Global Warming: Efficient Policies in the
Case of Multiple Pollutants
PETER MICHAELIS
The Kiel bzstituw of World Economics, P.O. Box 4309, D-2300 Kiel 1, Germany.
Abstract. This article investigates efficient policies against global warming in the case of
multiple greenhouse gases. In a dynamic optimization model conditions for an efficient combination of abatement activities are derived. It is shown how this solution can be decentralised
by a system of emission charges. Since the determination of the charge rates should be based
on a long time horizon, the impact of sequential planning methods is explored. The parameters
of the model are specified with respect to the main greenhouse gases (carbon dioxide,
methane, nitrous oxide, chlorofluorocarbons) and a scenario for an efficient charge system is
calculated. For the main emission sources the tax base and the likely range of tax rates is
derived. The results illustrate that efficient policy measures against global warming will not
only affect the use of fossil fuels but will also impose a considerable burden on modern
agriculture specialising in livestock and in intensive farming techniques.
Key words. Environmental policy, greenhouse effect, carbon equivalent taxation, sequential
planning.
Introduction
The recent discussion on measures against global warming concentrates
almost exclusively on the reduction of carbon dioxide emissions. ~ However,
since there exist several other pollutants 2 which also contribute to the
increase in temperature there is no reason to believe that a CO:-policy alone
will ensure efficiency in terms of overall abatement costs. In fact, reduction
measures which aim exclusively at carbon dioxide can be efficient only if the
abatement cost of all other greenhouse gases are prohibitively high -- a
condition which can not be expected to be fulfilled in reality? Therefore, in
order to sustain a desired level of mean temperature it may be less costly to
refrain in part from the required CO2-reduction and to reduce the emissions
of, e.g., methane by an amount which is equivalent in terms of the prevented
greenhouse effect. However, substitution possibilities like this raise the
questions how to identify and how to pursue efficient policies against global
warming in the case of multiple pollutants.
The present paper investigates these questions within the framework of a
dynamic optimization model describing the respective economy-environment
interactions in a considerably simplified manner (see Section 1). In Section 2,
conditions for an efficient solution are analysed, Section 3 addresses the
decentralization of this solution by means of emission charges, and the policy
implications of sequential planning are explored in Section 4. Section 5
presents some empirical results regarding the properties of an efficient
Envtronmentat and Resource Economics 2:61--77, 1992.
9 1992 Khtwer Academic Pubhshers. Printed in the Netherlands.
62
Peter Michaehs
charge system on greenhouse gases. In Section 6, the choice of the appropriate tax base is discussed and the likely range of tax rates is is derived.
Finally, Section 7 completes the paper with some policy conclusions.
1. The Model
Assume there exist n greenhouse gases Gz (i = 1, 2, . . . , n), let ~(t) denote
the basic emission levels which would occur in period t without abatement
activities and let v,(t) denote the amount of pollutants prevented by abatement activities in period t. The basic emission levels ~(t) are assumed to
grow with an exogenous rate g, i.e., ~(t) = (1 + g~)~(0). Hence, the amount
of greenhouse gas G, actually emitted in period t, e,(t), is given by:
e,(t) = (1 + g,)'0,(0) - v,(t).
(1)
The emitted pollutants accumulate in the atmosphere over time, with s,(t)
indicating the stock of greenhouse gas G~ in the end of period t. Accumulated stocks, in turn, are partly degraded by natural disintegration processes.
For simplification it is assumed that these processes can be described by
constant disintegration rates q, (0 < q~ ~< 1) indicating that the degradation
of the stock s,(t) during the course of one period is qA(t). Hence, the change
in stock between two subsequent periods t and t + 1 can be characterized by
the difference equation:
s,(t + 1) -- s~(t) = e,(t + 1) -- q/z(t).
(2)
Assuming that there are no initial stocks, i.e., s,(0) = 0 for all i, the relationship between previous emissions and the current stock can be calculated
from (1) and (2): 4
s~(t) = i (1 -- q J - r
+ g,)~&,(0) -- v,(r)].
