Permit markets, seller cartels and the impact
of strategic buyers∗
O. Godal†and F. Meland‡
Abstract
The literature on emissions trading and strategic behavior under the
Kyoto Protocol typically claims that a sellers’ cartel featuring countries
of the former Soviet Union can be quite profitable for its members. Using a Cournot-type quota exchange model, we show that this conclusion
is sensitive to the assumption that large permit buyers, like the EU and
Japan, are supposed to behave as price takers. Our result is driven by
the same mechanisms as those found in Salant, Switzer and Reynolds
(1983). We also discuss alternative models of permit exchange.
Keywords: emissions trading, Kyoto Protocol, cartel formation, merger
profitability.
JEL codes: C71, C72, L13, Q58.
∗
We thank Sjur Didrik Flåm, Bjørn Olav Johansen, Kjell Erik Lommerud, Odd Rune
Straume, Sylvie Thoron, Sigve Tjøtta, Steinar Vagstad, two referees and seminar/conference
participants in Bergen, Kyoto and Zaragoza for valuable comments and advice. Both authors
appreciate financial support from the NFR (Renergi). O. Godal also thanks the NFR
(Samstemt) and the CLIPORE program of MISTRA.
†
Department of Economics, University of Bergen. E-mail: [email protected]. Part
of this work was carried out during tenure as a Mistra Climate Policy Research (Clipore)
Scholar at the Department of Economics, Göteborg University.
‡
Corresponding author. Stein Rokkan Centre of Social Sciences and Department of
Economics, University of Bergen, Pb. 7802, 5020 Bergen, Norway. Phone: (+47)55589230.
Fax: (+47)55589210. E-mail: [email protected].
1
Introduction
There is substantial literature dealing with simulations of the permit market
under the Kyoto agreement. In many papers, it is assumed that the countries
of the former Soviet Union (and in some cases, Eastern Europe) act as a single
strategic agent on the supply side of the market, with other countries being
price takers.1 These studies typically find that permit suppliers can benefit
substantially by forming an ‘organization of permit exporting countries’ and
that this, quite naturally, impedes overall efficiency. For instance, Manne and
Richels (2004) conclude that “If the majority of ‘hot air’ [i.e., excess permits]
is concentrated in a small number of countries in Eastern Europe and the
former Soviet Union, these countries may be able to organize a sellers’ cartel
and extract sizable economic rents.” Results of this kind have led to a concern
about whether international permit markets, such as the one under the Kyoto
Protocol, will perform well when it comes to achieving overall efficiency (e.g.,
Olmstead and Stavins, 2006).
In this paper, we study cartel profitability under the assumption that buyers may also behave strategically. We think this is a scenario that should not
be ruled out–particularly when it comes to the Kyoto permit market, in which
there are most likely to be some relatively large and nonanonymous agents on
the demand side. Our main result is that standard economic arguments do
not immediately support the conclusion that an organization of permit exporting countries will be profitable. This result is put forth both through
a tractable example and simulations of possible trading scenarios under the
Kyoto Protocol.
If one assumes that agents in a permit market choose the level of quotas to
put up for sale, the setting has a Cournot flavor. A permit exchange setting like
the one we study, however, is slightly different from standard Cournot. First, in
the Cournot set-up, the strategic agents are sellers, while buyers are typically
assumed to be many and price taking. In permit markets, whether agents come
forward as buyers or sellers is endogenously determined, and, quite reasonably,
1
See, for instance, Babiker et al. (2002), Böhringer (2002), Böhringer and Löschel (2003),
Böhringer et al. (2007), Elzen and Moor (2002), Godal and Klaassen (2006), Klepper and
Peterson (2005), Löschel and Zhang (2002), Manne and Richels (2004) and the survey by
Springer (2003).
there may be large strategic agents on both sides. Second, the total available
amount of the good at hand is fixed. However, the intuitive explanation for
some of our results is very much the same as in the classical Cournot oligopoly
literature: it is well known that a (noncost-reducing) coalition of strategic
sellers will be profitable for the members of the coalition only if a sufficient
number of strategists take part (see Salant et al., 1983). The reason for this is
that sales by the different sellers are strategic substitutes–the merger causes
a decrease in the merging parties’ sales, increasing the optimal sales by the
outsider(s). This effect, which is larger the more outside strategists there
are, hurts the merging parties. A similar effect surfaces when we introduce
strategic buyers: if sellers cooperate, reducing the supply of quotas, strategic
buyers respond by decreasing their own consumption, i.e., purchases drop.
This hurts the cooperating sellers–and in qualitatively the same way as sales
increases by nonmerging strategic sellers.
We also discuss other types of cartels. Mixed cartels, between sellers and
buyers, turn out to be profitable for cartel members, and total costs for all
countries decrease as well. Sellers and buyers can, by cooperating, circumvent
the inefficient withholding of purchases (by buyers) and sales (by sellers). Additionally, we provide simulations that confirm that our results about seller
cartels are robust to a number of changes in assumptions. However, this does
not necessarily apply to a change in the underlying model of trade, and we
therefore include a discussion of some alternative models.
The paper is organized as follows. In Section 2, we present the basic
model of strategic exchange. We show here that permit consumption levels are
strategic substitutes when costs are quadratic. This is important in explaining
our main results, which appear in Section 3, for a simple and tractable instance,
and in Section 4, for the Kyoto case. Section 5 provides the sensitivity analysis.
Section 6 discusses the choice of model apparatus, while Section 7 concludes
and offers a remark on endogenous cartels.
2
The setting
Our basic model of strategic permit trading will be the dominant agent—
competitive fringe model, introduced by Hahn (1984) and extended by West-
skog (1996) by allowing for more than one strategic agent. We consider governments that have ratified the Kyoto agreement with binding commitments
to be the decision makers, and they are collected in a set, I. Each of them has
an endowment, ei , of permits to pollute. Besides being transferable, permits
are assumed homogeneous, perfectly divisible and exogenously given. When
agent i keeps the amount xi for private use, he incurs nonnegative, decreasing,
convex and twice differentiable costs, ci (xi ). The residual, ei −xi , is exchanged
in a common market at unit price, p.
We assume that each i ∈ I is either member of a (nonempty) competitive
fringe, named F , consisting of ‘small’ agents who are price takers, or belongs
to a set of strategists, named S. The model may be seen as consisting of two
stages, where strategists set their quantities before the price takers clear the
market. Every agent i ∈ I aims at
minimizing {ci (xi ) + p (xi − ei )}
(1)
with respect to xi , where members of the fringe take p as given. The solution
to (1) for these agents, which is characterized by
c′i (xi ) + p = 0,
(2)
generates demand xi (p) for permits by price takers. Strategists, however,
recognize that p is affected by their own choice, xi , such that
c′i (xi ) + p +
∂p
(xi − ei ) = 0.
∂xi
(3)
What remains to be explained is precisely how the endogenous price curve, p,
depends on xi , i ∈ S.
Market clearing requires
xi (p) =
ei −
xi .
