The incentives for merger in a noncompetitive permit market
Abstract
A group of small competitive permits traders, who face an imperfectly competitive permit
market, may consider cooperation (merger) to be able to jointly act strategically in the permit
market. It is a well known result in the literature that horizontal merger of Cournot players
may be unprofitable. We show that the profitability of merger among competitive agents
differ substantially from the profitability of merger among Cournot players. Furthermore, we
show how the profitability of a merger depends on whether the merged agents are on the same
side of the market as the preexistent dominant agent (s).
1 Introduction
The starting point of this analysis is that a group of small competitive permits traders, who
face an imperfectly competitive permit market, consider cooperation (merger) to be able to
jointly act strategically in the permit market. In the Kyoto protocol, the only policy instrument
for distributing costs between participants is the initial allocation of tradable permits across
countries. Burden sharing consideration in the distribution of permits can gives some agents
an opportunity to exercise market power in the emissions permits market.1 A number of
studies have concluded that Russia, and other former Soviet republics and Eastern European
countries, will become large sellers of permits in the first Kyoto period (see Weyant and Hill
(1999) and Weyant (1999)). Böhringer (2002) concludes that the Former Soviet Union can
significantly increase its benefit of the Kyoto agreement by exploiting its market power in the
permit market, which implies that marginal abatement cost are not equalized across the
participating countries. Negotiations for the post-Kyoto commitment period (2013 and
beyond) have already started but no consensus has emerged yet. Due to the poor global
emission reduction achieved by the Kyoto Protocol it reasonable to assume that if the
1
Hahn (1984) shows that the opportunities for an agent to exercise market power could be undermined (i.e. the cost-effective
outcome is achieved) by an appropriate distribution of permits between agents. However, burden sharing considerations
may prevent a distribution of permits which undermine market power.
agreement is prolonged, it will be more stringent and probably involve more countries with
binding emission target than in the first commitment period2.
As long as the initial distribution of permits is the only instrument for burden sharing, it is not
unreasonable to expect that some countries gain market power also in a post Kyoto period3.
Whether market power will be exercised on the demand side, supply side or both sides of the
market depends on the initial distribution of permits across countries and the participants’
abatement cost.
The starting point of this analysis is the allocation of permits leaves at least one agent with
market power. A group of small traders, who realize they face an imperfectly competitive
permit market, consider cooperation to jointly be able to act strategically in the permit market.
Depending on whether the individually competitive agents are net seller or buyers they merge
into a seller or buyer cartel. An obvious candidate for cooperation on the permit market is the
EU countries, which presently cooperate on a common climate policy in addition to their
commitments under the Kyoto protocol, and has established an internal emission trading
scheme (EU-ETS). For instance, by determining to which degree the emission target shall be
met by domestic measures relative to permit purchase (the supplementary principle), EU can
act as a strategic buyer in the international permit market. This is analyzed in Ellerman
(2000).
The profitability of merger has been widely analyzed in the literature, both theoretically (see
Salant et al. (1983), Perry and Porter (1985), Fauli-Oller (1997) and Huck and Konrad (2004))
and empirically (see among others, Ravenscraft and Scherer (1989)). Salant et al. (1983) show
that horizontal mergers may reduce the joint profit of the firms that collude (insiders). Merger
makes the colluding firms internalize the losses they impart to each other. This implies that
for any given output of the non colluding firms (outsiders), the colluding firms contract their
