BENEFITS, COSTS, AND COOPERATION
IN GREENHOUSE GAS ABATEMENT
BERTRAND HAMAIDE 1 and JOHN J. BOLAND 2
1 R. Nouvelle, B7120 Vellereille-les-Brayeux, Belgium
2 The Johns Hopkins University, Baltimore, MD 21218-2686, U.S.A.
Abstract. Abatement cost and benefit projections through 2100 are computed, assembled and interpreted with respect to various levels of emission reduction. Mathematical expressions describing
regional costs and benefits as a function of abatement strategy are developed. Using these data and
expressions, optimal abatement strategies are defined for noncooperative and cooperative (Pareto
optimal) policies. The cooperative solution calls for an average emissions reduction of 16.6 percent
over the 1990–2100 period, as compared to 5.8 percent in the noncooperative case. Achieving the
cooperative solution would require side payments to China and potentially to the U.S., as well as
stringent (though beneficial) restrictions on non-OECD countries. It is argued that Pareto optimality
is technically achievable but possibly infeasible in the real world.
1. Introduction
In 1896, a Swedish chemist – Svante Arrhenius – theorized that the rapid increase
in the use of coal in Europe since the industrial revolution would lead to increased
atmospheric carbon dioxide (CO2 ) concentrations, and that this would cause a rise
in global average temperature (Stone, 1992). A century ago, this prospect might
not have seemed imminent but today the carbon dioxide buildup is a reality, and is
viewed by some as a credible threat to continued human habitation of the earth.
To slow or halt the rise of global average temperature, it is necessary to substantially reduce emissions of carbon dioxide and other greenhouse gases. With respect
to carbon dioxide, this can be accomplished by refraining from tropical deforestation and above all by cutting fossil fuel use. In addition to having a beneficial effect
on climate change, less reliance on fossil fuels will also reduce air pollution and
oil security problems that are linked through the gases, pollutants and technologies
associated with fossil fuel combustion (MacKenzie, 1989). Therefore, even if the
importance of global warming is in doubt, reducing carbon dioxide emissions is
likely to be associated with other beneficial effects. This paper, however, focuses
on the linkage between carbon dioxide emissions and global warming.
Climate change is a worldwide problem and its abatement will require a worldwide solution: ‘no nation has either the political mandate or the economic power to
affect a change of this type alone’ (World Commission on Environment and Development (WCED), 1987, p. 176). Industrialized market countries are currently the
most important emitters of greenhouse gases. This is the result of energy use levels
Climatic Change 47: 239–258, 2000.
© 2000 Kluwer Academic Publishers. Printed in the Netherlands.
240
BERTRAND HAMAIDE AND JOHN J. BOLAND
which are high in absolute and relative terms. In the transition economies of Central
and Eastern Europe and the former Soviet republics, high levels of greenhouse gas
emissions are mainly due to inefficient energy use. Emissions from developing
countries are mostly explained by changes in land use (such as deforestation). This
means that actions must be taken everywhere or at least in most of the world if a
major reduction in greenhouse gas emission is to be achieved.
The whole world may not be ready for immediate action against global warming
but at least most nations expressed an interest in preserving global environment by
participating in an international conference at Rio de Janeiro, Brazil, in June 1992.
Organized as the United Nations Conference on Environment and Development
(UNCED), the Rio Conference was widely described as the first ‘Earth Summit’.
For the purpose of this paper, the most important result of the Rio Conference was
the Framework Convention on Climate Change.
In order to limit global warming, the Framework Convention calls for a stabilization of the greenhouse gas concentration in the atmosphere! at some unspecified
future time. Subsequent discussions among nations, as articulated in the 1997
Kyoto Conference and the 1998 Buenos Aires Conference, led to agreement on
a compliance window of 2008–2012, by which time the signatories propose to
have reduced emissions to some assigned percentage below the 1990 level. Each
nation has a specific target percentage reduction (e.g., 8 percent for the European
Community, 7 percent for the U.S., zero percent for the Russian Federation), but
the global reduction is intended to be 5 percent.
2. The Problem Statement
The emission of greenhouse gases into the atmosphere causes a public bad (negative public good externality) and therefore constitutes a market failure. Said another
way, market forces alone cannot lead to the ‘optimal’ quantity of pollution, that
which is consistent with a Pareto optimum for national or global economies. This
result is illustrated in Figure 1.
The amount of greenhouse gas reduction is found by:
"j = Ejb − Ej ,
(1)
where Ejb and Ej are respectively the baseline (‘no-action’ level) emissions and
the current emissions in country j (j = 1, 2, . . . , N) and are expressed in billion
equivalent tons of carbon. "j is thus the incremental reduction in emissions.
When a country j undertakes abatement "j , it incurs a cost which depends
on the amount of abatement: Cj = Cj ("j ) where Cj is assumed to be twice
differentiable with the first and second derivatives strictly positive: C "" > 0,
! The stabilization of greenhouse gas emissions is generally the commitment made by OECD
countries.
BENEFITS, COSTS, AND COOPERATION IN GREENHOUSE GAS ABATEMENT
241
Figure 1. The market failure: Nash solution and Pareto optimality.
C "" > 0. These assumptions are corroborated empirically by Nordhaus (1991).
The total cost function can be seen in the upper panel of Figure 1, and the marginal
cost function is in the lower panel.
Each region’s benefit from environmental improvement is a function of the
overall global abatement, not merely of the region’s own actions. Even a region
which elects to do nothing (a free rider) benefits from a cleaner global environment.