(4)
i∈F
i∈I
i∈S
Differentiating (4) with respect to xi , i ∈ S, and recalling the relationship
between the derivative of a function and that of its inverse, one gets
∂p
1
=
1
∂xi
i∈F c′′ (xi )
i
(5)
∂p
for each strategist i ∈ S.2 Because costs are convex, ∂x
is positive. This coni
firms intuition, as xi is consumption, not sales. To evaluate whether mergers
are profitable, we introduce
T Ci := ci (x∗i ) + p (x∗i − ei )
as the value function associated with (1) for an equilibrium profile (x∗i )i∈I .
When discussing a cartel between, say, agents i and j, we abuse notation and
write T Ci+j for their joint total costs. We will only examine cartels between
agents that would be strategic if standing alone.3 Moreover, we assume that
side payments may take place and that the agents in a cartel minimize joint
total costs (including permit sales revenues or purchase costs). For further
discussion of this, see Section 5.5.
2.1
Quadratic costs and strategic substitutes
We confine the analysis to quadratic-constant costs of the form
1
(b x − ai )2 when xi ≤ ai /bi
2bi i i
ci (xi ) =
0
when xi > ai /bi ,
(6)
where ai , bi > 0, so that c′i (xi ) = min{0, −ai + bi xi }. The number ai /bi has
a most natural interpretation in our setting and is often labeled ‘business as
usual emissions’–i.e., the amount an agent would emit when spending nothing
on emissions reductions. Until we get to our Kyoto example, we work under
the hypothesis that endowments are smaller than business as usual emissions,
so that c′i (xi ) = −ai + bi xi on relevant domains.
With affine marginal costs, we derive from (2) that xi = (ai − p)/bi . For
ease of exposition, write
ai
1
A :=
and B :=
.
b
b
i
i
i∈F
i∈F
Market clearing (4) then yields
A − i∈I ei + i∈S xi
∂p
1
p=
and
= .
B
∂xi
B
2
3
(7)
Formula (5) is simply a special, one-dimensional, case of Flåm et al. (2008, Eq. 6).
Hagem (2008) considers when it is beneficial for price takers to form a strategic unit.
Inserting this into the first order condition (3) for a strategic agent, we derive–
through simple algebra–that for each i ∈ S,


1
ai B − A +
(8)
xi =
ej + ei −
xj  .
(Bbi + 2)
j∈I
j∈S\{i}
Expression (8) tells us that permit consumption levels are strategic substitutes
among the strategists regardless of whether an agent is a net buyer or seller,
and regardless of whether other strategists are net buyers or sellers (individually or in aggregate). Anything leading to lower permit consumption (higher
sales, lower purchases) among some strategists will lead other strategists to
increase permit consumption. This is an important building block for our
results.
3
A tractable example
For illustration, not realism, this section considers a special case and shows
that the presence of strategic buyers can make a seller cartel unprofitable.
Suppose that six agents are present,
each with ai = bi = 1 and (e1 , ..., e6 ) =
∂p
1
(0, 0, e, e, 2e, 2e), where e ∈ 0, 12 . This implies that ∂x
= #F
for each i ∈ S,
i
where #F is the number of price takers.
We first replicate the standard results in the Kyoto cartel literature (Case
1). Then we look at two cases to examine the effect of strategic buyers being
present in the market. With our parameters, agents 1 and 2 will be buyers,
while 5 and 6 become sellers.
Case 1 (Profitability of a sellers’ cartel without strategic buyers)
Suppose agents 1—4 are price takers, while 5 and 6 are modeled as independent
strategists. The solution to the model is x1 , x2 , x3 , x4 = 13
e, x5 , x6 = 87 e and
14
13
p = 1 − 14 e. The total costs of agents 5 and 6 are
T C5 + T C6 = 1 − 4e +
where 142/49 ≈ 2.898.
142 2
e,
49
Suppose now that agents 5 and 6 cooperate, and minimize joint costs.
This yields x1 , x2 , x3 , x4 = 78 e and x5 = x6 = 54 e; hence, consumption increases
and sales are reduced for the coalition partners–confirming commonplace economic intuition. The clearing price, p = 1 − 78 e, goes up, and the combined
total costs when agents 5 and 6 cooperate are
T C5+6 = 1 − 4e +
23 2
e,
8
which is less than T C5 + T C6 as 23/8 = 2.875. Thus, the cartel between the
two well-endowed agents is beneficial for those agents, as should be expected,
because all strategists participate in the cartel (monopolization).
Case 2 (Profitability of a sellers’ cartel with one strategic outside buyer)
Suppose next that agents 1, 5 and 6 are strategic, while 2, 3 and 4 are price
takers.4 Solving the resulting game yields, without a cartel, x5 , x6 = 17
e,
14
5
20
4
x1 = 7 e and p = 1 − 21 e. With a cartel between agents 5 and 6, x5 , x6 = 3 e,
x1 = 23 e and p = 1 − 89 e. This implies that
1747 2
e and
588
80
= 1 − 4e + e2 .
27
T C5 + T C6 = 1 − 4e +
33T C5+6
Because 1747/588 ≈ 2.971 while 80/27 ≈ 2.963, the presence of a strategic
buyer reduces the profitability of the merger. Nevertheless, a sellers’ cartel is
still beneficial for those taking part.
Case 3 (Profitability of a sellers’ cartel with two strategic outside buyers)
Suppose now that agents 1, 2, 5 and 6 are strategists. We then get, without
a cartel, x5 , x6 = 43 e, x1 , x2 = 23 e and p = 1 − e. With a cartel between agents
8
5 and 6, the equilibrium is x5 , x6 = 19
e, x1 , x2 = 13
e and p = 1 − 12
e. Total
13
13
costs for the two strategic sellers in the two cases are
4
Note that this not only changes the number of strategists, it also affects the slope of the
price curve given in (7), because there is now one less price taker. However, all qualitative
results presented here would be replicated were we to study a situation in which we added
a new strategic buyer rather than convert some of the fringe players.
28 2
e and
9
529 2
e.
= 1 − 4e +
169
T C5 + T C6 = 1 − 4e +
T C5+6
As 28/9 ≈ 3.111 while 529/169 ≈ 3.130, cartelization yields higher costs.
Hence, incorporation of sufficient buyer power makes the seller cartel unprofitable.
So why may ‘monopolization’ become unprofitable in the presence of a
sufficient number of strategic buyers? Generally speaking, we know from the
standard oligopoly literature that in markets with strategic sellers, each seller
will make choices that affect other sellers negatively as compared with what
they could have achieved under full cooperation (no one takes into account
the impact of price changes on other strategists). If some of the agents join
forces, they can internalize this adverse effect among themselves, which, in
absence of responses by agents that are not members of the cartel, will typically lead to lower sales and higher prices, and higher profits for the cartel
members. However, outside sellers will typically have incentives to respond to
such cartelization–normally (in the Cournot setting) by increasing their own
sales, which contributes to making it less interesting to form a cartel. These
mechanisms are described in Salant et al. (1983), and the only new item in our
setting is the presence of outside strategic buyers. By formula (8), such buyers
will typically reduce purchases in the face of cartelization by sellers, contributing to lower prices. This makes the cartel less profitable, and in qualitatively
the same way as the actions of outside strategic sellers.5
This general idea extends to other types of cartels as well: buyer cartels
may become unprofitable because of the presence of strategic sellers. Seller
strategists will reduce sales as a strategic response to the formation of a buyers’
cartel, reducing the associated price decrease and hurting the cartel members.