aggregate output, compared to the pre merger output. This will, ceteris paribus, increase their
2
39 signatories of the Kyoto Protocol listed in the so-called Annex-B and representing about two thirds of global emissions
in 1990, promised to reduce their greenhouse gas emissions by 5.2 percent compared to 1990 levels by 2008-12 (Kyotoperiod). The United States later withdrew, and the global emission reduction achieved by the Protocol is insignificant. See
Hagem and Holtsmark (2001) and Böhringer and Löschel (2003).
3
For instance, Russia obtained quite lax emission reduction requirements under the Kyoto Protocol, i.e. large allotments of
free permits. This was probably necessary to achieve participation from Russia under the Protocol. In the future, allocating
large allotments of free permits could also be an instrument for achieving participation from additional countries in a
Kyoto-like agreement. Further, Ringius et al. (2002) discuss the importance of fairness in international climate policy and
argue that the differentiation of targets in the Kyoto Protocol evidences the need for fairness and justice in global climate
policy. In the Kyoto Protocol, these fairness considerations are taken care of through the initial permit allocation between
agents.
2
joint profit. However, lower output from the insiders makes it profitable for the outsiders to
increase their production. As the output of the outsiders increase, the profits of the insiders
decrease. The increase in production from the outsiders following the merger may reduce
insiders profit more than the increase in profits that would have occurred had outsiders’
production remained constant. If that is the case; the merger is unprofitable for the colluding
firms. By the use of a Cournot model with n identical firms with constant marginal cost and
linear demand, Salant et al. (1983) shows that it is sufficient for a merger to be unprofitable
that less than 80 percent of the firms collude. Perry and Porter (1985) argue that Salant et al.
(1983) understates the incentives for merger. They show that incentives for merger can be
significantly larger when mergers influence the firms production cost. Merger increases the
output the insiders can produce at a given average costs. In our model we ignore any
economies of scale, so cartelization does not affect the joint marginal production cost or fixed
cost. Cartelization therefore unambiguously leads to contraction of output in a seller cartel (or
a contraction of demand, in a buyer cartel). The profit increase following from the contraction
is (partly) offset by the preexistent dominant agent’s optimal response. However, our
conclusions about the profitability of merger differ from the conclusions in Salant et al.
(1983) because we consider merger among a group of agents that had a competitive
premerger behaviour, whereas Salant et al. (1983) considered merger between a group of
Cournot players. Furthermore, we show how the profitability of a merger depends on whether
the merged agents are on the same side of the market as the preexistent dominant agent (s).
We show that when some (premerger) competitive agents merge into a cartel that behaves
non-competitively, the preexistent dominant agents’ optimization problem alters as the slope
of the residual inverse demand (supply) function changes. The preexistent dominant agents’
response to the change in this function benefits the cartel if they are on the same side of the
market, and hurts them if they are on the other side of the market.
This explains why it is less likely that a group of buyers find it profitable to establish a buyer
cartel in a market characterized by a dominant seller, whereas it can be profitable for a group
of sellers to establish a seller cartel in the same market. This result is of relevance when
considering different possibilities for cooperation on the market for emission permits under a
post-Kyoto protocol.
3
2 The model
We treat the permit market as a market for a commodity where all agents participating in the
market have an initial endowment of the commodity traded. Whether an agent becomes a
buyer or a seller depends on the initial endowment, the benefit of consuming the good and the
equilibrium price. The starting point of our analysis is that the market consists of one larger
dominant agent and group of competitive agents. The group of competitive agents consists of