Of course, if a region does abate, the global environment and therefore the region’s
benefits will be increased to some extent. As shown in Figure 1, country j ’s benefit
function is Bj = Bj ("), where " = #i ("i ), the overall global reduction in emissions. The shape of the benefit curve reflects the generally accepted assumptions
that B " > 0 and B "" < 0. The other benefit curve B(") represents total global
benefit or the sum of benefits across all regions. In Figure 1, total benefit curves
are shown in the upper panel, corresponding marginal benefit curves in the lower
section.
If country j ignores the external cost or benefit its emissions policy may impose
on others, its optimal level of emissions reduction is found by maximizing its
242
BERTRAND HAMAIDE AND JOHN J. BOLAND
own social welfare taking the other nations’ decisions as given.! This independent regional optimization gives an abatement level of a (Figure 1). The necessary
condition for this result is:
∂Cj ("j )
∂Bj (") ! !
=
.
∂"j
∂"j
(2)
Global economic efficiency,! ! ! on the other hand, gives abatement level b in
Figure 1, reflecting the following necessary condition:
#
N "
∂Cj ("j ) ! ∂Bk (")
.
=
∂"j
∂"
j
k=1
(3)
If countries reach an agreement (that is, if they cooperate with a common action),
they can attain Pareto optimality, maximizing total net benefits. On the other hand,
purely individualistic mechanisms generate a level of pollution ab higher than the
optimal level resulting in a smaller total net benefit and the systematic neglect of
social cost imposed on others by each country’s own individualistic behavior. This
outcome is an expression of noncooperation in individual maximization. In order
to achieve cooperation, side payments‡ may need to be given for some nations to
maintain their national wealth.
3. The Main Assumptions
For illustrative purposes, this paper divides the world into five decision making entities: the U.S., other OECD countries (OOECD), the former Soviet Union (FSU),
China, and the rest of the world (ROW). The division is at least partially arbitrary,
but useful for several reasons: all five players are important emitters of greenhouse
gases, limited data availability would make further disaggregation very difficult,
and the same division has already been adopted by others (OECD, 1993). Other
! Given this individualistic behavior, country j abates up to a point where its own marginal benefit
is equal to its own marginal abatement cost. The result is seen in the lower panel of Figure 1 and has
also been described by others including Pearson and Pryor (1978), Barrett (1990) and Hanley and
Spash (1993).
! ! Note that it is not C " (" ) = B " (" ) because B " (") is nonseparable. If the world is divided
j
j
j
j
j
into three regions and each region abates by 100 units, the regional benefit is computed on global
abatement " = 300 and not on regional abatement "j = 100 since each region benefits from global
and not local abatement.
! ! ! Global economic efficiency requires that the marginal social benefit of each region’s abatement
(defined as the marginal benefits accruing to each region summed over all regions) be equal to that
region’s marginal abatement cost.
‡ Side payments are not necessarily provided in cash. They can consist of technical assistance, a
foreign debt adjustment, or other transfers in kind taking place in the context of the overall relations
between countries. The theoretical framework with side payments used here is a cooperative game
with transferable utility
BENEFITS, COSTS, AND COOPERATION IN GREENHOUSE GAS ABATEMENT
243
TABLE I
Global damages at CO2 doubling (billions of 1990 USD)
Bi $90
U.S.
OOECD-U.S.
OECD
FSU
China
ROW
no OECD
TOT
Dam
GNP
%GNP = %j
70.7
5546
1.27
130.2
10200
1.28
200.9
15800
1.27
18.6
2680
0.69
23.8
1100
2.16
71.4
3340
2.14
113.8
7120
1.6
314.7
22920
1.37
Source: Manne and Richels (1992), Fankhauser and Pearce (1994).
studies have also disaggregated the world into a number of regions (Nordhaus and
Yang, 1996; Escapa and Gutierrez, 1997).
Calculations shown in this paper use the year 2100 as the end point. This
assumption emphasizes the long-term nature of global warming policies and expectations, even though most sources predict CO2 doubling at an earlier date. No
further abatement action (business as usual) policies are generally expected to result in a doubling of CO2 concentration in the upper atmosphere (as compared to
presumed pre-industrial level) shortly after 2050. A doubling of CO2 concentration
has no significance in itself; its only purpose is to provide a basis for comparing a
current situation (today’s concentration) to some clearly defined future condition.
The other main assumptions are as follows: (i) the climate effect of CO2 doubling is expected to be a rise in mean global temperature, at equilibrium, of 2.5 ◦ C
(υ = 2.5); (ii) benefits, computed as the value of damages that could be avoided
by taking action, and costs of abatement, computed as losses of output associated
with cutbacks in energy inputs $
required by the reduction
of CO2 emissions, are
$
assumed to be additive (B =
B
and
C
=
C
);
(iii) the real discount
j
j
j
j
rate is 2 percent (as supported by Hartman (1990), Howe (1990) and Lind (1990));
(iv) the variables E and " represent the sum
$ of emissions
$ and abatement
$ $ over
time $
(from 1990$to 2100),$
therefore
E =
t e(t) =
j Ej =
j
t ej (t),
$
" = t θ(t) = j "j = j t θj (t).!
4. Damages and Benefits of Damages Avoided
4.1.
DAMAGE ESTIMATION OF CO 2 DOUBLING
Table I shows prior estimates of annual global damages estimated at the time of
CO2 doubling, disaggregated by region and expressed in 1990 USD. Using these
data, damages at CO2 doubling are expressed as Dj∗ (t) = %j Qj (t), where Qj (t)
is the regional output and %j is the scale of damage at twice the pre-industrial
! E b for the U.S., OOECD, FSU, China and ROW from 1990 to 2100 is computed as the average
j
of estimations from Manne (1993) and Rutherford (1993) and are respectively 299.315, 320.780,
163.305, 365.136 and 640.912 billion tons of carbon.