(3)
T=I
According to meteorological evidence (e.g., IPCC 1990) it is further assumed
that the greenhouse potential of pollutant G~ can be described by a weight a~
indicating the amount of carbon dioxide which is equivalent to one unit of Gz
in terms of its greenhouse impact. 5 Therefore, the total stock of greenhouse
gases measured in terms of CO2-equivalents is given by the sum:
s(t) = i a,s,(t).
(4)
t=l
Since the adaptive capability of the earth's ecosystem is restricted to a rise in
global mean temperature of appr. 1 ~ to 2 ~ above preindustrial levels (cf.,
e.g., Swart/Hootsmans 1991), and since the increase in temperature depends
on the increase in s(t), 6 it is reasonable to assume that s(t) is not allowed to
Global Warmmg
63
exceed an exogenously given limit of s ~ units. Therefore, the ecological
constraint of the model is given by s(t) ~ s ~ for any period t = 1, 2 , . . . T.
Finally, the set of feasible abatement activities is characterized by n
abatement cost functions c,[v,(t)] which are assumed to be constant over time
and to possess the usual properties, i.e., c~ = 0 for v,(t) = 0, c I > 0 for
v,(t) > O, c; ~ oo for v,(t) ~ ~,(t) and c 7 > O.
2. Derivation of the Efficient S o l u t i o n
In order to obtain the efficient combination of abatement activities among
the different greenhouse gases and over time, the present value of the
aggregated abatement costs has to be minimized with respect to the constraint s(t) <<, s ~ for t -- 1, 2, . . . , T. However, this formulation of the
ecological constraint is unnecessarily strict for the problem at hand. Formally
it is conceivable that the constraint will be binding for t < T. This, however,
is extremely unlikely to happen. Achieving abatement levels which lead to
zero net emissions 7 imposes prohibitive costs because of low disintegration
rates and the absence of end-of-pipe technologies (see Section 5). Therefore,
the cost minimization problem will in this case have an interior solution and
the constraint s(t) ~< s ~ can be replaced by s ( T ) = s ~ Hence, the efficient
combination of abatement activities can easily be derived by minimizing the
Lagrangean:
T
(1 + r)~-tc,[v,(t)]
L: = Y~ i
t--1
+ o
t=l
~
t=l
]
a,(1 -- q~)T-t[(1 + g~)t~,(0)-- v,(t)] -- S~ . (5)
t=l
Minimizing (5) and eliminating the Lagrangean-multiplier a yields the
following conditions which hold along the efficient path for any pair of
pollutants t G,, Gj} and any pair of subsequent periods {t, t + 1} :s
c"[v'(t)] - a ~ [
c~[v,(t)]
a,
l-q'
l(r-~
1 -- qj
cT[vt(t + 1)] -- (1 + r) cT[v,(t)]"
(6a)
(6b)
(1 - q,)
The interpretation of these conditions is straightforward: (6a) indicates the
efficient combination of abatement activities within each period, i.e., the
static optimum. (6b) describes the movement of the system over time, i.e., the
dynamic efficiency conditions.
According to (6a) abatement activities have to be combined in such a way
64
Peter Michaelis
that the ratio of the marginal abatement cost equals the ratio of the greenhouse coefficients multiplied by the weighted ratio of the respective disintegration rates. This implies that the share of abatement activities regarding
pollutant G, is c.p. the greater the higher is the greenhouse coefficient a, and
the smaller is the disintegration rate q, compared to the other greenhouse
gases. Moreover, as can be seen from (6a), the influence of differences with
respect to the disintegration rates is the stronger the longer is the (remaining)
time horizon. This result is quite reasonable because the economic valuation
of the natural disintegration capacity crucially depends on the length of the
employed time horizon.
The decreasing influence of the disintegration rates causes a dynamic shift
in the combination of abatement activities: The share of abatement activities
regarding pollutants with comparably low disintegration rates decreases over
time while the share of abatement activities regarding pollutants with comparably high disintegration rates increases. 9, 10 This effect becomes even more
clear when looking at condition (6b) which indicates that the marginal
abatement cost increase over time by the rate (1 + r)/(1 - q~),ll i.e., the level
of abatement activities regarding G~ increases over time with a higher natural
disintegration rate %
Finally, it can be seen from (6a) and (6b) that the ratio of marginal
abatement cost across pollutants and periods is not affected by the growth
rates g. This implies that along the efficient path the growth in basic
emissions only effects the absolute level of abatement activities but not their
combination among the different pollutants and over time.