Notable exceptions to the above scenario, where outside strategists will not
5
When cooperating, it is reasonably assumed that the cartel parties cannot credibly
commit not to internalize the impact a cartel member’s choice of quantity has on another
cartel member. With the implied strategic response from outside sellers and buyers, one is
therefore not assured that the cartel can do as well as the members could do on their own
(when acting independently).
make a cartel unprofitable, appear when buyers and sellers join together (see
Section 4.2).
4
Simulations of the Kyoto Protocol case
The remainder of the paper considers the permit market under the Kyoto
agreement.
Parameters. The parameters are based on those used in Godal and Klaassen
(2006). They cover the period 2008—2012, and were derived from the MERGE
model developed by Manne and Richels (1992, 2004). For the purposes of
this paper, we found it necessary to disaggregate the quite large regions in
MERGE, so as to obtain a more realistic representation of the actual decision makers. Nevertheless, because 15 member states of the European Union
(EU15) have made use of Article 4 in the Protocol to comply as a group, we
will treat them as a single agent. This is further discussed in Section 5.
Cost functions are quadratic as in (6). The values of ai , bi , the endowment
ei , as well as the business as usual emissions (x̂i := ai /bi ) and marginal abatement costs in autarky, are given in Table 1 for each i ∈ I. Readers interested in
more details concerning how our parameters were derived may refer to the supplementary material available at http://www.folk.uib.no/secfe/Supplement.rar.
Table 1. The parameters used in the numerical analysis.6
Variable
Symbol
Units
Russian Fed.
Ukraine
Poland
Czech Republic
Romania
Bulgaria
Hungary
Slovakia
Lithuania
Estonia
Latvia
Slovenia
Iceland
Liechtenstein
Monaco
Norway
Switzerland
New Zealand
Australia
Canada
Japan
EU15
Total
Parameters for ci (·)
B-A-U
Endowment
M.C.
x̂i
ei
−c′i (ei )
MtC/yr
US$/tC
ai
bi
US$/tC
US$yr/M(tC)2
MtC/yr
1410
1410
1410
1410
1410
1410
1410
1410
1410
1410
1410
1410
1883
1883
1883
1883
1883
693.0
693.0
693.0
1727
1883
2.731
9.205
17.02
39.15
37.55
77.00
90.39
104.1
163.9
171.4
261.5
464.9
2876
29690
57180
175.7
139.1
67.17
6.122
3.663
4.933
1.858
516.3
153.2
82.84
36.02
37.55
18.31
15.60
13.54
8.603
8.226
5.392
3.033
0.655
0.06342
0.03293
10.72
13.54
10.32
113.2
189.2
350.1
1013
2599.8
768.2
227.9
115.9
50.91
51.39
25.07
21.82
18.54
11.78
11.26
7.380
4.151
0.6476
0.05250
0.02730
9.734
11.20
7.159
84.84
123.4
257.6
838.6
2647.6
0
0
0
0
0
0
0
0
0
0
0
0
21
324
322
173
325
212
174
241
456
325
We need to classify agents as strategists or price takers, and, importantly,
some must take the latter role. We are not aware of a clear theory that indicates how this should be done. Therefore, we follow Misiolek and Elder (1989,
6
The following abbreviations are used: M, million; B, billion; t, metric ton; C, carbon;
US$, US dollars in 1997 and yr, year.
p. 159)7 and simply use a simulation of the perfectly competitive equilibrium
to identify agents with a potentially dominant position in the market. Given
the nonparticipation of the US, the market shares for the largest traders in
Table 1 are as follows. On the supply side of the market, the main players
are Russia (64%) and the Ukraine (19%). The demand side is dominated
by the EU15 (45%) and Japan (24%).8 The other countries that have ratified the Kyoto Protocol have smaller market shares. It appears to us that the
commonplace practice of treating the EU15 and Japan as price takers is not
necessarily reasonable. In the remainder of this section, we discuss strategic
behavior among these four parties.
A notable feature of a perfectly competitive equilibrium for the above parameters is that it yields a permit price equal to zero.This is because aggregate
ai
projected emissions without emission
reductions ( i∈I bi = 2599.8 MtC/yr)
are smaller than total endowments ( i∈I ei = 2647.6 MtC/yr) when the US is
not on board, leading to a surplus of permits in total (i.e., hot air). This may
be explained by the economic collapse of the countries of the former Soviet
Union (most notably Russia and the Ukraine), which are not expecting a full
emissions recovery in the projected period (2008—2012). This result compares
well with other studies (see, e.g., Springer, 2003), which have projected an aggregate surplus or a very modest shortage of permits without the participation
of the US. Hot air is further discussed in Section 5.2.
The numerical analysis was carried out by first fixing the composition of
the cartel and then solving the game using the GAMS software. The outcomes
are discussed below. (More details about the computations are available in the
supplementary material.)
7
They argue: “The conventional method for assessing the potential for [cost-minimizing
manipulation] ... in a specific geographical market is to estimate the share of pollution rights
which would be purchased or sold by some small number of firms, if all firms were to act
as price takers. If this share is large, it is interpreted as evidence that the market may be
susceptible to manipulation”.
8
One should also note that the perfectly competitive allocation of permits is not unique,
because there is a surplus of permits available (hot air), and this could be distributed in a
continuum of ways. However, no matter how this surplus is divided, these four strategists
will be the largest sellers and buyers.
4.1
A cartel between Russia and the Ukraine
We first study a Russia—Ukraine cartel with three different assumptions: Case
1 is when Russia and the Ukraine are the only strategists. In Case 2, the EU15
is added to the set of strategists, while in Case 3, both EU15 and Japan act
strategically (and independently).
Table 2. Cartel between Russia and the Ukraine. All figures are total costs in
billion US dollars per year, unless otherwise indicated.
Case 1
No
cartel
Price (US$/tC)
Cartel
Precartel
Russia
Ukraine
EU15
Japan
(Rest of) Fringe
Total costs
Emissions red. (%)
Cost incr. cartel
74
−7.5∗
−5.7∗
11.5
6.3
−0.9
3.8
4.0
Cartel
102
−14.2∗
−13.1∗
cartel
cartel
15.0
8.4
−2.1
7.1
5.4
−1.1
Case 2
No
Cartel
cartel
75
−4.6∗
−4.6∗
14.2∗
6.3
−0.9
10.4
6.0
106
−9.3∗
−9.2∗
cartel
cartel
17.5∗
8.7
−2.3
14.6
7.4
−0.05
Case 3
No
Cartel
cartel
76
103
−6.7∗
−7.2∗
−3.6∗ cartel
−3.6∗ cartel
15.2∗ 18.0∗
7.3∗
9.2∗
−0.9 −2.2
14.5
18.4
7.1
8.2
0.4
An * indicates that the agent (or cartel) is modeled as a strategist. The main
body of the table lists costs for different agents, starting with cartel costs and
precartel costs of the cartel members.9 The last row shows the cost increase
for the cartel members relative to the corresponding no cartel case. With the
presence of hot air, total emissions will vary between scenarios. Emissions
reductions are calculated relative to aggregate business as usual emissions,
which are also the total emissions in the competitive scenario. In all cases,
strategic behavior leads to fewer quotas being traded, prices are higher than
in the perfect competition case and emissions fall.