244
BERTRAND HAMAIDE AND JOHN J. BOLAND
CO2 concentration. This parameter, estimated by Fankhauser and Pearce (1994) is
corroborated from a worldwide standpoint (%) and for the U.S. (%U.S. ) by other
studies (Nordhaus, 1991, 1994; Cline, 1992; Rose and Stevens, 1993) and shows
that in general, non-OECD countries are harmed more than rich nations in terms
of percentage of annual GDP.! According to the authors, the difference is, at least
partially, driven by health impacts and high proportion of global wetlands found in
developing countries.
4.2.
DAMAGE ESTIMATION OVER TIME
Most analysts have assumed that damages are not linear in time, but that they
tend to rise substantially faster at high CO2 concentrations.! ! Some, such as Cline
(1992) and Xepapadeas (1997), assume damages to be geometrically distributed
with respect to the amount of warming, as follows:
%
&
Dj (t)
(T (t) γ
.
(4)
= %j
Qj (t)
υ
(T (t) is the amount of global warming! ! ! at time t, υ is the benchmark temperature change at CO2 doubling and γ is a user given exponent representing the
nonlinearity in the damage function. Actually, three alternative values are given
for the nonlinear parameter (γ = 1, 2, 3) so that the expression encompasses more
than one nonlinear scheme and a weighted mean of these results is calculated using
weights (ω) of 0.2 for the linear scheme, 0.5 for the quadratic scheme and 0.3 for
γ = 3.
The remaining unknown, (T (t) is computed as a function of CO2 concentration
in time (Peck and Teisberg, 1993). The parameters are fitted so that (T (t) = 0 at
pre-industrial level of CO2 and (T (t) = υ when +(t) reaches 540 ppmv (parts
per million in volume). The corresponding values of α and β are 3.606 and 20.188.
The other unknown +(t) is estimated as a function of previous concentration and
emissions: +(t + 1) = A+(t) + (.ηe(t)) where A is a decay factor associated with
ocean absorption, . converts billion metric tons of carbon into ppmv of CO2 and
η is the airborne fraction of CO2 (all known parameters) (Chapman and Drennen,
1990).
Computations have been performed with Manne and Richels (MR) emissions
data (Manne and Richels, 1992; Manne, 1993) and compared with the contemporaneous IPCC predictions (IPCC, 1992). The results show that a doubling of
atmospheric CO2 , expected to occur around 2060 is associated with a temperature
! The GDP data used here come from Manne and Richels (1992) and all data are deflated to 1990
prices, using a production price index (Report to the President, 1994).
! ! See Nordhaus (1994), Peck and Teisberg (1993), Cline (1992), and Kosobud et al. (1984).
! ! ! It should be noted that the (T (t) function is equilibrium warming. The fact that actual temperature change lags the calculated equilibrium warming at any future time is not taken into account.
Also, the warming offset thought to be provided by sulfate emissions is not considered.
BENEFITS, COSTS, AND COOPERATION IN GREENHOUSE GAS ABATEMENT
245
Figure 2. Damage costs in time (billions of 1990 USD) in BaU conditions.
increase of 2.48 degrees which is indeed consistent with the benchmark warming of
the hypotheses. Moreover, the average of the lower (IPCC) and upper (MR) bounds
for the year 2100 is a temperature change of 3.66 degrees and thus corresponds to
an increase of 2.47 degrees during the twenty first century, very similar to the IPCC
prediction.
Solving Equation (4) with the upper bound of (T (t) – that is the MR model
– and with the weighted parameter γ (γ = #k wk γk with #k wk = 1) gives results shown as Figure 2 representing maximum expected regional damages in BaU
(Business-as-Usual) conditions, that is to say, without any restriction on greenhouse gas emissions. As expected, estimated damages are exponential with respect
to time.
4.3.
BENEFIT ESTIMATION OVER TIME
BaU damages over time (Djb (t)) are computed from Equation (4). If some actions
are taken, emissions (ej (t)) will decrease, so will +(t), (T (t) and Dj (t) via Equap
tion (4). The value of predicted damages with a restrictive policy is labeled Dj (t).
The benefit of a policy p then equals the difference between the baseline b and
p
p
the scenario damage path. That is, Bj (t) = Djb (t) − Dj (t), with B(t) = #j Bj (t)
(Cline, 1992).
4.4.
ESTIMATION OF BENEFITS WITH RESPECT TO ABATEMENT
Damages and benefits over time must be computed for a selected abatement policy
p, which is associated with an expected percentage reduction in emissions. Then,
the computed regional benefits for this particular level of abatement are discounted
back to 1990 and summed to a present value. Regional GDP projections are also
246
BERTRAND HAMAIDE AND JOHN J. BOLAND
TABLE II
Discounted global and disaggregated benefits in percentage of GDP and in billions of 1990 USD
for the whole period 1990–2100 (in parentheses)
%R
B(")
BU.S. (")
BOOECD (")
BFSU (")
BChina(")
BROW (")
10
20
40
60
100
0.18 (5617)
0.35 (10774)
0.65 (20034)
0.94 (28936)
1.60 (49478)
0.12 (657)
0.23 (1259)
0.45 (2408)
0.70 (3776)
1.18 (6349)
0.12 (1217)
0.24 (2433)
0.44 (4461)
0.63 (6387)
1.16 (10862)
0.09 (413)
0.17 (780)
0.31 (1423)
0.44 (2020)
0.77 (3534)
0.35 (1299)
0.66 (2450)
1.22 (4528)
1.74 (6458)
2.93 (10874)
0.29 (2031)
0.55 (3852)
1.03 (7214)
1.47 (10295)
2.55 (17859)
discounted back to 1990 and summed over time.! This gives one point in the benefit
(expressed as a percentage of GDP) versus abatement space. The same procedure
is followed for other abatement levels and the results are displayed in Table II.