3. Decentralisation by Emission Charges
The model presented above is based upon the minimization of an aggregated
cost function for the whole economy. So far the approach corresponds to an
economic system where all decisions are made by a central planning agency.
If one were to draw policy implications for market economies, one should -first of all -- find a mechanism which will ensure that the individual decisions
of all polluters lead to the efficient solution calculated above.
Consider a decentralized version of the present model where each greenhouse gas G, can be assigned to just one cost-minimizing polluter 12 El whose
feasible abatement activities are given by the above introduced cost function
c,[v,(t)]. A well-known result from the economic theory of environmental
policy indicates that cost-minimizing polluters, who face an emission charge,
will reduce their emissions to that level at which the charge rate per unit
equals marginal abatement cost (cf., e.g., Randall 1987: Chap. 20). Neglecting
comer solutions an equilibrium of the present economy thus implies that the
relationship p,(t) = c~[v,(O] holds for all i and t, where p~(t) indicates the
charge rate with respect to one unit of pollutant G~ emitted in period t. It can
be seen from (6a) and (6b) that the resulting equilibrium coincides with the
Global Warming
65
efficient solution if the charge rates satisfy the following conditions for any
pair of pollutants {G,, Gj} and any pair of subsequent periods {t, t + 1}:
p,(t)
pj(t)
a, [ l - q ,
= --
aj
pz(t + 1)
] {T-t}
(7a)
1 - qj
(1 + r) p,(t).
(1 -
(7b)
q~)
Conditions (7) describe a dynamic system of emission charges which for the
decentralized version of the present model ensure that the individual decisions of the polluters lead to an efficient combination of abatement activities
among the different pollutants and over time. 13 However, as can be easily
shown, conditions (7) provide only (n- T)-I independent equations for the
determination of the charge rates pz(t). Therefore, by (7) the charge rates can
be determined only up to a constant multiplier and the remaining degree of
freedom has to be used to achieve the ecological constraint s ( T ) = s ~ by
fixing the absolute level of the charge rates. Hence, the absolute level of the
charge rates depends on the magnitudes of s ~ and T, the initial emission
levels ~,(0), the growth rates g, and the abatement cost functions q[v~(t)],
while the ratio between the charge rates (regarding different pollutants and
different periods) solely depends on the ecological coefficients a, and % the
length of the time horizon T and the employed discount rate r. This implies:
The efficient system of charge rates can be calculated from (7) for alternative
time horizons and alternative discount rates if the charge rate regarding one
unit of carbon dioxide emitted in the first period, Pl(1), is known, 14 and the
magnitude of the ecological coefficients a, and q~ can be specified. This
becomes even more clear when reorganizing conditions (7) which yields the
following expression indicating the relative charge rates p,(t)/pl(1):
p,(t)
p1(1)
1 m qz
a~
1 -
ql
1 - - q,
(8)
Equation (8) reveals the interaction between the ecological coefficients a z
and % the time horizon T and the discount r in determining the relative
charge rates: The constant term a,[(1 -- q,)/(1 - ql)] r-1 indicates the basic
(first period-) level of relative charge rates while the time-dependent term
[(1 + r)/(1 - q,)]~- 1 describes the development of the rates over time. Hence
the basic level of the relative charge rate c.p. is the higher the greater is the
greenhouse coefficient a, and the smaller is the disintegration rate qz compared to the one of carbon dioxide. 15 Moreover, the influence of this latter
ratio (1 - q~)/(1 - ql) is the higher the longer is the employed time horizon
T.16 Finally, it can be seen from (8), that for a given value of p1(1) the charge
66
PeterMichaelis
rates p,(t) are increasing over time, where the increase is the stronger the
higher are the discount rate and the respective disintegration rate.
4. Sequential Planning
Hitherto the analysis relied on the assumption of a fixed and finite time
horizon. This, however, may be questionable in the case at hand since it
turned out that not only the ratio between the charge rates but also their
absolute level crucially depend on the length of the employed time horizon.