both buyer and sellers, but is on aggregate on the other side of the market as the dominant
agent. All agents have identical benefit function of consuming the good e. We divided the
group of competitive agents in two groups; 1 and 2. Let Bi  ei  denote the (aggregate) benefit
of consuming e i in group i, i=1, 2, and let BD  eD  denote the dominant agent’s benefit of
consuming e D . We assume that benefits are strictly increasing and concave: B  0, B  0 .
The competitive agents’ consumption of the commodity equals the initial endowment of the
commodity Xi plus net purchase x i ;
ei  Xi  x i
(1)
Let p denote the price of the commodity.
The competitive agents choose their trade in x i in order to maximize individual welfare:
max Wi  Bi  x i   p  x i
xi
(2)
subject to (1)
The solution of this maximization exercise gives rise to the following first-order conditions:
Bi  ei   p
(3)
The emission constraint (1) and (3) gives the demand functions x i (p) , i=1,2.
Let q define the supply of the commodity from the dominant agent;
eD  X D  q
4
(4)
Market clearance implies;
q  x1  x 2
(5)
The standard approach in the literature when there are several small competitive suppliers in
addition to a dominant seller is to model the market as a dominant agent with a competitive
fringe, where the dominant agent behaves as a Stackelberg leader with respect to the
competitive fringe. This is the approach we follow in this paper, although we analyze the
possibilities that the competitive fringe and the dominant agent can be on both side of the
market. Alternatively, we could have modeled the market as a dominant agent facing a net
inverse demand (supply) function from the competitive agents, who on aggregate is on the
other side of the market as the dominant agent. This is the approach followed in several
studies of market power in the permit market (see Hahn (1984) and Hagem and Westskog
(1998). These two approaches lead to identical outcomes. This is proved in appendix A.
Let the agents in group 2 constitute what we refer to as the competitive fringe. The
equilibrium conditions given by (3), and the market clearance condition, (5), gives the inverse
demand function for group 1, p(x1 )  p(q  x 2 ) , and the following expression for the
competitive fringe’s (group 2) first order condition
p(q  x 2 )  B2  x 2 
(6)
Equation (6) implicitly defines x 2 (q) , and the inverse residual demand function facing the
dominant agent is
p(q  x 2 (q))
(7)
The dominant agent’s optimization problem is
max WD  p(q  x 2 (q))  q
q
(8)
First order condition:
p  (1 
x 2
)q  p  0
q
5
(9)
Let x1c , x c2 , q c , pc denote the solution to or (3), (7) and (9), and let W1c , W2c , WDc denote the
corresponding welfare levels.
3 Part of the fringe merge into a cartel
In this section we analyze the case where one group of the competitive agents (group 2)
considers merging into a cartel. The potentially merging agents can either be competitive
sellers or competitive buyers. We consider the cartelization as a two stage game. In the first
stage, the agents decide whether to merge or not. In the second stage, if they have merged,
they decide their aggregate demand/supply, given Cournot competition on the output market.
We assume that when the agents make their merger decision in period 1 they can correctly
anticipate the Cournot-Nash-equilibrium of the output market that emerge in second stage.
Hence, merger only occurs if it turns out to be profitable in stage 2.
The inverse demand function given by (3) (for i=1), and the market clearance condition given
by (5) leads to the following inverse demand function;
p(q  x 2 )
(10)
max W2  B2 (e2 )  p(q  x 2 )  x 2
(11)
Cartel’s optimization problem;
x2
subject to (1).
Dominant agent’s optimization problem;
max WD  BD (eD )  p(q  x 2 )  q
(12)
q
This leads to the following two first order conditions for the Cartel and the dominant agent,
respectively;
B2  e2   p  p  x 2
(13)
BD  eD   p  p  q
(14)
6
From (13) and (14) we find the reaction functions (optimal response functions) x 2 (q) and
q(x 2 ) . The slopes of the reaction functions are found from total differentiating (13) and (14).
To ensure the existence of a unique stable equilibrium, we assume that the reaction functions
are upward sloping, with a value less than 1;
0
dx 2
p  p  x 2