4.5.
THE BENEFIT CURVE
The results shown in the first column of Table II are points on a global benefit curve;
the remaining columns define regional benefit curves. The curves themselves are
fitted to the data using three different formulations: a linear function, simple OLS
(Ordinary Least Squares) regression passing through the origin (giving B "" = 0); a
logarithmic function defined over " > 0; and a polynomial function of second
order passing through the origin. The best fit was provided by the polynomial
function, as follows:
!
Bj (") = σj "2 + αj θ ⇒ B(") =
Bj (") = σ "2 + α" .
(5)
j
The estimated parameters and R 2 are displayed in Table III. The resulting global
benefit curve is displayed as Figure 3, where the abscissa has been written in
percentage of abatement (R) instead of in billion tons of carbon (") used in the
computations for ease of exposition.
5. Abatement Costs
5.1.
COST VERSUS ABATEMENT
In the late 1980s and early 1990s, various authors tried to estimate global abatement cost. Nordhaus (1994) compared a number of published models in terms
! The discounted GDP over the period 1990–2100 for the U.S., OOECD, FSU, China and ROW
is respectively 537,312, 1,013,880, 458,987, 371,141 and 700,349 billions of 1990 dollars.
BENEFITS, COSTS, AND COOPERATION IN GREENHOUSE GAS ABATEMENT
247
TABLE III
Disaggregated benefit curve: value of the parameters and the R 2 statistic
σj
αj
R2
U.S.A.
OOECD
FSU
China
ROW
World
–0.0001
3.4
0.9997
–0.0001
6.2
0.9988
–0.000005
2.0
0.9978
–0.0002
6.4
0.9987
–0.00003
10.0
0.9986
–0.0004
28.0
0.9989
of percentage difference of carbon emissions from a baseline path and found an
aggregate formula relating cost to output and reduction of greenhouse gases. His
conclusion is that the initial reductions are very inexpensive (because of the low
cost of reducing CFC emissions) but curbing greenhouse gases soon reaches a
condition of diminishing returns, resulting in an exponential curve.
More recently, some authors began to estimate disaggregate abatement costs
(OECD, 1993). In the OECD study, Manne (1993) displays time series data for a
few policies. These can be reworked so as to reveal the implied relationship of cost
to abatement. The procedure is as follows: (i) abatement effort is inferred from the
three or four abatement policies at various points in time and (ii) the regional cost
converted to 1990 present value is computed at each time t for each policy and
summed until 2100. One thus gets three or four points in the cost versus abatement
space and the others can be extrapolated! by the disaggregation of Nordhaus’ cost
formula.! !
Both theories are now taken into account. Even though they are very different
(one is an aggregate model, the other one is a disaggregated model; one assumes
low cost for the first reductions, the other one does not), they also have many
similarities (they both display nonlinear cost curves of a similar shape, their cost
assumptions regarding the total phasing out of greenhouse gas emissions are almost the same) and they are possibly the two most frequently cited abatement cost
models in the literature. There is no objective basis for choosing one model over
the other. If one is to pick Nordhaus’ model, no disaggregation exists and if one is
to pick MR’s model, nothing is known of the interesting early phases of abatement.
Therefore, the choice here should not be to select one or the other approach, but to
incorporate the best features of both models.
The first step is to include Nordhaus’ inexpensive first emissions reductions in a
regional framework. In doing so, at each level of abatement "j , Nordhaus’ global
! The reason for extrapolating the other points with a formula is that the most lenient policy
described in Manne (1993) brings about at least a 45 percent emissions reduction. And the comparison between the global benefit curve derived in the last section and Nordhaus’ cost curve is only
interesting
# phases of abatement (C > B when R > 0.5).
" in the early
! ! ln Cj ("j ) = ξ + δ ln(" ) where Q represents GDP.
j
j
j
j
Qj
248
BERTRAND HAMAIDE AND JOHN J. BOLAND
Figure 3. Global benefit of emissions reduction in percentage of GWP.
$
cost estimate C(") is divided by j CjMR obtained from the equation in the second
footnote of the previous page and multiplied by the regional cost CjMR ("j ). The
second step is simply to compute the average value of the two regional costs.
5.2.
THE COST CURVE
The classical cost curve, as displayed in Figure 1, can be described by various
functional forms having positive first and second derivatives. Two functions have
been tested: the power function used by Nordhaus and a polynomial function of
order two forced to pass through the origin:
Cj ("j ) = λj "j + µj "2j .
(6)
Both formulations fit the data fairly well; the polynomial function is chosen and the
values of the parameters and R 2 are displayed in Table IV. Therefore, various estimates of the sum of regional costs, as presented by Manne (1993), OECD (1993)
and Nordhaus (1994), are used to develop a fitted global cost curve, displayed as
Figure 4.
6. Cooperation for Economic Efficiency
6.1.
THE OBJECTIVES FOR COOPERATION AND NONCOOPERATION
The objective function for each region can be written (using Equations (5) and (6))
as:
max Wj = [αj " + σj "2 − (λj "j + µj "2j )]
"j
∀j = 1, 2, . . . , N
(7)
BENEFITS, COSTS, AND COOPERATION IN GREENHOUSE GAS ABATEMENT
249
TABLE IV
Disaggregated cost curve: value of the parameters and the R 2 statistic
µj
λj
R2
U.S.A.
OOECD
FSU
China
ROW
World
0.26
4.76
0.9981
0.26
3.71
0.9997
3.06
–106.7
0.9968
0.16
9.06
0.9998
0.20
–22.82
0.9979
0.074
–14.51
0.9990
Figure 4. Global cost of emissions reduction in percentage of GWP.