Moreover, the notion of a finite horizon which is held fixed even when the
final period is approached seems to be highly unrealistic from a political
point of view. On the other hand, the idea of a decision maker who plans
over an infinite number of time periods also seems to be unsatisfactory due
to several reasons (e.g., uncertainty about the distant future, planning costs,
etc.). A possible way out of this dilemma may be to assume that the time
horizon is finite but 'sufficiently long' concerning the issue of global warming.
According to Cline (1991) this would require the use of a horizon in the
order of at least 250 to 300 years. However, from the political economy of
public decision making there is ample evidence to believe that the political
process is not able to cope with the demand for such a long time horizon
(e.g., Downs 1957).
A sensible way to overcome these calamities concerning the time horizon
is offered by the idea of sequential overlapping planning. 17 Under this regime
plans are set up with a finite time horizon of T periods and after a certain
number of periods, S (S < T), plans are reevaluated with the time horizon
being T periods as before. 18 Continuous repetition of this procedure leads to
an (at least in principle) infinite number of overlapping T-period plans, and
the resulting sequence of the first S periods of each plan constitutes the time
path that is actually realized. 19 This approach seems to facilitate a more
realistic description of the long term aspects of political decision making than
the notion of a single (finite or infinite) time horizon.
In order to explore the implications of sequential planning for the model
under consideration we assume that the evaluation of the charge rates, as
discussed in Sections 2 and 3, is continuously repeated according to the
procedure described above. We denote by pT(t) the charge rate regarding
pollutant G, at period t which results from the ~-th evaluation procedure; i.e.,
the superscript ~ = 1 indicates the first planning sequence running from t =
1 to t -- T, the superscript z = 2 refers to the second sequence running from
t -- S + 1 to t = S + T and so on. Since of each planning sequence only
these charge rates come into force, which are calculated for the first S
periods, the actually realized time path of G(t) is given by: p~(1), p~(2) . . . . .
pl(S), pZ,(s + 1), pZ(S + 2 ) , . . . , pZ,(s + s), p~(ZS + 1), p3(2S + 2 ) , . . .
Figure 1 illustrates the qualitative properties of this time path. z~ In order
to facilitate a lucid graphical presentation it is assumed that the charge rates
67
Global Warming
pi(t)
I
I
pi3(T+l)
pl2(s+l)
I
I
.................
I
s
i
pil(1)
S
T
I
I
2S
S+T
pi(t)/pj(t)
r l-qi.] T-S
I
1
S
2S
T-I
~"ijLI
_'i"Z~j
J
Fig. 1. The effects of sequential overlapping planning.
p,(t)
are reevaluated after three quarters of the time horizon have passed (i.e.,
S = 0 . 7 5 T ) although a more frequent reevaluation may be more realistic.
The upper panel shows the time path of the absolute level of p,(t) and the
lower panel indicates how the charge rates' ratio p,(t)/pj(t) evolves over time.
In constructing the upper panel of Figure 1 it is assumed that the efficient
first period rate on carbon dioxide, pl(1), is known from explicitly solving
the minimization problem (5) for the time horizon t = 1, 2 , . . . , T. Based on
this information all other initial charge rates can be obtained from (8): p](1) =
a,[(1 - q~)/(1 - ql)]r-~pl(l). Starting from these initial levels the charge
rates increase according to condition (7b) by the factor (1 + r)/(1 - qi) until
period t = T is reached. In period S < T, however, the cost minimizing
policy is reevaluated employing a new time horizon running from t = S + 1
to t = S + T. F r o m this calculation it turns out that the charge rates for the
next period suggested by the old plan, i.e., the p](S + 1), are too low in view
of the fact that a part of the 'budget' s ~ is already used up while the time
horizon has been prolonged to cover again a time span of T periods. Hence,
in period t = S + 1 environmental policy switches to the new plan and the
68
Peter Michaelis
charge rates jump to higher levels p~(S + 1) > p~(S + 1). Starting from
these levels the rates again increase according to (7b) until the next reevaluation takes place in period t = 2S.