Case 1: When Russia and the Ukraine are the only strategists, independent strategic behavior elevates the quota price from zero (the competitive
outcome) to 74 US$/tC. As should be expected, a cartel between these two
9
Note that in the cases where the EU15 and Japan are not strategists, and these are part
of the Fringe, costs of these agents are still given separately in the table, hence the term
‘(Rest of) Fringe’.
parties will increase the price further, and with it total costs. The cartel benefits from such ‘monopolization’. The buyers EU15 and Japan lose, while the
rest of the Fringe, which is a net seller, free rides on the higher price and
benefits in aggregate.
Case 2: We next move the EU15 from the Fringe to the set of strategists. The
cartel between Russia and the Ukraine is still profitable, although less so than
in Case 1. Russia and the Ukraine decrease sales to keep prices up, while the
EU15 lowers purchases, inducing the opposite price movement. Overall, the
price increases, and to a larger extent than in Case 1. Noting that the Fringe
also includes EU15 in Case 1, the two cases are not directly comparable in this
respect. However, part of the reason prices increase more in Case 2 is that
the coalition parties reduce sales much more when the EU15 is a strategist.
Understanding the strategic incentives of the EU15, the coalition parties cut
sales even further. This hurts the coalition members, relative to a situation in
which there was no strategic response from the EU15.
Case 3: Finally, in the case in which both the EU15 and Japan are treated as
strategists, the cartel is no longer profitable because of the response from the
two strategic buyers.10 Again, the reason is that the reduction in purchases
by the strategic buyers must be counteracted by further sales reductions by
the sellers, yielding lower revenues. In this case, the price increase induced by
the cartel is also somewhat lower than in Case 2 and Case 3.
In conclusion, the above results do not lend immediate support to the modeling practice of lumping Russia and the Ukraine (and other sellers) together
as if they were to form a cartel. The reason monopolization is profitable in
studies that aggregate these countries into a single strategic unit is that the
demand side is assumed to be price taking, as in Case 1 above.
From the above table, it is also evident that both an increased number
of strategists and cartelization increase total costs. We will see later that
cartelization may decrease total costs if sellers and buyers form a cartel.
10
Including Canada (the ‘largest’ buyer in the competitive scenario that is assumed to
belong to the Fringe) in the strategic buyer list will decrease the profitability of the merger
even further.
In light of what was discussed under Case 2–in which EU15 is actually
hurt by acting as a strategist–one may wonder if it would be interesting for
any of the buyers to try to commit to being a price taker. It may be argued
that the EU15, having committed to fulfilling the Protocol as a single group,
has done exactly the opposite. One may note, however, that if the EU15 acts
strategically, Japan is better off as a strategist, because this would make the
cartel between Russia and the Ukraine unprofitable, reducing Japan’s costs. It
can be shown that the same holds for the EU15 if Japan is a strategist. Thus,
being a strategic buyer may pay off if sufficient numbers of other buyers are
also acting strategically. However, further discussion of these issues requires
an analysis of equilibrium cartel formations and is beyond the scope of this
paper.11
4.2
Some other Kyoto cartels
In this section, we discuss cartels between buyers, and between buyers and
sellers.
Buyers’ cartels: If the EU15 and Japan were to cooperate, one could expect
the scenario to unfold like the one we have presented so far: such a cartel will
be profitable when seller strategists are few. However, recall that the price in
the competitive equilibrium is zero in this parameterized case. Consequently,
restricting demand to decrease prices makes no sense, and there is no change
in behavior among buyers when they cooperate. Accordingly, a cartel between
EU15 and Japan does not reduce or increase costs for the coalition partners,
11
These issues also relate to the question of whether permit trade should be modeled
among firms or governments. The claim in the literature that a permit seller cartel is
something to worry about is based on the (implicit) assumption that trade is between
governments. If not, it would not be obvious how Russia could maintain a lower domestic
marginal abatement cost than, say, the EU. Our main objective is to say that if one sticks
with this “trade among governments” assumption, then a cartel may not be profitable. If
Russia and the Ukraine do not allow their firms to participate in an international permit
market among firms, but permit-importing countries allow for such international trade, then
a cartel may well be profitable along the above lines. However, determining the countries
that will allow their firms to participate in international trade is a question that seems to
require a fairly detailed and separate analysis (this choice should be endogenous), and is
not dealt with here.
or, indeed, for any other agent if there are no other strategists. However,
this changes when, for instance, Russia is modeled as a strategist. A cartel
consisting of EU15 and Japan then induces a price reduction from 57 to 38
US$/tC because of the lower purchases of the cartel, but the strategic sales
reduction by Russia nonetheless makes the cartel unprofitable. The reason is
that, given the sales reduction by Russia, the price reduction obtained is so
small that it does not compensate for the lower purchases (and consequently
higher abatement costs) of the cartel members. Naturally, the same cartel is
even less profitable if we include the Ukraine as a strategist alongside Russia.
Mixed cartels: Turning to buyer—seller cartels, the above situation changes
considerably. Table 3 shows the situation with the same four strategists as
before (Russia, Ukraine, EU15 and Japan).
Table 3. Other cartels. All figures are total costs in billion US dollars per
year, unless otherwise indicated.
No cartel
Price (US$/tC)
Cartel
Precartel
Russia
Ukraine
EU15
Japan
Fringe
Total costs
Emissions red. (%)
Cost incr. cartel
76
−3.6∗
−3.6∗
15.2∗
7.3∗
−0.9
14.5
7.1
Mixed cartels
Rus.+EU15 Jap.+Ukr.
40
−1.0∗
11.7∗
cartel
−1.0∗
cartel
4.6∗
0.0
2.5
2.1
−12.7
67
0.5∗
3.7∗
−2.8∗
cartel
14.3∗
cartel
−0.6
11.4
6.2
−3.2
Grand coalition
All strategists
9
−0.1∗
15.4∗
cartel
cartel
cartel
cartel
0.1
0.03
0.2
−15.4
Both a coalition between Russia and EU15, and between the Ukraine and
Japan, do yield total cost savings for the involved parties. Additional simulations, not presented here, demonstrate that all other two-party cartels involving a buyer and a seller are also profitable, with cost savings lying somewhere
between these two extremes. In the case of a cartel between Russia and EU15,
the two parties incur no costs of their own, and act as a net strategic seller.
Together, a seller and a buyer can avoid the common tragedy of holding back
on supply and demand (to induce a price increase and decrease, respectively).
Outside strategists never win as much as the members of the cartel, which
means that there is no ‘merger paradox’ (wanting to outwait others to undertake a merger). Also, total costs clearly decrease.
Finally, lumping all strategists in a ‘grand coalition’ reduces total costs
and emissions reductions almost to the competitive level. The Fringe becomes
a net buyer and the coalition–being self-sufficient with emission quotas–
monopolizes on this excess demand. This explains why costs and emissions
reductions are not zero.
5
Sensitivity analysis
In this section, we make several adjustments to our previous set-up and examine the effects.
5.1
Choosing strategists
Even though the size of each player in the competitive scenario provides us
with a seemingly reasonable ranking of the potential strategists, our choice is
nonetheless arbitrary, in that we have no ex ante reason to choose a specific
number of strategists. We next take the two largest agents in the Fringe–
Poland (seller) and Canada (buyer)–and add them to the set of strategists.