$
with " =
j "j . And since benefits and costs are additive by hypothesis, the
global objective function is:
max
"1 , ..., "N
with α =
(8) is:
'
2
W = α" + σ " −
$
i
αi and σ =
$
i
N
!
i=1
(λi "i +
µi "2i )
(
(8)
σi . The first order condition for maximizing Equation
α + 2σ " = λj + 2µj "j
∀j = 1, 2, . . . , N
(9)
which implies the equalization of marginal costs across regions:
λj + 2µj "j = λk + 2µk "k
∀k = 1, 2, . . . , N and k ' = j
(10)
250
BERTRAND HAMAIDE AND JOHN J. BOLAND
and the optimal abatement for each region, assuming a cooperative global solution,
is


!
λj − α
σ

"j =
∀j = 1, 2, . . . , N .
(11)
"i 
−
2(σ − µj ) σ − µj i'=j
Optimal abatements for regions j and k (k ' = j ) can be compared by rearranging
Equation (10):
"k =
λj − λk
µj
+
"j .
2µk
µk
(12)
Writing Equation (12) for each k ' = j and substituting into Equation (11), gives
after rearrangement
! " λj − λi #
λj − α − 2σ
2µi
i' =j
"j =
∀j = 1, 2, . . . , N .
(13)
!
2(σ − µj ) + 2σ µj
(1/µi )
i' =j
This describes the abatement action which each region must take to reach the
cooperative global optimum.
Conversely, the Nash (noncooperative) solution is found by taking the partial
derivative of Equation (7) with respect to "j and setting the result equal to zero.
Rearrangement of this result gives the optimal abatement for region j , when it acts
alone in a noncooperative setting.


!
λ j − αj
σj

"j =
∀j ∈ n = 1, 2, . . . , N.
(14)
"i 
−
2(σj − µj ) σj − µj i'=j
6.2.
SIMPLIFYING NONCOOPERATIVE ABATEMENT COMPUTATIONS
Equation (14) is a system of N equations with N unknowns where abatement in
region j is chosen as a function of abatement in all the other regions whose "i ' = 0
(i ' = j ). Before attempting a solution, it is therefore interesting to first see if any
"j might be equal to zero. Taking the first derivatives of Equations (5) and (6) and
comparing the intercept at the origin, one sees that λj > αj for the U.S. and China
meaning that their optimal non-cooperative strategy is to abate nothing. In these
two regions, Bj" and Cj" (Figure 1) would actually intersect in the negative quadrant.
It would mean that at noncooperative equilibrium, they would increase their emissions. Since this is contrary to the commitment of the Framework Convention of
Climate Change (at least for OECD countries up to now), a nonnegativity constraint
"j ≥ 0
∀j = 1, 2, . . . , N
(15)
BENEFITS, COSTS, AND COOPERATION IN GREENHOUSE GAS ABATEMENT
251
as been added to the noncooperative maximization problem of Equation (7).!
Equation (14) can now be simplified to


N−2
!
λ i − αi
σi 
"i =
"s 
−
2(σi − µi ) σi − µi s'=i
(16)
∀i = j, k, m and N − 2 = {FSU, OOECD, ROW}
with j , k and m representing FSU, OOECD and ROW, respectively, and with
"U.S.A. = "China = 0.
Let ai and bi be denoted by the following relations:
ai =
and
bi =
λ i − αi
2(σi − µi )
(17)
σi
.
σi − µi
(18)
Equation (16) can then be rewritten
"j = aj − bj "k − bj "m
"k = ak − bk "j − bk "m
"m = am − bm "j − bm "k
(19)
and is solvable since it is a system of three equations with three unknowns.
6.3.
OPTIMAL ABATEMENT RESULTS
The results for the cooperative and noncooperative formulations are displayed in
Table V where abatement is expressed both in percentage reduction (Rj = "j /Ej )
and in billion tons of carbon ("j ). All results represent the total effort undertaken
between today and the year 2100.
As observed earlier, cost and benefit data used here imply that it is not in the
economic interest of either China or the U.S. to abate greenhouse gas emissions
in the absence of cooperation. Globally, the noncooperative action brings about
very limited overall abatement (5.8 percent of global emissions). The Pareto optimal greenhouse gas curtailment, on the other hand, amounts to 16.6 percent of
global emissions. This shows that cooperation, taking into account costs imposed
on others, has a major effect on resulting emissions.
The amount of abatement undertaken by developing countries (except the FSU)
in the cooperative setting is very high. The explanation for this disproportionate
effort lies in their abatement cost curves, displayed in Figure 5 along with the those
of the other regions and the global benefit curve (from Figure 1).
! Note that it could also be added for the cooperative problem of Equation (8) but would not
change the solution since these constraints would not be binding.
252
BERTRAND HAMAIDE AND JOHN J. BOLAND
TABLE V
Regional optimal cooperative and non cooperative
abatement in percentage of regional emissions and in
billion tons of carbon over 1990–2100 (in parentheses)
U.S.A.
OOECD
FSU
China
ROW
Total
Non cooperation
Cooperation
0% (0)
1.5% (4.79)
10.9% (17.76)
0% (0)
12.8% (82.04)
14.7% (44.23)
14.5% (46.25)
13.3% (21.70)
17.6% (64.36)
18.9% (120.55)
5.8% (104.59)
16.6% (297.09)
Figure 5. Comparison of regional abatement cost curves.