In constructing the lower panel of Figure 1 it is assumed that pollutant G,
exhibits a higher disintegration rate than Gj (i.e., qi > qj). From condition
(7a) it can be seen that the charge rates' initial ratio is given by p~(1)/pj(1) =
(a/aj)[(1 - q,)/(1 - qj)]r-1. Moreover, since q~ > qj implies [(1 - q~)/(1 qj)] < 1 it is known from (7a) that p~(t)/pj(t) increases over time. This trend,
however, does not last infinitely. According to (7a) the ratio between the two
charge rates is the higher the closer is the end of the currently employed time
horizon. From this it follows that p~(t)/pj(t) reaches it's maximum level of
( a / a j ) [ ( 1 - q~)/(1 - qj)]r-s in period t = S and drops back to the intial
level of (a/aj)[(1 - q,)/(1 - qj)]r-1 in period t = S + 1 when the time
horizon is prolonged to cover again a time span of T periods. Hence, the
time path of p,(t)/pj(t) exhibits a ratchet-like shape as depicted in the lower
panel of Figure 1. This implies that the economic valuation of the relative
importance of the different pollutants is revised each time the cost minimizing policy is recalculated employing a prolonged time horizon.
Finally, an interesting special case should be emphasized: If the charge
rates are reevaluated each period (i.e., S = 1), then the above described
'policy cycles' vanish and the charge rates' ratio remains constant at the level
(a/aj)[(1 - q~)/(1 - qj)]r-1. In this case the ratio between the charge rates
only depends on the pollutants' ecological characteristics and the employed
time horizon. In particular, it can be seen that the relative price on pollutants
with comparatively low disintegration rates (like, e.g., nitrous oxide -- see
Section 5) is the higher the longer is the time span T covered by each
planning sequence.
5. Empirical Results
An empircial application of the present model first of all requires a specification of the coefficients ct~ and q~ with respect to carbon dioxide (CO2) ,
methane (CU4) , nitrous oxide (N20) and the chlorofluorocarbons CFCI~ and
CFC12. At present these five greenhouse gases together contribute approximately 90% to the man-made greenhouse effect (see IPCC 1990). They
therefore may be regarded as the most important pollutants driving global
warming. 21
The first row of Table I indicates the relative greenhouse potentials per
ton of CH4, N20 , CFCll and CFC12 as published by the Intergovernmental
Panel on Climate Change (cf. IPCC 1990). These figures can be used
directly as estimates of the greenhouse coefficients O~t.22 In contrast to this,
direct estimates of the disintegration rates qz are not available. However, it is
known that most gases are degraded exponentially in time. Considering one
ton of pollutant G, released to the atmosphere in period 1 and indicating by
69
Global Warming
Table I. Estimates of the ecologicalcoefficients(source: IPCC 1990: own calculations)
Greenhouse coefficienta,
Atmospheric hfetlme c,
Disintegration rate q,
CO,
CH4
N20
CFC 11
1
120
0.0083
58
206
3.970
10
150
60
0.0952
0.0066
0.0165
CFC 12
5,750
130
0.0077
Ez(t) the remaining fraction still present in the atmosphere in period t this
degradation process is usually described by:
Ez(t) = e-l('- 1)/c,l.
(9)
The coefficients c~ are frequently termed as the gases' "atmospheric lifetime".
They indicate the number of years which pass until a given amount of the
respective gas has been reduced by natural processes to roughly one third of
its initial magnitude. These figures, published by the IPCC (1990), are used
to calculate the disintegration rates indicated in Table I. For this purpose we
employ the observation that the exponential degradation process described
by (9) coincides with the degradation process generated by the model's
disintegration rates if the choosen rates satisfy the following condition:
(10)
q, = 1 - e -O/cO.
