. In symmetry, q�i;G and@q�i;G@ki
can be written as follows 21
q�;i;G =(4a(1 + k2)� 2k3)� (2k + 3k)z
2(4 + 5k2 + k4)(23)
@q�i;G@ki
= �2k2(16 + 18k2 + 6k3 � k4) + �1 � �22(2 + k2)(4 + 5k2 + k4)2
(24)
where �1 = ak(12+k2(25+22k2+9k3)) and �2 = z(16+k2(56+52k2+14k6�3k8)). Unfortunately, the closed-form solution for the �rst order condition
is again very intrincate, therefore we resort to the implicit function theorem
to characterise the relationship between the optimal k and z. Focusing on
the symmetric case and on the combinations of parameters where the SOCs
hold22, we can show that there is only one root in the relevant intervals (k 2(0; 1], z > 0). This implies that there is a unique symmetric equilibrium in
the relevant parameter space. The following remark characterises the optimal
(symmetric) choice of technology in the presence of the environmentalists (the
proof is in the appendix):
Remark 3 There is a critical value of z, zcv, above (below) which k�G(z) isdecreasing (increasing) in z. The critical value of z is increasing in a.
21Symmetry has been imposed only after having calculated the derivative. After sub-stituting x�(ki; kj) into q�i , we have calculated its derivative with respect of ki. Thisderivative evaluated in symmetry (ki = kj = k) is shown in (24).22The second order conditions for a maximum are available from the authors upon
request.
16
In other words, there is a U-shape relationship between the technological
choice and the degree of impure altruism. As z increases, �rms will tend
to invest in technologies that are less polluting (lower k) up until a critical
point of z, where increases in z will actually lead to investments in more
polluting technologies. The intuition behind this result is the following: As
z increases, the environmentalists tend to withdraw more permits from the
market. This has two e¤ects: First, �rms tend to choose cleaner technologies,
as the marginal cost of producing is higher due to the lower number of permits
which are required per unit of output. Second, �rms reduce their output
levels (note that q�i is decreasing in x). As �rms reduce their production
levels, the investment in cleaner technologies becomes less pro�table. The
interaction between these two e¤ects will determine the technology choice.
For low levels of z, the �rst e¤ect dominates the second e¤ect. However, for
high levels of z, the second e¤ect dominates. The remark also states that zcvis increasing in a, implying that zcv will be further away from the origin the
higher a is (that is, the curve shifts outwards).23 This implies that higher
values of z will be required for k�G(z) to be increasing if a is high than if a is
low. The reason behind this is that a is directly related with the pro�tability
of investing in R&D (recall that high a implies large market sizes). Large
market sizes make the second e¤ect above less likely to outweight the �rst
e¤ect.
We �nish this section discussing the strategic interaction between �rms
when the environmentalists are present in the ETS. In the previous section
we showed �rms�technological choices could be either strategic substitutes or
strategic complements depending on the technology and market size condi-
tions. When the environmentalists are present in the ETS, �rms�technologi-
cal choices will be more likely to be strategic substitutes.24 The intuitionis the following: If �rm i chooses a more polluting technology (higher k), the
23Further, for very low a, zcv would be negative. In such case, k�G(z) would be strictlyincreasing for any z > 0.24The derivation of this result is available from the authors upon request.
17
environmentalists will tend to increase the number of permits they withdraw.
Therefore, the best reply of �rm j would be to choose a cleaner technolgy
instead to compensate for the increase emissions by �rm i.
5 Comparative Analysis
In this section we compare the equilibrium level of emissions and technol-
ogy choice across the two cases solved above, namely the ETS without the
environmentalists� participation and the ETS with the environmentalists�
participation. Before we compare the two cases (non-participation vs. par-
ticipation of the environmentalists), it is useful to study the e¤ect of degree
of impure altruism on output and emissions levels. We conduct this analysis
in the next subsection.