This yields, additionally, the possibility of studying ‘nonmonopolizing’ twoparty cartels. Results for seller cartels when EU15, Japan and Canada all act
strategically and independently are shown in Table 4.
Table 4. Seller cartels in which there are six strategists. All figures are total
costs in billion US dollars per year, unless otherwise indicated.
Price (US$/tC)
Cartel
Precartel
Russia
Ukraine
Poland
EU15
Japan
Canada
Fringe
Total costs
Emissions red. (%)
Cost incr. cartel
No cartel
Russia and Ukraine
79
97
−2.8∗
−3.7∗
cartel
cartel
−2.8∗
20.3∗
10.2∗
5.8∗
−3.4
27.2
9.8
1.0
−1.9∗
−1.9∗
−1.9∗
19.0∗
9.1∗
5.2∗
−2.6
25.0
9.3
Russia, Poland
and Ukraine
124
−4.6∗
−5.6∗
cartel
cartel
cartel
22.1∗
11.8∗
6.5∗
−4.9
30.9
10.6
1.0
In Table 4, we have presented a single two-party cartel–that between Russia
and the Ukraine. However, if we were to study, instead, Russia and Poland, or
the Ukraine and Poland, the same qualitative and quantitative results would
prevail for the cartel members and outsiders. This happens because all of the
strategic sellers are effectively equal, because they all have zero marginal costs.
The results show that cartelization is not profitable. Similar conclusions
are obtained for buyer cartels. One may note that two-party cartels also suffer
from the usual spill-over to a third party on the same side of the market: if
sellers form a cartel, other (strategic) sellers will increase sales as a response.
It is the combined strategic responses from strategic buyers and outside
sellers that determine whether a cartel is profitable or not.
5.2
Hot air
Suppose that permit buyers stay away from hot air, but are willing to pay for
actual emissions reductions in Russia and the Ukraine–perhaps via the Joint
Implementation mechanism. To implement such a scenario in our model, we
limit the endowments in countries with hot air to the business as usual levels.
This may also mimic a future scenario where these countries are given smaller
emissions quotas.
The major change from the previous situations is that the competitive scenario will yield a positive quota price, in this case 200 US$/tC, bringing with
it emissions reductions of 14%. There is no change in the ranking among the
big sellers and buyers, with EU15 and Japan taking the lion’s share of all purchases (51% and 39%, respectively), and Russia and the Ukraine dominating
the supply side (55% and 16%, respectively). Table 5 is most comparable with
Table 2. Recall that an * indicates that a player acts strategically.
Table 5. Cartel between Russia and the Ukraine, without hot air. All figures are total costs in billion US dollars per year, unless otherwise indicated.
Case 1
No
cartel
Price (US$/tC)
Cartel
Precartel
Russia
Ukraine
EU15
Japan
(Rest of) Fringe
Total costs
Emissions red. (%)
Cost incr. cartel
209
−7.7∗
−2.4∗
24.8
14.9
7.3
37.0
14.2
Cartel
214
−10.1∗
−10.0∗
cartel
cartel
25.1
15.1
7.2
37.3
14.2
−0.1
Case 2
No
Cartel
cartel
199
−6.5∗
−2.1∗
24.8∗
14.4
7.6
38.1
14.2
205
−8.7∗
−8.7∗
cartel
cartel
25.1∗
14.7
7.4
38.6
14.2
−0.01
Case 3
No
Cartel
cartel
190
197
−7.5∗
−7.6∗
∗
−5.7 cartel
−1.9∗ cartel
24.5∗ 25.0∗
14.3∗ 14.7∗
7.8
7.6
39.1
39.8
14.2
14.2
0.1
Table 5 shows that also in the absence of hot air, a seller cartel becomes unprofitable when both Japan and the EU15 are modeled as strategists. Emissions
reductions are, of course, higher than in the previous comparable simulations
with hot air, and also the same in all cases. The latter follows from the fact
that all sellers have positive marginal costs, and therefore all quotas are used
in equilibrium.
5.3
The enlarged EU
The EU ratified the Kyoto Protocol (UNFCCC, 1997) in 2002 and, in accordance with Article 4, the 15 EU members of 2002 signed the Protocol as a
single group. Since then, more countries have joined the EU, but we have so
far treated these as part of the Fringe. As stated in Massai (2007, p. 312),
“The EC’s legal position within the FCCC and the Kyoto protocol will be
affected by the inclusion of the 10 new member states, but only in regard
to future commitment periods”. Accordingly, we have not included the new
members when discussing strategic actions on behalf of the EU. However, as
an exercise to check how results may vary, and as a possible prelude to what
may come after 2012, we here check whether our main results change if we
instead treat the EU as consisting of all its member states, which amounts to
27 countries under the Kyoto Protocol. Because we have not included Malta
and Cyprus in our analysis, we call this enlarged entity EU25. In this section,
we continue to assume that there are two strategic players on each side of the
market and include hot air in the model.12
Clearly, the competitive scenario is not affected by the EU extension. However, with more permit-rich countries, like Poland, included in the EU, Japan
becomes the biggest buyer, leaving the EU second (34% versus 30%). Russia
and the Ukraine are no longer just the largest sellers–they are the only sellers.
Table 6 replicates Table 2 for this case, but in Case 2 we assume Japan, rather
than the EU, to be acting strategically, as Japan is the largest buyer in the
competitive scenario. An * signals which players are treated as strategists.
12
The parameters calculated and used for EU25 are ai = 1773, bi = 1.427 and ei = 1157.
Table 6. Cartel between Russia and the Ukraine, enlarged EU. All figures are
total costs in billion US dollars per year, unless otherwise indicated.
Case 1
No
cartel
Price (US$/tC)
Cartel
Precartel
Russia
Ukraine
EU25
Japan
(Rest of) Fringe
Total costs
Emissions red. (%)
Cost incr. cartel
74
−7.5∗
−5.6∗
4.4
6.3
6.2
3.7
4.0
Cartel
102
−14.2∗
−13.1∗
cartel
cartel
5.1
8.4
7.8
7.1
5.4
−1.1
Case 2
No
cartel
76
−6.6∗
−5.7∗
4.5
6.7∗
6.3
5.1
4.5
Cartel
106
−13.0∗
−12.4∗
cartel
cartel
5.1
8.9∗
8.1
9.0
6.0
−0.7
Case 3
No
cartel
Cartel
110
148
−10.1∗
−11.2∗
−5.6∗ cartel
−5.6∗ cartel
5.2∗
5.1∗
∗
10.1
12.3∗
8.2
9.8
12.3
17.1
6.8
8.1
1.1
Our main conclusion regarding seller cartels still holds. Note, however, that
from the last two columns we see that EU25 wins from the formation of a
cartel between Russia and the Ukraine. This is because the price becomes so
high that EU25 switches from being a buyer to being a seller, even though not
a very big one. Finally, Japan and Canada are large buyers in these cases.
Including, instead, EU25 as a Fringe player, with Japan and Canada acting
strategically, our main result still stands.
5.4
Emissions trading with the US
Although the US did not ratify the Kyoto Protocol, they may be part of a
future trading scheme. In this section, we look at the effects of possible US
participation, given the endowment it received under the Kyoto agreement.