However, two qualifications regarding the calculated disintegration rates
should be mentioned. First, the disintegration capacity of real ecosystems
may be influenced by the accumulated stock of pollutants, and therefore it
may be unsatisfactory from an empirical point of view to employ a model
with constant disintegration rates. Second, the atmospheric lifetime used to
calculate the disintegration rate of carbon dioxide is not unambiguous. The
time span of 120 years indicates the number of years which pass until
roughly two third of an initial amount of carbon dioxide is absorbed by the
oceans. However, this timespan also includes periods in which the carbon
dioxide does not contribute to global warming because it is converted into
biomass. Therefore, it would also be reasonable to employ a higher disintegration rate for carbon dioxide and hence the relative charge rates for
methane, nitrous oxides and chlorofluorocarbons calculated subsequently are
more likely to be interpreted as lower bounds. -'3
Inserting a, and q, from Table I into (8) yields the following system of
equations determining the relative charge rates regarding carbon dioxide
(G1), methane (G2), nitrous oxide (G3), CFCll(G4) and CFC 12(O5):
p~(t) =
[(1 + r)/0.9917] ' - 1 " pl(1),
(10a)
p2(t) = 5 8 - 0 . 9 1 2 4 r - 1.
[(1 + r)/0.9048]'-1, pl(1),
(10b)
70
Peter Mtchaelis
p3(t) = 206" 1.0017 r - l "
[(1 + r)/0.9934] ' - ~ - pl(1),
(10c)
P4(t) = 3,970" 0.9917 r - 1 . [(1 + r)/0.9835] ' - 1 . p~(1),
(a0d)
Ps(t) = 5,750" 1.0006 r - l - [(1 + r)/0.9923] ~-1. P1(1).
(10e)
In order to further explore the empirical implications of the present model it
would be highly interesting to specify the cost functions c,[vi] and the remaining parameters and to solve the model for a numerical value of P1(1) which
yields together with (10a) to (10e) an efficient intertemporal charge system
that is consistent with the restriction s ( T ) ~ s ~ This, however, would lead far
beyond the scope of the present analysis since -- except for the case of
carbon dioxide -- empirical estimates of abatement costs for greenhouse
gases are not available. Hence, at the current state of the art, an empirical
specification of q[vi] is not possible for most of the pollutants under consideration and therefore the optimal level of pl(1) can not be determined.
But despite the lack of exact knowledge of c,[v,] some interesting empirical
results concerning the ratio between the charge rates and their development
over time can be derived. Hence, as long as empirical cost functions are not
available, it seems sensible to refrain from the attempt to determine the
absolute level of the charge rates and to restrict the analysis to an assessment
of the ratio between the charge rates and their development over time. This
can be done by applying exogenously given values of p1(1) to equations (10a)
to (10e). This approach, of course, leads to scenarios which are somewhat
arbitrary concerning the absolute level of the resulting charge rates. However, this arbitrariness can considerably be reduced by choosing an initial
charge rate with respect to CO~ that is realistic in view of the empirical
literature concerning the taxation of carbon dioxide (see, e.g., Hoeller et al.
1990). Table II presents such a scenario which is based on a time horizon of
20 years, a discount rate of 4% (i.e., r = 0.04) and a fairly moderate 24 initial
charge rate regarding carbon dioxide of US-S50 per ton.
It should be noted, however, that the scenario presented is based on the
assumption that the available abatement technologies do not change over
time. Hence, the emission taxes would only apply as long as new abatement
technologies have not come forward. The implementation of this charge
system would however stimulate technical progress which in turn would
decrease abatement costs and slow down the increase in charge rates. 25
Nevertheless, the figures presented in Table II show clearly that -- even in
the case of a fairly moderate charge rate on carbon dioxide -- an efficient
solution requires considerably high charge rates on methane, nitrous oxide
and chlorofluorocarbons.