5.1 E¤ect of the degree of impure altruism on output
and emissions
Here we analyse the relationship between the degree of impure altruism (z)
and the equilibrium levels of output and emissions. The equilibrium level of
output is
q�i;G =(4a(1 + k�G
2)� 2k�G3)� (2k�G + 3k�G3)z2(4 + 5k�G
2 + k�G4)
(25)
Before proceeding to analyse whether the output is increasing in z, it is
relevant to show the relationship between the equilibrium output and the
technology choice when the greens participate in the ETS:
Remark 4 The equilibrium output level is decreasing in k.
Proof.@q�i;G@k�G
evaluated in symmetry can be written as@q�i;G@k�G
= �12(4+5k2+4k4)2
(t1+
t2), where t1 = 8ak + 8z + k2(24 + 26z) and t2 = k4(10 + 9z) � k6(2 + 3z):
18
Given that k lies within the interval (0; 1), it is easy to see that t2 > 0, and
therefore (t1 + t2) > 0. As a consequence,@q�i;G@k�G
< 0. QED.
In other words, the more polluting the chosen technologies are, the less
�rms produce. Regarding the analysis of the relationship betweek q�i;G and
z, it is important to notice that an increase in z will have two e¤ects on q�i;G,
a direct e¤ect and an indirect e¤ect, through k�G, given that k�G is a function
of z. That is
dq�i;Gdz
=@q�i;G@z
+@q�i;G@k�G
@k�G@z
(26)
The analysis of the above decomposition results in the following remark:
Remark 5 The equilibrium level of output when the environmentalists par-
ticipate in the ETS may only be increasing in z if z is relatively small
(z < zcv) and���@q�i;G@k�G
@k�G@z
��� > ���@q�i;G@z ���.Proof. It is easy to see from (19), that holding k constant,
@q�i;G@z
< 0.
Further, from remark 4, we know that the equilibrium ouput is decreasing
in k. Lastly, as we have shown in section 4, we know that @k�G@z
is negative
(positive) in z for z < (>) zcv. All in all,dq�i;Gdz
is necessarily negative for
relatively high values of z and is positive for relatively low values of z if and
only if���@q�i;G@k�G
@k�G@z
��� > ���@q�i;G@z ��� : The rest of the remark follows.Regarding emissions (y�i;G = k
�i;Gq
�i;G) and its relationship with z, we can
also decompose the e¤ect of z on y�i;G as follows
dy�i;Gdz
=@k�G@zq�i;G +
@q�i;G@z
k�i;G (27)
The analysis of the separate e¤ects indy�i;Gdz
leads to the following remark:
Remark 6 The total level of emissions will be increasing in z if
i) z is low ( z < zcv) and���@q�i;G@z k�i;G��� > ���@k�G@z q�i;G��� or
19
if ii) z is high ( z > zcv) and���@q�i;G@z k�i;G��� <���@k�G@z q�i;G���.
Proof. We know that q�i;G > 0 and k�i;G > 0: Further, following remark 5, we
know that q�i;G can only be increasing in z for relatively high values of z. We
also know that k�G is U-shaped with respect to z: Therefore for low values of
z (where @k�G@z< 0), the level of emissions can be increasing in z if
@q�i;G@z
> 0
and���@q�i;G@z k�i;G��� > ���@k�G@z q�i;G���. For high values of z (where @k�G
@z> 0),
@q�i;G@z
is
negative and therefore the total level of emissions could be increasing in z if���@q�i;G@z k�i;G��� < ���@k�G@z q�i;G���. QED.5.2 Technology Choice
Here we compare the technology choice with and without the enviorn-
mentalists�participation. We have shown before that k�G is a U-shaped with
respect to z. Further, k�NG is not a function of z. The following lemma com-
pares k�G and k�NG and shows that k
�G > k
�NG for at least one range of values
of z for each pair (a; ). For the purpose of making the comparison of k�Gand k�NG more clear, let us provisionally relax the assumption that z > 0.
Remark 7 For each pair of values (a; ), there is a critical value of z, zlbeyond which k�G(z) > k
�NG.