ROW has the lowest abatement cost overall, with negative costs over a relatively
large range (meaning that these units of abatement are costless from a greenhouse
gas policy point of view). The point where the slope of the abatement cost curve
for the ROW region (marginal cost) equals the slope of the global benefit curve
(marginal benefit) corresponds to a much higher abatement total than for any other
region. Since this point defines optimal cooperative abatement, the economic efficiency argument for relatively large amounts of abatement by the ROW region
is clear. A similar, but less dramatic, result can be observed for China. According
to Figure 5 and Table V, countries ranked by order of abatement, from the highest
to the lowest, are ROW, China, OOECD, U.S.A. and FSU; the three last regions
having a similarly small optimal abatement quota.
BENEFITS, COSTS, AND COOPERATION IN GREENHOUSE GAS ABATEMENT
253
TABLE VI
Disaggregated cooperative and non cooperative net payoffs over the whole
period (W ) in billions of 1990 dollars
U.S.
OOECD
FSU
China
ROW
W
6.4.
Cooperation
Bj (") Cj ("j )
Wj
Non cooperation
Bj (") Cj ("j )
Wj
1001
1833
594
1884
2968
282
1105
1468
637
2813
354
647
209
667
1045
354
624
1139
667
1571
719
728
–874
1247
155
6305
0
23
–930
0
–526
4355
NET PAYOFFS
At this point it is possible to compute net benefits for each region in both cooperative and noncooperative games. This is done by solving Equation (7) with
the noncooperative abatement values and Equation (8) with cooperative abatement
values. Benefits, costs and net payoffs are summarized in Table VI.
When countries do not cooperate, supposing they are rational, they abate up
to the point where their own marginal benefit equals their own marginal cost. By
choosing this Nash strategy, they all derive some positive net payoffs. The major
winners of such a strategy are of course the U.S. and China since they do not
decrease their emissions and choose, instead, to become free riders, benefiting from
other nations’ restrictions. The developed world would then account for less than
25 percent of the net social welfare gain because there are other winners: the former
Soviet Union and the ROW. For the former, it actually pays to reduce emissions and
remove inefficiencies of old infrastructure (as noted by Bohm and Larsen, 1994) –
abatement cost is negative for the Nash game. And the ROW enjoys a substantial
net payoff because benefit is the highest of all regions and abatement cost is also
negative.
With the exception of free riding countries at the Nash equilibrium, the other
regions would be better off by cooperating and yet no region has an incentive
to deviate from its Nash strategy. Nevertheless, there is ground for reaching full
cooperation because social welfare over the whole 1990–2100 period is more
than 1900 billion dollars higher if countries reach an agreement for a cooperative
optimum, and if the agreement can be made binding on all parties. The OECD
countries are the major winners in the case of cooperation (they nearly double their
net gain compared to the Nash strategy) because they derive large benefits from
global cooperative abatement undertaken mostly by non-OECD nations.
254
BERTRAND HAMAIDE AND JOHN J. BOLAND
In a cooperative agreement, the ROW region provides about 40 percent of global
abatement because it has the lowest abatement costs. It nevertheless increases its
net payoff by 1000 billion dollars if it does choose the cooperative solution, which
would justify its ratification of a worldwide agreement on economic terms.
The FSU region abates only a little more in the cooperative case than in the
noncooperative setting (21.7 > 17.76), which enables it to remain in the range
of negative abatement costs and to experience increased net benefits. When one
considers the shape of the FSU abatement cost function in Figure 5, it is clear that
the cooperative outcome could not be much larger than the noncooperative result;
the FSU has indeed the steepest cost curve of all five players.
The case of China and the U.S. is a little different since they both have to incur
abatement costs not required by the noncooperative strategy. At full cooperation,
the U.S. abates about the same as the OOECD, incurs a similar cost (see Figure 5)
but has a smaller benefit and loses a little more than 120 billion dollars. China’s
benefits are substantial but it has the highest cost of all regions which more than
offsets its gain and makes it worse off than in noncooperation. Therefore, China
would not be expected to participate in an agreement unless it is compensated.
6.5.
COMPENSATION FOR REACHING A GLOBAL AGREEMENT
On the whole, full cooperation is advised since social welfare is much higher
at Pareto optimality than at the Nash equilibrium. But cooperation may only be
possible if China and the U.S. are compensated for the loss they incur: the difference between their noncooperative and their cooperative net payoffs. Where these
amounts are known, no nation would be expected to accept an agreement if it is not
at least as well off with it as without it.
For example, according to this logic China should receive a side payment of at
least 30 billion USD for the 1990–2100 period. This payment might be funded by
the OOECD countries because of the long history of exploitation of the commons
by the industrialized world. OOECD countries should be particularly willing to
make this payment because their additional gain from cooperation is substantial
(451 billion USD). China should be willing to accept the payment and provide the
requested abatement because its overall economic situation would not be worse
than if each region follows its Nash strategy.
The question of the U.S. is more difficult from a ‘fairness’ standpoint. Theoretically, it can also be compensated by OOECD countries but the authors think it may
be difficult to justify a subsidization of the U.S. by other OECD nations. Moreover,
it is does not seem realistic to expect the developing world, which bears a larger
burden than the U.S. in terms of percentage reduction of their own emissions, to
provide such a subsidy.
BENEFITS, COSTS, AND COOPERATION IN GREENHOUSE GAS ABATEMENT
6.6.