The results given in Table 7 consider three scenarios: first, for reference, the
competitive equilibrium; then we assume that the US, EU15, Japan, Russia
and the Ukraine are strategic and independent, before finally looking at the
effect of a Russia—Ukraine cartel.
Table 7. Seller cartel in the presence of the US. All figures are in billion US
dollars per year, unless otherwise indicated.
Price (US$/tC)
Cartel
Precartel
Russia
Ukraine
EU15
Japan
US
(Rest of) Fringe
Total costs
Emissions red. (%)
Cost incr. cartel
Comp. eq.
No cartel
143
115
−39.6
−11.8
19.5
11.1
62.7
−4.7
37.2
11.8
Cartel
149
−13.9∗
−16.7∗
∗
−8.3
cartel
∗
−8.3
cartel
∗
19.1
21.8∗
∗
10.0
12.1∗
73.3∗
78.2∗
−2.8
−5.2
82.9
93.1
15.9
17.1
2.8
This time, the competitive price is strictly positive, at the high end, as compared with other studies. With strategic behavior, the price drops, because
the strategic demand effect dominates the strategic supply effect. Total costs
more than double. Again, the Russia—Ukraine cartel is not profitable because
of the response from the strategic buyers.
Because the competitive equilibrium price is not zero, a buyer cartel can
be strictly profitable. Assuming only the US and EU15 to be strategists, these
will win from the formation of a cartel. However, and as with the EU15—
Japan cartel of Section 4.2, the buyer cartel becomes unprofitable if Russia is
modeled as a strategist.
5.5
Side payments
So far, we have assumed that cartel members can make side payments, and that
there is no agreement between such agents limiting their ability to minimize
joint costs. Here we briefly discuss these assumptions.
What happens if side payments are not possible? For mixed cartels, this
will typically be problematic. Our main results, however, regard the profitabil-
ity of seller cartels, and for the instances where the sellers have zero marginal
costs (as they do in Section 4.1), side payments are not needed for the sellers
to be able to minimize total costs. The lower total sales by the sellers can be
divided between the cartel members in such a way that all are better off (in the
cases where cartels are profitable, i.e. cases 1 and 2). However, when sellers
have positive marginal costs (as in Section 5.2), the lack of side payments may
prevent the sellers from equalizing marginal costs. Say now that sellers are
restricted by this, so that they minimize joint costs subject to the constraint
that they must both be better off. How will this influence cartel profitability?
First, in the absence of strategic responses, this is clearly negative for the cartel, since they are not able to realize all potential cost savings. Thus in case 1
in Section 5.2, where there are no outside strategists, cartel profitability will
be reduced. The Ukraine, which in this case loses from forming a cartel with
Russia if they minimize joint costs, must then be allowed to increase sales.
Using an iterative process in GAMS we find that, somewhat unsurpricingly,
Russia responds by decreasing sales, but total sales by the cartel go up relative
to the case without the restriction. However, the cartel is still profitable. In
case 2, there is an added feedback through the actions of the strategic buyer
EU15. If Russia and the Ukraine increase sales as a result of the fact that they
cannot make side payments, the EU15 will increase purchases, which is good
for the cartel members. As one may expect, however, this secondary effect
does not compensate for the cartel members’ increased abatement costs. The
cartel is therefore less profitable when banning side payments, and in contrast
to what was the case in Section 5.2, it becomes unprofitable.
The above discussion relates to a more general question about how sidedeals can be set up at the cartel formation stage to influence how much the
cartel will supply or demand. Basically, if the cartel members can make binding
commitments (via side payments and threats) to be aggressive, they may enjoy
Stackelberg leadership.13 However, all parties will have such incentives, and
it is not immediately clear if it will be possible to make such commitments.
Furthermore, this basic problem of benefitting from tying one’s hands applies
to all strategic interaction scenarios with a first mover advantage, and in any
case, a thorough discussion of such items would be better suited alongside an
13
For instance, two parties can make a deal where a very large amount of money has to
be paid to the other party if they fail to sell exactly half of the Stackelberg amount each.
analysis of equilibrium cartel formation (see also Section 7). This is beyond
the scope of the present paper.
5.6
A different underlying model of permit exchange
So far, our model has been based on Hahn (1984) and Westskog (1996), and
the game has had a clear Cournot flavor. In this section, we study cartel profitability using a different underlying model of exchange, namely, one similar
to that elaborated in Malueg and Yates (2009), see also Wirl (2009). As we
shall see, the game will have Bertrand-type elements, and it is therefore no
surprise that some of our results will change.
As in the previous set-up, the game studied here has a two-stage structure.
First, all agents pretend that the intercept of their affine marginal abatement cost curves is a number, Ai . Recall that the true marginal cost curve is
−c′i (xi ) = ai − bi xi when xi ≤ ai /bi , where ai is the actual intercept. Trade
is then perfectly competitive on the chosen Ai and on the true slope bi . In
Malueg and Yates (2009), the slopes are the same across agents, but we can
easily implement their basic set-up even when agents’ marginal cost curves
have different slopes.
Anyone not member of a cartel aims, at the first stage of the game, to find
an Ai that
minimizes {ci (xi ) + p (xi − ei )} ,
(9)
perfectly understanding that xi and p will depend on Ai . Those, if any, who
are members of a cartel, C, choose a collection, (Ai )i∈C , in order to
minimize
{ci (xi ) + p (xi − ei )} .
i∈C
At the second, market stage of the game, xi and p are those that satisfy
−Ai + bi xi + p = 0,
for all i ∈ I, and
i∈I
xi =
i∈I
ei .
(10)
(11)
Because each agent here chooses their Ai instead of their use of quotas, we
are moving away from the Cournot-like scenario discussed so far. Also note
that increasing one’s Ai means increasing one’s own use (demand for quotas
increases at the second stage), which implies less sales. Even though we will
argue below that this setting has Bertrand-type elements, in contrast to a pure
Bertrand scenario, the agents do not set prices, and there will be a continuous
response to an increase in Ai , even though there is a homogenous traded good.
The necessary first order optimality conditions associated with this game,
as programmed in GAMS, are provided in the Appendix. Unsurprisingly, the
first order conditions will imply that if sellers form a cartel, they will (credibly)
sell less (which in this set-up implies increasing demand by increasing their
posted levels of Ai ), because they internalize the negative effect one agent’s
sales have on other agents in the cartel. Buyers in a cartel will, for the same
reason, decrease demand (reduce their posted levels of Ai ). This is, of course
good for the cartel members, but, as before, we need to look at the strategic
response by other strategists to gauge whether cartelization will be profitable.
In the Appendix, the best reply functions for agents with and without hot air
are characterized.
For a strategic agent without hot air (positive marginal costs) in equilibrium, and who is not member of a cartel, the best reply function is given
by
Aj
ei β i − β 2i j∈I ej
Ai
ai
β 2i
+
=
+
,
(12)
bi
bi (1 + β i )
bj
1 − β 2i
1 − β 2i
j∈I\{i}
where β i :=
1
bi
1
j∈I bj
.