1
dq B2  2p  p  x 2
(15)
dq
p  p  q

1
dx 2 2p  p  q
(16)
0
Note that if the cartel is a net seller of permits ( x 2 is negative), the reaction functions are
downward sloping measured in sale (  x 2 ), as is the standard assumption in Cournot models
with strategic sellers. Hence, the dominant agent’s optimal response to a decrease in sale from
the fringe (increased x 2 ), is to increase q, which again hurts the cartel as increased sale
implies lower price.
If the cartel is a net buyer of permits ( x 2 is positive), the reaction functions are upward
sloping. The dominant agent’s optimal response to a decrease in demand is to contract sale,
which again hurts the cartel as decreased sale implies higher price.
Hence, in both cases, the positive effect on profit of contracting sale/purchase can be more
than offset by the reaction from the dominant agent.
M
M
Let x1M , x M
2 , q , p denote the solution to (3) (for i =1), (10), (13) and (14), and let
W1M , W2M , WDM denote the corresponding welfare levels.
An action is said to have a positive strategic effect if other producers’ responses to the action
increases the profit of the producers taking the actions. If, on the other hand, other producers’
responses decrease the producer’s profit, the action is said to have a negative strategic effect
(e.g. Tirole (1988), chapter 8). By comparing the equilibrium in the case with and without
merger, we can derive the following proposition;
7
Proposition 1
Consider a competitive environment with a dominant agent and a competitive fringe. If a
subgroup of the fringe agents merges and face Cournot competition in the output market, the
strategic effect of the merger is unambiguously negative (ambiguous) if the merged agents are
on different (the same) side of the market as the preexistent dominant agent.
Proof: see appendix B
When a group of competitive agents merge into a cartel the strategic effect of that action is
two-fold;
i)
Merger implies that agents, that did not previously act strategically, become a
Cournot player. This leads to shift in the inverse demand function in the
preexistent dominant agent’s welfare function. The inverse demand function
becomes less elastic (for the premerger output). The dominant agent takes
advantages of this and contract supply if it is a net seller and contract demand if it
is a net buyer. This effect leads (ceteris paribus) to an increase in the equilibrium
price if the dominant agent is a net seller and a decrease in the price if the
dominant agent is a net buyer. Hence, this action reduces the merged agents’
aggregate profit if they are on the same side of the market as the dominant agent,
whereas their profit decreases if they are on the opposite side of the market.
ii)
The merged agents take into account the losses they impart to the whole group by
increased supply/demand. Optimal aggregate supply/demand is contracted
(compared to premerger aggregate output). We see from (16) that the dominant
agent’s optimal response to a contraction in demand from the merged agent
(reduced x 2 ) is to reduce its own supply if it is a seller, and increase its demand if
it is a net buyer ( q  0 ). This response hurts the buyer-cartel since it drives up the
equilibrium price. In case of a seller-cartel, the dominant agent’s optimal response
to a contraction in supply from the cartel is to increase its own supply if it is a
seller and decrease its own demand if it is a buyer. This hurts the seller-cartel as it
causes the equilibrium price to fall.
If the sum of the two effects i) and ii) is negative, cartelization has a negative strategic effect.
8
In figure 1 and 2 we have depicted the consequences of merger in the case of a dominant
seller (assuming linear response functions). Figure 1 depicts the case of a sellercartel (x 2  0) , and figure 2 the case of a buyer-cartel ( x 2  0 ). The lines q1(x 2 ) and q2(x 2 ) in
figure 1 represent two alternatives for the optimal response function from the dominant agent,
given by (14), and the line x 2 (q) represents the optimal response function from the cartel,
q1(x 2 )
q2(x 2 )
x2
x 2 (q)
q1M
qc
q2 M
q
x2 M
2
x1M
2
x c2
given by (13).
Figure 1. Dominant seller and a seller-Cartel
We know from the comparison of (6) with (13), that for q  q c , the cartel’s optimal sale is less
than in the premerger situation ( x c2 ), and from the comparison of (9) with (14), we know that
for x  x c2 , the dominant agent’s optimal sale is less than in the premerger situation ( q c ).
In figure 1 we see that the two alternative response functions q2(x 2 ) and q1(x 2 ) , which both
satisfy (14), give an equilibrium outcome for q which is higher ( q2 M ) and lower ( q1M )
than q c , respectively. Hence, we cannot in general determine whether the merger leads to a
negative or positive strategic effect, that is whether q has increased or decreased compared to
the premerger output.
9
x M2
q(x M
2 )
xM
2 (q)
x M2
q
q
c
Figure 2. Dominant seller and a Buyer-Cartel
In the case of a buyer-cartel , we know from the comparison of (6) with (13), that for q  q c ,
the cartel’s optimal purchase is less than in the premerger situation ( x c2 ), and from the
comparison of (9) with (14), we know that for x  x c2 , the dominant agent’s optimal sale is
less than in the premerger situation ( q c ). Hence, in the case of a buyer-cartel, the response
c
functions must intercept for q M  qc and x M
2  x 2 to satisfy (13) and (14).
Whether a merger is profitable or not depend on whether the increase in profit due to reduced
aggregate output/sale from the merged agent is more than offset by the decrease in profit