255
THE NORDHAUS - YANG ANALYSIS
As noted earlier, several other analysts have developed disaggregate global models
of climate strategies. One of these, published in 1996 by Nordhaus and Yang (NY),
is notable both for its similarities to and its differences from the model presented
here. NY also presents disaggregate cooperative and noncooperative analyses of
globally optimal climate strategies, although derived from a more disaggregate and
more complex model than ours. The main differences between the two approaches
include: (i) our model is essentially static whereas NY is fully dynamic, (ii) we use
a global real discount rate of 2% whereas NY uses region and time specific discount
rates which average about 4.5% per year over the next century and (iii) some data
used for abatement and cost functions are obtained from different sources. On
the other hand, computations of future greenhouse gas concentrations are very
similar: we estimate the CO2 doubling date at 2060 while NY give it at 2065
under business-as-usual conditions. Also, both studies anticipate a shift of emission
burden from developed towards developing countries over the next century.
Interestingly, both our study and NY show that noncooperative net payoffs are
positive in all regions, that full cooperation would be possible if side payments
were permitted (NY does not calculate the results of this option), and that the U.S.
would be worse off under full cooperation. Both studies also show that, in the case
of cooperation, the biggest abatement effort would be made by developing countries on economic grounds alone. However, the more disaggregate NY analysis
concludes that China has the lowest marginal abatement cost, compared to ROW
in our model. The reason may be that the scale of damage %j used by NY for China
is smaller than ours (1.5% instead of 2.16%) whereas it is the same for ROW.
There are three main areas where results differ significantly: in the distribution
of regional effort, in the total global effort, and in the absolute value of net payoffs.
In NY, the largest effort under noncooperation is undertaken by the current largest
emitters (Europe and the U.S.) whereas we find that most of the burden will be
borne by ROW and FSU. This difference reflects our argument that ROW and FSU
will experience negative abatement costs in the early phase of emissions reduction.
This also explains why we find a much higher value for noncooperative global
abatement (5.8%) than NY (2.3% in year 2000). Because cooperative abatement
values also depend on abatement cost assumptions, our global values are again
higher (16.6%) than in NY (9.7% in 2000 but as the equilibrium cooperative abatement increases over time, the difference is much smaller by 2100). Net payoffs
are also very much less important in NY both in noncooperative and cooperative
formulations (43 and 344 billion 1990 U.S. dollars respectively for NY and 4355
and 6305 for our analysis). These differences appear to be largely due to different
discount rates.
256
BERTRAND HAMAIDE AND JOHN J. BOLAND
7. Conclusions and Caveats
When choosing their Nash strategy (full noncooperation), every region either does
nothing or abates in a way that produces a positive net payoff. But global social
welfare is much lower than at Pareto optimality (full cooperation). In the case of
full cooperation, China and the U.S.A. experience the smallest net gains. Since the
global benefit gained from cooperation is much larger than the amount these two
regions lose, there is a possibility of compensation by means of side payments from
one or more of the players that stand to gain. Cooperation is thus economically
feasible, social welfare is maximized and Pareto optimality is reached.
However, another objective may be even more important than efficiency for
the whole scheme to be applicable in the real world, that of ‘perceived fairness’.
Even though it is individually rational, full noncooperation may be considered as
unfair by developing countries since they bear 95 percent of the noncooperative
abatement and since the best strategy for the U.S. is to continue to emit greenhouse
gases without further restriction. The perceived fairness of any economic policy in
an interdependent world is not subject to economic analysis but may well influence
political acceptability.
The problem at full cooperation is that non-OECD regions – mainly ROW but
also China – are required to abate more than wealthier regions, both in absolute
tons and in percentages. As mentioned in OECD (1995, p. 79), ‘(cost effective)
agreements achieve lower costs of abatement by shifting the burden of stabilizing
emissions to countries with low marginal abatement costs. Typically, these tend to
be the coal-based developing economies of India and China whose real incomes,
relative to no climate agreement, fall more than any other country/region’. If these
regions perceive the Pareto optimal policy as ‘unfair’, they are unlikely to go along
with the agreement even if they benefit from it or can be fully compensated for the
loss they may incur. The suggestion that the U.S. should be compensated for its
loss in agreeing to cooperate can only worsen the situation. It is therefore thought
that the behavior of all players will be somewhere between full cooperation and
full noncooperation. Pareto optimality is thus not likely to be reached in the real
world even though it is mathematically feasible when side payments are allowed.
The model presented here considers the evolution of costs and benefits over
a 100+ year period. But because these costs and benefits are reduced to present
values, the model is a de facto static analysis of a dynamic issue. It is therefore
possible that the conclusions presented may differ from those obtained from a fully
dynamic analysis. Moreover, the fact that the less developed regions should not
be compensated for joining the cooperative outcome may be due to the use of a
uniform real discount rate of 2% for all present value computations. Had a higher
discount rate been adopted for the developing world, as some have suggested, the
solution might have been different.
In addition to the obvious sensitivity to discount rate assumptions, the results are
also dependent on predicted abatement costs. As a matter of fact, our assumption
BENEFITS, COSTS, AND COOPERATION IN GREENHOUSE GAS ABATEMENT
257
that ROW and FSU will experience negative abatement costs in the early phases of
any global strategy easily explains why most of the abatement burden will be borne
by developing instead of developed countries, even in the noncooperative case.
Other abatement cost options could lead to other results, as clearly demonstrated by
Nordhaus and Yang (1996). By no means should these assumptions be understood
as a rationale for advocating non-participation by industrial countries in cooperative agreements. As in all such modeling procedures, results are driven by uncertain
data and assumptions. The outcomes presented here can only be viewed as credible
predictions of the future to the extent that the underlying data and assumptions are
also seen as credible.
In summary, the findings of this study should be interpreted with caution. The
analysis utilizes estimates of abatement amounts, benefits, and costs which are
themselves uncertain, taken from other authors and certainly not precise statements of actual future outcomes. Certain assumptions, such as the uniform discount
rate, may be arguable. However, it is believed that the results reflect a plausible
scenario. The modest purpose of the study is to demonstrate the existence of a
large difference between noncooperative and cooperative policies, as well as the
possibilities and limitations of the use of side payments to facilitate international
or interregional agreements.