Here we see that the posted levels of the intercepts are strategic complements. That is, if a seller cartel increases their levels of Aj (demanding more,
increasing the price), outside strategists will optimally respond by demanding
more, which is unambiguously beneficial for the seller cartel. Similarly, for
a buyer cartel, they will reduce demand to decrease prices, and the response
by outside strategists is to demand less, which increases the profitability of
the cartel. Clearly, these results have less to do with Cournot, and relate
more to a Bertrand scenario in which prices are typically strategic complements (differentiated products), and in which, therefore, mergers are generally
profitable.
However, we cannot conclude from this that all one-sided cartels in our
Kyoto setting will be profitable. Things turn out to be quite different for
agents that have zero marginal costs. Their best reply functions are
A
ei + (1 − 2β i ) j∈I ej − (1 − 2β i ) j∈I\{i} bjj
Ai
=
.
(13)
bi
2(1 − β i )
This implies that these agents will behave oppositely to the agents that have
positive marginal costs. If a seller cartel increases its levels of Aj , outside
sellers (buyers do not have hot air) with zero marginal costs will respond by
decreasing theirs (i.e., demand less), which hurts the cartel.
All this implies that both seller and buyer cartels will always be profitable if
there are no outside agents with zero marginal costs; however, this can change
if some outside agents (sellers) have hot air.
Our simulations confirm the above scenario. Note that in this set-up that
there is no need for anyone to be a price taker; therefore, below, we treat
everyone as acting strategically. First we compare two scenarios: one with all
agents acting independently, the other with all sellers forming a cartel. The
results are as follows.
Table 8. No cartel and a sellers’ cartel, all agents being strategic. Marginal
costs US$/tC, Total costs BUS$/yr.
No cartel
Marg. costs Total costs
Price
Cartel
Precartel
Russian Fed.
Ukraine
Poland
Czech Rep.
Romania
Bulgaria
Hungary
Slovakia
Lithuania
Estonia
Latvia
Slovenia
Iceland
Liechtenstein
Monaco
Norway
Switzerland
New Zealand
Australia
Canada
Japan
EU15
Total costs
Emissions red. (%)
Cost incr. cartel
50
0
7
31
42
42
46
47
47
49
49
49
50
50
50
50
51
52
52
61
79
95
131
−3.8
−3.8
−1.7
−0.8
−0.7
−0.4
−0.3
−0.3
−0.2
−0.2
−0.1
−0.1
−0.0
0.0
0.0
0.0
0.1
0.1
1.2
3.1
4.6
9.9
6.8
5.0
Cartel 1
Total costs
Cartel 2
Total costs
135
−22.1
−12.2
cartel
cartel
cartel
cartel
cartel
cartel
cartel
cartel
cartel
cartel
cartel
cartel
cartel
0.0
0.0
0.1
0.3
0.3
2.3
6.4
10.8
19.6
17.7
7.9
−9.8
73
−8.4
−8.5
−7.9
cartel
cartel
cartel
cartel
cartel
cartel
cartel
cartel
cartel
cartel
cartel
cartel
0.0
0.0
0.1
0.2
0.2
1.6
4.2
6.4
12.8
9.1
5.6
0.1
We are not aware of any numerical illustration, in the literature, of a permit
market manipulated via the abatement cost function. We therefore discuss
the no cartel case briefly. First, the permit price increases from 0 in the com-
petitive case to about 50 US$/tC. Permit sellers have lower (true) marginal
abatement costs than the price, while the opposite applies for buyers. The
total costs of the agreement, 6.7 BUS$/yr, are much lower than the most
comparable figure for the dominant agent— competitive fringe model, with six
strategists, in which the corresponding figure was 24.6 BUS$/yr (see Table 4).
As such, within this framework, market power seems to be less of a problem
when it comes to efficiency.
Regarding the effects of cartelization, we see that it is profitable for the
cartel members to form a cartel if all sellers participate (Cartel 1), even with
strategic buyers present. Given our previous discussion, this comes as no
surprise, because there are no zero-cost countries left outside the cartel that
could potentially respond in a nonbeneficial way. A more interesting question
is, therefore, whether a two-country cartel may be profitable. Looking at the
two largest buyers, it can be shown that such a cartel (between Russia and
the Ukraine) is profitable. Thus, the negative strategic effect by outside zerocost sellers will not be sufficient to make such a cartel unprofitable. However,
when we look, instead, at a cartel between all sellers except Russia (Cartel 2,
above), the situation changes. The fact that Russia is now not part of the
coalition, and has zero marginal costs, makes the coalition unprofitable. The
same applies to all buyer coalitions. In the latter case, even though other
buyers will respond by decreasing demand, the zero-cost sellers respond by
increasing demand, and buyer cartels are therefore unprofitable.
All in all, a larger number of seller cartels can be identified as profitable
within this set-up. Even so, unprofitable seller cartels can also be identified
here.
6
Remarks on model formulation
We have avoided treating many relevant aspects of emissions trading. For
instance, our setting is partial, static and free of uncertainty, to mention but
a few. Moreover, we have only considered trade among governments, and not
dealt with how these will regulate firms. Furthermore, and in contrast to, e.g.,
Barrett (2003), Carraro (2003), and Helm (2003), permits are taken as given.
We will not deal with these issues here, but in light of the somewhat different
results we obtained using the alternative models of permit trade above, we try
to shed some light on the choice of underlying model of trade in the rest of
this section.
So far in our discussion, our main attention has been on the dominant
agent—competitive fringe model. A reason for this choice is that it has been
the most popular model in the literature on permit markets. While some of the
literature on cartel profitability under the Kyoto Protocol (mentioned in our
first footnote) explicitly refers to that model, some does not. The argument
is typically put forward by calculating what happens if countries of the former Soviet Union monopolize supply, and then comparing that outcome with
perfect competition. The monopoly outcome is then interpreted to correspond
with the seller cartel case, everyone else being price takers.
One may note that our permit market setting is nothing other than a pure
exchange economy. In fact, it is a very simple and convenient case. There are
only two goods–permits and money–and utility functions are quasi-linear.
This implies that every theory for a more general pure exchange economy is,
in principle, directly applicable to permit markets. Furthermore, there are
many models for pure exchange available. A survey is not appropriate here,
but consideration of a few selected passages seems in order.
The dominant agent—competitive fringe model shares some aspects with
exchange models in which some agents are assumed to be strategic “atoms”
and the remainder to form an atomless sector (often named an “ocean”), as
in, for example, Shitowitz (1973). To the best of our knowledge, none has
convincingly explained the criteria for classifying agents as one or the other.
That choice has an impact on the outcomes.
In Section 5.6, we considered a version of the model proposed by Malueg
and Yates (2009), who make reference to so-called supply-function equilibrium
(see Klemperer and Meyer, 1989, and Hendricks and McAfee, 2009). It appears to us that the game considered in Malueg and Yates (2009), as well as
Wirl (2009), date back at least to footnote 10 in Hurwitz (1972):
“One version of the game we imagine the traders playing is as follows: each trader
picks an indifference map, a price-adjustment mechanism of Lange type is operated
until market-clearing equilibrium prices are found, and then each trader collects the
value his true utility function takes for the bundle which he obtains at the equilib-
rium”.
Not everyone has expressed enthusiasm for this type of game; Bonniseau and
Florig (2003, p. 728) suggest that: “Allowing for such sophisticated strategies,
almost anything becomes an equilibrium unless one imposes restrictions on the
type of preferences and endowments one may announce.” Above, we assumed
that all agents could manipulate exactly one and the same parameter in their
true utility function. That choice was arbitrary, and other choices are possible.