following from the negative (positive) strategic effect of the merger.
In Salant et al. (1983) the strategic effect of merger only followed from the merged agents
contraction in output (as described in ii) above) as their starting point of their analysis is that
the countries that merged where Cournot players prior to the merger. The strategic effect of
merger was unambiguously negative in their model (ignoring economies of scale). If the
negative strategic effect of a contraction in output more than offset the positive effect on
profit of the contraction in the merged agent’s output, merger has a negative effect on the
10
merged agents’ aggregate profit. In our model, by assuming merger of competitive agents we
have showed that there can be a positive strategic effect of merger, which unambiguously
makes the merger profitable.
In order to highlight differences in benefit of a merger depending on whether the merged
agents are on the same or opposite side of the market as the preexistent dominant agent, we
consider below a situation where the merged agents become Stackelberg leaders in the output
market. In that case the merged agents can never be worse off be restricting output, as they
have the opportunity to fix their demand/supply at the premerger quantity.
4 Part of the fringe merge into a cartel- Stackelberg Leadership
In this section we consider the case where a part of the fringe not only determine to establish a
cartel in period 1, but are also able to commit to a certain purchase/sale in period 2. Hence,
the agents take into account the dominant agents’ optimal response given by (14) when they
determine their joint output/purchase. The cartel is faced by the following inverse demand
function in the second period;
p(q(x 2 )  x 2 )
(17)
where q(x2) is given by (14).
The cartel’s optimizing problem in period one is given by
max W2  B2 (e2 )  p(q(x 2 )  x 2 )  x 2
x2
(18)
subject to (1).
This leads to the following first order condition
B2  e 2   p  (
q
 1)  x 2  p  0
x 2
Let x1S , x S2 , q S , pS denote the solution to (3) (for i =1), (14), (17) and (19). Let W1S , W2S , WDS
denote the corresponding welfare levels.
11
(19)
Furthermore, since the merged agent can commit to a certain sale/purchase in period 1, and
the response function from the dominant agent is known to the agents, the merged agent can
never be worse off be choosing another output/demand than the premerger (competitive)
output. So if the merged agents choose another output/demand than the competitive level,
they get better off than keeping the premerger competitive level.
However, although the changes in the merged agents output cannot make them worse off, the
negative strategic effect due to a shift in the demand function (as explained by i) above) can
still make merger unprofitable if the merged agents are on the other side of the market than
the preexistent dominant agent. Hence, we get the following proposition;
Proposition 2
Consider a competitive environment with a dominant agent and a competitive fringe. If a
subgroup of the fringe agents merge and become a Stackelberg leader in the output game,
merger is always profitable for the colluding agent if they are on the same side of the market
as the preexistent dominant agent, but can be unprofitable if they are on the other side of the
market.
Proof of proposition 2: see appendix B
5 Concluding remarks
In this paper we have evaluated the profitability of merger in a non-competitive permit
market. The international permit price is of great significant for countries’ cost of meeting
their commitments under an international climate regime. Manipulation of the permit price
through strategic behaviour in the permit market does not only affect the cost effectiveness of
reaching a global emission target, but also the distribution of cost across countries. Hence, the
competitive environment on the permit market may affect the countries willingness to accept
tough targets. A group of small competitive trader like the EU-countries, which most likely
become large net buyers of permits in a post-Kyoto agreement, as they have announced
willingness to except though targets, may therefore be severely affect by strategic behaviour
in the permit market. Strategic behaviour among permit sellers increases the EU-countries
compliance cost as the permit price is above the competitive level. And, as shown in the
12
paper, coordination of permit purchase (merger), in order to reduce the permit price, may only
lead to an even higher permit price. However, if the permit market is characterized by a large
buyer, it is more likely that coordination of permit purchase among EU-countries may become
profitable. If for instance USA decides to join a following up agreement to the Kyoto
protocol, they become large buyer of permits, if the distribution of permits across countries in
a post Kyoto period does not deviate too much from the Kyoto target. Hence, we may find a
post Kyoto permit market characterized by to large buyers, U.S. and EU-countries.
Appendix A
Below we model the market as a dominant agent facing a net demand function from the fringe
and show that the equilibrium outcome of this modelling approach is identical to the approach
followed in section 2.
From (1), (3) and (5) we find that;
q  x1 (p)  x 2 (p)
(20)
The inverse net demand function is given by
P(x1  x 2 )  P(q)
(21)
The dominant supplier’s optimization problem is
max WD  BD  x D   P(q)  q
(22)
BD (eD )  P  q  P
(23)
q
First order condition gives;
From (3) and (5), we se that equilibrium in the market implies that
B1  q  x 2   B2 (x 2 )
We find from total differentiation of (24) that
13
(24)
dx 2
B1