References
Barrett, S.: 1990, ‘The Problem of Global Environmental Protection’, Oxford Rev. Econ. Pol. 6,
68–79.
Bohm, P. and Larsen, P.: 1994, ‘Fairness in a Tradable Permit Treaty for Carbon Emissions
Reductions in Europe and the Former Soviet Union’, Environ. Resour. Econ. 4, 219–240.
Chapman, D. and Drennen, T.: 1990, ‘Equity and Effectiveness of Possible CO2 Proposals’,
Contemp. Pol. Issues 8, 16–28.
Cline, W. R.: 1992, The Economics of Global Warming, Institute for International Economics,
Washington, D.C., p. 399.
Dalton, M. G.: 1997, ‘The Welfare Bias from Omitting Climate Variability in Economic Studies of
Global Warming’, J. Environ. Econ. Manage. 33, 221–239.
Escapa, M. and Gutierrez, M.: 1997, ‘Distribution of Potential Gains from International Environmental Agreements: The Case of the Greenhouse Effect’, J. Environ. Econ. Manage. 33,
1–16.
Fankhauser, S. and Pearce, D.: 1994, ‘The Social Costs of Greenhouse Gas Emissions’, in OECD
(ed.), The Economics of Climate Change: Proceedings of an OECD/IEA Conference, OECD,
Paris, pp. 71–86.
Hanley, N. and Spash, C.: 1993, Cost-Benefit Analysis and the Environment, Edward Elgar Publishing
Ltd, Hants, U.K., p. 278.
Hartman, R.: 1990, ‘One Thousand Points of Light Seeking a Number: A Case Study of GBO’s
Search for a Discount Rate Policy’, J. Environ. Econ. Manage. 18, 53–57.
Howe, C.: 1990, ‘The Social Discount Rate’, J. Environ. Econ. Manage. 18, 51–52.
IPCC: 1992, Climate Change: The Supplementary Report to the IPCC Scientific Assessment,
Cambridge University Press, Cambridge, U.K.
258
BERTRAND HAMAIDE AND JOHN J. BOLAND
Kosobud, R. F., Daly, T. A., and Chang, Y. I.: 1984, ‘Decentralized CO2 Abatement Policy and
Energy Technology Choices in the Long Run’, in Itterlag, R. (ed.), Government and Energy
Policy, International Association of Energy Economists, Washington, D.C., pp. 584–600.
Lind, R. C.: 1990, ‘Reassessing the Government’s Discount Rate Policy in Light of New Theory and
Data in a World Economy with a High Degree of Capital Mobility’, J. Environ. Econ. Manage.
18, 58–80.
MacKenzie, J.: 1989, Breathing Easier: Taking Actions on Climate Change, Air Pollution and Energy
Security, World Resource Institute, Washington, D.C.
Manne, A. S.: 1993, ‘Global 2100: Alternative Scenarios for Reducing Carbon Emissions’, in OECD
(ed.), The Costs of Cutting Carbon Emissions: Results from Global Models, OECD, Paris, pp.
55–66.
Manne, A. S. and Richels, R. G.: 1992, Buying Greenhouse Insurance: The Economic Costs of CO2
Emission Limits, MIT Press, Cambridge, MA.
Nordhaus, W.: 1991, ‘Economic Approaches to Greenhouse Warming’, in Dornbusch, R. and Poterba, J. (eds.), Global Warming: Economic Policy Responses, MIT Press, Cambridge, MA, pp.
33–66.
Nordhaus, W. D.: 1994, Managing the Global Commons: The Economics of Climate Change, MIT
Press, Cambridge, MA, p. 213.
Nordhaus, W. and Yang, Z.: 1996, ‘A Regional Dynamic General-Equilibrium Model of Alternative
Climate-Change Strategies’, Amer. Econ. Rev. 86 (4), 741–765.
OECD: 1993, ‘The Costs of Cutting Carbon Emissions: Results from Global Models’, in OECD
Documents, Organization for Economic Cooperation and Development, Paris.
OECD: 1995, Global Warming: Economic Dimensions and Policy Responses, Organization for
Economic Cooperation and Development, Paris.
Pearson, C. and Pryor, A.: 1978, Environment: North and South, John Wiley and Sons, New York.
Peck, S. C. and Teisberg, T. J.: 1993, ‘Global Warming Uncertainties and the Value of Information:
An Analysis Using CETA’, Resour. Energy Econ. 15, 71–97.
Report to the President: 1994, U.S. Government Printing Office, Washington, D.C.
Rose, A. and Stevens, B.: 1993, ‘The Efficiency and Equity of Marketable Permits for CO2
Emissions’, Resour. Energy Econ. 15, 117–146.
Rutherford, T.: 1993, ‘The Welfare Effects of Fossil Carbon Restrictions: Results from a Recursively
Dynamic Trade Model’, in OECD (ed.), The Costs of Cutting Carbon Emissions: Results from
Global Models, OECD, Paris, pp. 95–106.
Stone, P. H.: 1992, ‘Forecast Cloudy’, Technol. Rev. March, 34–40.
World Commission on Environment and Development: 1987, Our Common Future, Oxford University Press, p. 400.
Xepapadeas, A. and Yiannaka, A.: 1997, ‘Measuring Benefits and Damages from Carbon Dioxide Emissions and International Agreements to Slow Down Greenhouse Warming’, in Carraro,
C. (ed.), International Environmental Negotiations: Strategic Policy Issues, Edward Elgar
Publishing, Brookfield, VT, pp. 150–171.
(Received 4 June 1997; in revised form 13 January 2000)