Another strand of literature has modeled exchange economies in which
agents misrepresent their endowment, e.g., Aumann and Peleg (1974), MasColell (1976), Guesnerie and Laffont (1978) and Postlewaite (1979) are early
works along these lines. Malueg and Yates (2009, p. 558) argue that because
the initial allocation (in a Kyoto-type setting) is public knowledge, it makes
better sense to model the abatement cost function as being private information
rather than manipulation via endowment. We sympathize with this argument.
Nevertheless, Postlewaite (1979, p. 255) notes that “Even if it were possible
to determine true endowments, given a private ownership structure, there is
no way of preventing an agent from destroying all or some portion of his
endowment”.
It is also known that manipulation via endowment can yield the same outcome as a game manipulated via preferences, given a suitable restriction on
the class of functions that can be reported. For instance, the no cartel equilibrium reported in Table 8 is nothing other than the outcome of an endowment
withholding game à la Postlewaite (1979), if one adopts the strategy sets in
Safra (1985). Not everyone is happy with Postlewaite’s and Safra’s endowment withholding models; Lahmandi (2001, p. 666) remarks that “...while we
consider that an agent, after deciding the amount to be sent on the market,
maximizes his utility taking into account what he has ‘left at home’, Safra
considers that an agent makes his shopping as if he forgot such a quantity. We
think that such a hypothesis is hardly defensible”.
Then there are others, again, who are not very satisfied with any of the literature mentioned thus far, at times because that literature does not eliminate
the “Walrasian auctioneer”. One noncooperative game without this auctioneer, or at least in which his job is considerably easier, is Shapley and Shubik’s
(1977) strategic market game. Again, this model is directly applicable to per-
mit markets. We have not considered that game here. The reason is that
there are conditions under which the only equilibrium point in that game is
no trade. As it turns out, our parameters satisfy those conditions; see Godal
(2009).
All in all, there seems to be a number of potential models that may be
relevant to permit market settings, and we think these issues deserve more
attention, as also noted below.
7
Final remarks
This paper has revisited the common claim that an organization of permit
exporting countries (consisting of former Soviet states and some Eastern European countries) is something one should anticipate and worry about, when
it comes to permit trading under the Kyoto agreement. Within a dominant
agent—competitive fringe environment, standard economic arguments do not
provide immediate support for such a conclusion. The reason is that strategic
buyers may make such an endeavor unprofitable. In a Cournot-type model,
when large sellers cooperate to increase prices, the best response of large buyers, like the EU, is to make more emissions reductions themselves, reducing
quota purchases aimed at pushing the equilibrium price down. No matter
whether prices actually decrease or sellers counter this by restricting sales further, the strategic response of the buyers reduces the profitability of a cartel,
and with our parameters and sufficient buyer power, such cartels become unprofitable. On the other hand, in a “manipulation via technology” type of
economic environment, sellers’ cartels can be profitable, and when so, at the
expense of efficiency.
We have not discussed endogenous cartels in this paper, the main reasons
being that we are not sure of the underlying model of trade that should be
selected.14 Also not included in our analysis are the costs of organizing a
cartel. Setting these issues aside, applying the dominant agent—competitive
fringe model, and sticking with the notion of internal and external stability
from d’Aspremont et al. (1984), the grand coalition of strategists will be a
14
Endogenous cartels are discussed in, for instance, d’Aspremont et al. (1984), Horn and
Persson (2001), and Carraro (2003).
stable cartel when we allow for unconstrained side payments. The figures of
that scenario were presented in Table 3, and as seen there, such a coalition
would lead to reduced total costs and lower emissions reductions relative to
the comparable alternatives. If, given the same simplifications, one were to
adopt other models of underlying strategic trade in which all agents typically
can be modeled as strategic, then we suspect that the grand coalition of all
agents in the economy would be stable, and bring us back to the competitive
allocation. On the face of it, this may seem to circumvent the problem of finding
the most appropriate underlying model. However, endogenous cartels without
side payments would arguably be a more interesting scenario for international
emissions trading. We expect such an analysis to be difficult, both in general
and in a fully parameterized model, and we do not believe the results would
be independent of the chosen baseline model. To us, therefore, it seems that
the issue of choosing the most appropriate model for permit exchange stands
out as a particularly relevant topic for future research.
Appendix
Rearranging (10) yields
xi =
Ai − p
.
bi
(14)
Inserting (14) in (11) one gets
p=
Write β i :=
1
bi
1
j∈I bj
Aj
j∈I bj
−
j∈I
ej
1
j∈I bj
.
(15)
∈ (0, 1) . We then get
∂p
∂xi
1
= β i and
= (1 − β i ) > 0.
∂Ai
∂Ai
bi
(16)
1 ∂p
∂xj
=−
< 0.
∂Ai
bj ∂Ai
(17)
Also,
Hence, a choice Ai for someone who is not in a cartel satisfies
c′i (xi )
∂xi
∂xi
∂p
+p
+
(xi − ei ) = 0,
∂Ai
∂Ai ∂Ai
which, for programming purposes, is convenient to rewrite as
1
∂p
1 ′
′
(ci (xi ) + p) +
− (ci (xi ) + p) + (xi − ei ) = 0.
bi ∂Ai
bi
For an agent in a cartel, Ai must satisfy
c′i (xi )
∂xi
∂xi
∂p
+p
+
(xi − ei )
∂Ai
∂Ai ∂Ai
∂xj
∂xj
∂p
′
+
cj (xj )
+p
+
(xj − ej ) = 0.
∂Ai
∂Ai ∂Ai
j∈C{i}
(18)
By making use of (16) and (17), the left hand side of the last string may be
written as
1
∂p
1
∂p
∂p
′
ci (xi )
1−
+p
1−
+
(xi − ei ) +
bi
∂Ai
bi
∂Ai
∂Ai
1 ∂p
1 ∂p
∂p
′
cj (xj ) −
+p −
+
(xj − ej ) .
bj ∂Ai
bj ∂Ai
∂Ai
j∈C{i}
This equals
c′i (xi )
1 ∂p
∂p
1
1 ′
1 ∂p
c (xj ) −
+p −
+
+p +
(xj − ej ) .
bi
bi j∈C j
bj ∂Ai
bj ∂Ai
∂Ai
Therefore, the first order optimality condition for a cartel member amounts to
∂p 1 ′
1 ′
(c (xi ) + p) +
−
c (xj ) + p + (xj − ej ) = 0.
bi i
∂Ai j∈C
bj j
We will now find the best reply functions. For agents with nonzero marginal
costs, (18) can be written
1
(−ai + bi xi + p) (1 − β i ) + β i (xi − ei ) = 0.
bi
(19)
Inserting (14) and (15) in (19), we get, with some manipulation,
Aj
Ai
ai
− β 2i
= (1 − β i ) + ei β i − β 2i
ej ,
bi
b
b
j
i
j∈I
j∈I
which, solved for Abii , yields (12).
Similarly, if marginal costs are zero, (18) becomes
1
p (1 − β i ) + β i (xi − ei ) = 0.
bi
Again, inserting (14) and (15) in (20) yields (13).
(20)
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