dq B1  B2
(25)

 dx 
B1 
P  B1 1  2   B1 1 

dq 

 B1  B2 
(26)
And from (21) we find that
We can hence write the first order condition (23) as

B1 
B1 1 
  q  B1  0


B

B

1
2 
(27)
We see from total differentiation of (6) that
dx 2
p1

dq p  B2
Hence, the first order condition (9) corresponds to the first order condition (23) (after
inserting p  B1 from (3)).
14
(28)
Appendix B
Proof of proposition 1:
In case of a seller-cartel, the strategic effect of merger is negative if it causes the dominant
agent to increase sale (restrict purchase) as this causes the equilibrium price to decrease,
which hurts the seller-cartel. In case of a buyer-cartel, the strategic effect of merger is
negative if it causes the dominant agent to decrease sale (increase purchase) as this causes the
equilibrium price to rise, which hurts the buyer-cartel. The merger has two effects on the
dominant agent’s optimal choice of q, as described above:
i)
By comparing first order condition in the case of no cartel (9) with the first order
condition in the case of a cartel (14), we see that for x 2  x c2 , the dominant agent’s
optimal q decreases (increases) compared to the premerger situation for q > 0 (q <0).
(For a given x2, the dominant agent’s sale/purchase is lower than in the case with a
no-cartel as 1> (1 
ii)
dx 2
) and B  0 ).
dq
We see by comparing (6) with (13), that for q  q c , the cartel’s optimal purchase /sale
is less than in the premerger situation as p  x 2 is negative (positive) for
x 2  0 (x 2  0) . Given the slope of the response function, (16), the dominant agent’s
optimal response to the cartel’s contraction in purchase is to decrease its own sale
(increase its own purchase) and the dominant agent’s optimal response to the cartel’s
contraction in sale is to increase its own sale (decrease its own purchase).
The first effect, i), benefits the cartel if it is on the same side of the market as the dominant
agent, and hurts the cartel if it is on the other side of the market. The second effect always
hurts the cartel. If the cartel is on the same side off the market as the dominant agent, the
strategic effect is positive (negative) if the first (latter) effect outweighs the latter (first). If the
cartel is on the other side of the market as the dominant agent, both effects hurt the cartel.
Proof of proposition 2:
See proof for proposition 1. One effect of merger is identical to the one described in i) in the
proof of proposition 1. We see by comparing (6) with (19) that x S2 in general differ from x c2 .
However, when the cartel optimizes their welfare function they take into account the response
function of the dominant agent. The welfare effect of choosing x S2  x c2 can therefore not be
15
negative. Hence, the welfare effect of merger can only be negative if the cartel is on different
side of the market as the dominant agent, and the negative strategic effect described in i) in
the proof of proposition 1. more than outweigh the non-negative welfare effect of choosing
x S2  x c2 . Below we provide an example where merger decreases welfare (and will therefore
not occur) even though the merged agents become Stackelberg leaders.
To simplify we disregard the dominant agent’s benefit of emission ( BD  eD   0 ), and assume
constant marginal benefit functions for the group of premerger competitive agents.
1
Bi  ei   10  ei  ei 2
4
i  1, 2
(29)
Let the initials endowment of the commodity be X1  X 2  5 , and X D  20 .
When both subgroups 1and 2 behave competitively, we find from (3), (7) and (9) the
equilibrium outcomes and the corresponding welfare levels;
1
x1f  x f2  5, q f  10, p f  2,5 , W1f  W2f  81 , WDf  25
4
If the merged agents can behave as Stackelberg-leaders, the equilibrium outcomes found from
(3) (for i =1), (14), (17) and (19) and the corresponding welfare levels are;
x1S  3,8 , x S2  2,5 , qS  6,3 , p M  3,1 , W1S  78,5 W2S  78,1 WDS  19,5
In this example we find that W2f  W2f .
16
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