Proof. From remark 3 we know that there is a critical value of z, zcv, above(below) which k�G(z) is decreasing (increasing) in z. We also know that k
�NG
does not depend on z, that is, it is constant. It follows that k�G and k�NG may
cross once, twice or k�G > k�NG within the feasible range of z, z > 0:The rest
of the remark follows from the functional form of k�G: QED.
The intuition for the result above follows: The participation of the envi-
ronmentalists will lead to higher permit prices than in they were not partici-
pating. This will lead to the two e¤ects discussed above: Technology substi-
tution (higher permit prices make the cleaner technology relatively cheaper)
and output reduction (�rms produce less because the increase in the price of
20
permits implies an increase in their marginal cost of production). As z in-
creases, the second e¤ect becomes stronger reducing the incentives to invest
on "cleaner" technologies. It follows that there is a value of z (zl) which is
high enough to induce the adoption of a more polluting technology than the
one that would be adopted in the absence of the environmentalists. Below
this value of z, the participation of the environmentalists will lead to the
adoption of cleaner technologies. For completeness, let us discuss the case
where z is relatively low. In such a case, x�G could be zero or negative.25 This
implies a corner solution in the sense that the environmentalists would not
withdraw any permits from the ETS. For low values of z, the environmen-
talists would choose not to participate in the permits market and therefore,
allowing the environmentalists to participate. Therefore, the two cases (al-
lowing and not allowing the environmentalists to participate) may lead to
the same results for low values of z.
We can illustrate the above with some numerical examples. Recall that
the technological choice (in the absence of the environmentalists) depends on
a and : Take the case of a = 1:5 and = 1, the technology choice when the
environmentalists are absent from the ETS yields k�NG = 0:830. Interestingly,
the presence of the environmental group would render more polluting tech-
nology choices (k higher than 0:830) for z > 1:912. Furthermore, if z < 0:445
the environmentalists would not participate in the ETS (even if allowed). If
0:445 < z < 1:912, the environmenalists� participation would lead to the
adoption of less polluting technologies.
5.3 Emissions and Output Levels
In this section, we compare the equilibrium levels of output and emissions
across the two cases (with and without the environmentalits�participation
in the ETS). First, it is important to notice that for a given k, �rms produce
more in the absence of the environmentalists. This also leads to a higher
25This requires also a to be low relative to :
21
level of emissions. The following remark explains.
Remark 8 The equilibrium output and emissions levels are lower when the
environmentalits participate than when they do not participate for a givenk.
Proof. We know that the equilibrium output will be higher if x = 0 than
is if x > 0, given that @q�i@x< 0: Recall that the emissions levels in market i
are calculated as yi = kiqi. For a given k, therefore, the di¤erence between
the emissions levels with and without the environmentalists�participation is
determined by the di¤erence in the equilibrium output levels. QED.
However, as the participation of the environmentalists� in the permits
market will in�uence �rms�technological choice, it is necessary to go beyond
the analysis of output and emissions levels for given values of k. In the
previous section, we have shown that �rms will choose a more polluting
technology in the absence than in the presence of the environmentalists for
intermediate values of z and that for low or high levels of z, the opposite
holds. As a consequence of this, and given that the equilibrium output levels
are decreasing in k, we can state the following.
Remark 9 For relatively high values of z, �rms choose a more pollutingtechnology (higher k) but produce less if the environmentalists are present in
the ETS. For intermediate values of z, the opposite holds. For low values of
z , the environmentalists may choose not to participate in the ETS.
Proof. From remark 8, we know that the equilibrium output level is higher
without than with the environmentalists for a given k. Furthermore, from
remarks 1 and 5 we know that the equilibrium level of output is increasing
in k in both cases. From remark 7 we know that �rms choose less (more)
polluting technologies when the environmentalists are present than when
they are absent for high values of z but the opposite holds for intermediate
values of z. Further, we know that x > 0 requires z to be relatively large.
22
In other words, for low values of z, the environmentalists may choose not to
participate in the ETS. The rest of the remark follows. QED.
The last result does not mean that the total level of emissions would
actually increase if environmentalists who are characterised by high degrees
of impure altruism participated in the ETS. In fact, remark 9 emphasizes the
existence of a trade-o¤ between the technology choice and also the level of
output. Interestingly, higher degrees of impure altruism can actually induce
�rms to adopt worse technologies but can also lead to lower output and
emissions levels. We can use some numerical examples to illustrate this. Let
us assume that a = 1 and = 1; in such a case, the equilibrium technology
choice in the absence of the environmentalists is k�NG = 0:933 and the total
output (qi+qj) and total emissions (yi+yj) are respectively 0:432 and 0:406.
Now assume that the environmentalists are characterised by a (relatively)
high degree of impure altruism, for example, z = 1:1. In such a case, the
equilibrium technology choice is more polluting (k�G = 0:963) but the total
emissions level is lower (yi+yj = 0:086). In contrast, if the environmentalists
were characterised by an intermediate z, for example, z = 0:5, they would
induce the adoption of a less polluting (k�G = 0:90) although at the expense
of a rise in the level of total emissions (yi + yj = 0:392):The reason for this
is that in the �rst case (z = 1:1) �rms adjust their output level downwards
(total output in this case is 0:090) while in the second case (z = 0:5), they
do the opposite (total output is 0:434).
6 Conclusions
In this paper we examine the participation of environmental groups in
the Emissions Trading System (ETS) and its e¤ects on �rms�technological
choices. We analyze the case where there are two �rms in the tradable permits
market which are acting as duopsonists in the product market and can choose
their manufacturing technologies among a continuum of technologies which
23
di¤er in their degree of environmental friendliness and their set-up costs.We
assume that "greener" technologies are more expensive to adopt. In the
spirit of Andreoni (1989, 1990), we consider that the environmentalists are
impurely altruistic, that is, they do not only decide on the number of permits
to withdraw based on standard social welfare evaluation, but also take into
account the increase in satisfaction they obtain from withdrawing permits.
We show that the environmentalists�participation in the ETS can induce
�rms to choose a "greener" technology than they would choose in their ab-
sence. However, this requires that the environmental group is characterized
by intermediate degrees of impure altruism. Hence allowing the environmen-
talists to participation in the ETS can be used as a policy tool to accelerate
the adoption of less polluting technologies.
However, for very high degrees of impure altruism the presence of the
environmental group in the ETS could actually induce the �rms to adopt a
more polluting (non-green) technology. This does not imply that the total
level of emissions would actually increase. In fact, two aspects of the problem
must be considered: the technology choice and the level of output. Higher
degrees of impure altruism can actually induce �rms to adopt worse tech-
nologies but could also lead to lower output levels. In fact, the interaction
between these two e¤ects could lead to lower emissions levels for high degrees
of impure altruism.
From the policy point of view it is important to be aware of the di¤erent
outcomes that will be achieved depending on the priorities of the third parties
participating in the ETS. If the third parties highly prioritise the reduction
of available permits over other surplus related objectives, their participation
will lead to a reduction of emissions at the expense of consumer and pro-
ducer welfare. However, if they do not give such priority to the withdrawal
of permits, their participation could lead to technological improvements but
not deliver in terms of total emissions. Hence, if the policy maker�s primary
objective is to reduce the level of total emissions, allowing the participa-
24
tion of third parties with a strong preference for the withdrawal of permits
would be a good policy option although it would not induce the adoption of
less polluting manufacturing technologies but, rather, a reduction in output
levels.
25
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8 Appendix
Proof of remark 2. The FOC @�i@ki
= 0 evaluated in symmetry can be
written as
@�i;NG@ki
= 2 (1�k)�4a2k(1 + k2)(2 + k2)2(4 + 3k2)
(4(1 + k2) + k2(4 + 3k2))3+
2a2k(2 + k2)
(4(1 + k2) + k2(4 + 3k2))2
which we can rewrite as
@�i;NG@ki
= a2�2
a2(1� k)� 4k(1 + k
2)(2 + k2)2(4 + 3k2)
(4(1 + k2) + k2(4 + 3k2))3+
2k(2 + k2)
(4(1 + k2) + k2(4 + 3k2))2
�and rearranging
@�i;NG@ki
=�2a2
(2 + k2)(2 + 3k2)3
where =� a2(2 + 3k2)3((k � 1)(2 + k2)) + k(6 + 11k2 + 6k4)
�. Crucially
@�i@ki
= 0 if and only if = 0: Using the implicit function theorem we can
characterise the optimal k that makes , and therefore @�i@ki= 0. The deriva-
tive of with respect of a2is given by
@
@( a2)= (2 + 3k2)3((k � 1)(2 + k2))
It is immediate to see that (2 + 3k2)3 > 0 and ((k � 1)(2 + k2)) for 8k 2(0; 1]:Therefore @
@( a2)< 0: On the other hand, the derivative of with respect
of k is given by
30
@
@k= 6 + 33k2 + 30k4 +
a2(2 + 3k2)2(4� 40k + 48k2 � 24k3 + 27k4)
which is positive under condition 1 (SOC ful�lled). To sum up, @@(
a2)< 0
and @@k> 0. Using the implicit function theorem, we therefore know that
@k�i;NG@(
a2)= �
@@(
a2)
@@k
< 0
QED
Proof of strategic substitutability/complementarity: Condition 1implies that the SOC for a maximum is ful�lled, that is @2�i
@k2i< 0: Using the
implicit function theorem, we can characterise the sign of the relationship
between ki and kj in equilibrium, that is sign( @ki@kj) = sign(�
@�i@kj@�i@ki
): It follows
that if @�i@kj
> 0, then @ki@kj
> 0 (strategic complements) and if @�i@kj
< 0, then@ki@kj
> 0 (strategic substitutes). Calculating the derivative of �i with respect
to kj and applying symmetry yields
@�i@kj
=�2a2k(1 + k2)�
(4(1 + k2) + k2(4 + 3k2))3
where � = (8 � 8k4 � 4k2(3 + k2) + k4(�4 + 3k2) + k2(8 + 6k2 � 6k4)).It is obvious that the denominator of @�i
@kjis positive and that k(1 + k2) is
positive. Therefore, the sign of � will determine the sign of @�i@kj: In fact, �
is positive if k < 0:816497 and negative if k > 0:816497. This implies that
for k < 0:816497, @�i@kj
< 0 and as a consequence, @ki@kj
is negative (technology
choices are strategic substitutes) and for k > 0:816497, @�i@kj
> 0 and as a
consequence, @ki@kj
is positive (technology choices are strategic complements).
QED.
Proof of remark 3: Using the implicit function theorem, the slope of
the function k�i (z) is given by@k�i@z= �
@2�i;G
@ki@z
@2�i;G
@k2i
. Focusing on the case where
31
a, and z take values that guarantee that the SOC for a maximum is met,@2�i;G@k2i
< 0: Therefore, the sign of @k�i
@zdepends on the sign of @
2�i;G@ki@z
: If it is
positive (negative), then @k�i@z> (<)0. The cross derivative @2�i;G
@ki@zis given by
@2�i;G@ki@z
=a� + z+ �
2(1 + k)2(2 + k2)(4 + 2k2)3
where � = �64 � 392k2 � 762k4 � 762k4 � 593k6 � 144k8 + 15k10; =
64k+384k3+784k5+664k7+204k9 and � = 96k3+344k5+380k7+140k9.
It is easy to check that the denominator of @2�i;G@ki@z
is positive and therefore,
the sign of @2�i;G@ki@z
depends on its of the numerator. Further, it is easy to
check that �<0; > 0 and � > 0 for any k 2 (0; 1]. The denominator willbe positive if a� + z + � > 0 and negative if a� + z + � < 0: Solving
the equation a� + z+ � = 0, we can �nd the critical value of z, zcv above
(below) which @2�i;NG@ki@z
is positive (negative). As a consequence, if z > (<)
zcv,@k�i@z> (<)0. This critical value is zcv = ���a�
: As � < 0, it is easy to
check that @zcv@a> 0, therefore, the critical value is increasing in a. QED.
32