Table II can either be interpreted as the efficient charge policy concerning
a single finite planning horizon of 20 years or as the first building block of a
continuous planning sequence as discussed in Section 4. In the latter case one
could imagine that, for example, only the charge rates calculated for the first
71
Global Warming
Table II. Tax-Scenarto [US-Sper ton] for p1(1) = 50, r = 0.04 and T = 20
t= 1
t=2
t=
t=
t=
t=
t=
t=
t=
t=
t=
t=
t=
t=
t=
t=
t=
t=
t=
t=
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
CO 2
CH 4
N20
CFC 11
CFC 12
50.0
52.4
55.0
57.7
60.5
63.4
66.5
69.7
73.1
76.7
80.4
84.3
88.5
92.8
97.3
102.0
107.0
112.2
117.7
123.4
508
584
671
772
887
1,019
1,172
1,347
1,548
1,779
2,045
2,350
2,701
3,105
3,569
4,102
4,714
5,418
6,228
7,158
10,631
11,131
11,653
12,200
12,773
13,373
14,001
14,659
15,347
16,068
16,822
17,612
18,439
19,305
20,211
21,160
22,154
23,194
24,283
25,423
169.433
179,171
189,470
200,360
211,877
224,055
236,934
250,552
264,954
280,183
296,287
313,318
331,327
350,317
370,510
391,806
414,326
438,141
463,325
489,956
291.023
305,001
319,651
335,004
351,094
367,958
385,631
404,153
423,357
443,909
465,230
487,576
510,994
535,538
561,260
588,218
616,471
646,080
677,112
709,634
five p e r i o d s c o m e into force (i.e., S = 5) a n d in the next period e n v i r o n m e n t a l policy switches to a n e w p l a n r u n n i n g from t = 6 to t = 25 which
i n d u c e s a j u m p in charge rates.
If o n e finally assumes the special case of S = 1, t h e n the a b o v e m e n t i o n e d
j u m p i n charge rates appears every p e r i o d a n d only the rates calculated for
t -- 1 c o m e into force. I n this case the increase in charge rates can n o t b e
d e t e r m i n e d without explicitly solving the model, b u t f r o m Section 4 it is
k n o w n that the ratio of charge rates r e m a i n s c o n s t a n t at the level ( a / a j ) [ ( 1 qz)/(1 - q j ) ] r - J . F o r T = 20 this implies that the efficient charge rate
regarding o n e t o n of m e t h a n e is a b o u t t e n times as high as the rate regarding
o n e t o n of c a r b o n dioxide. C o n c e r n i n g the o t h e r g r e e n h o u s e gases the
respective ratios c o m p a r e d with c a r b o n dioxide are a b o u t 213 for n i t r o u s
oxide, a b o u t 3,390 for C F C l l a n d a b o u t 5,820 for CFC12.
6. Defining the Tax Base
T h e charge system suggested a b o v e requires a n identification of the m a i n
e m i s s i o n sources a n d an a p p r o p r i a t e definition of the respective tax bases.
T h e only e x e m p t i o n f r o m this is the case of the c h l o r o f l u o r o c a r b o n s : E v e n
for a m o d e r a t e charge rate o n c a r b o n dioxide an efficient solution requires
charge rates o n C F C s which can be c o n s i d e r e d p r o h i b i t i v e 26 in view of the
72
Peter Michaelis
availability of close substitutes a low cost (see Hoeller et al. 1990: 7). 27
Hence, a total ban of these substances can be recommended from an economic point of view. This implies that it is not necessary at all to include
CFCs in the tax-scheme.
Concerning the other greenhouse gases under consideration -- carbon
dioxide, methane and nitrous oxide -- the main emission sources may vary
from country to country. 28 The following discussion refers to the case of the
Federal Republic of Germany, but the main line of argumentation may apply
also to comparable countries of the northern hemisphere.
With respect to carbon dioxide the assessment of the tax base is straightforward: CO 2 is an unalterable by-product of the combustion of fossil fuels,
i.e., there exists an almost proportional relationship between the emitted
carbon dioxide and the amount of fuel burned. 29 Therefore, the charge on
CO 2 should be designed as a product charge on fossil fuels, which is fixed
according to their respective carbon content.
In the case of nitrous oxide, however, the assessment of the tax base is less
obvious. For the Federal Republic of Germany (and comparable countries)
the main source of man-made NzO is the use of nitrogen fertilizer (see, e.g.,
Enquete 1990: 103). Hence, a product charge on this kind of fertilizer seems
to be a reasonable way to tax the emission of N20. According to empirical
evidence, roughly 2--3% of the utilized fertilizer is converted into N20 and
emitted into the atmosphere (see Sauerbeck/Brunnert 1990: 50). Accounting
for the relative molecular mass of nitrogen and oxygen this leads to an
emission coefficient of about 0.04 tons of N20 per ton of nitrogen fertilizer.
With respect to the scenario presented in Table II, this implies an initial (i.e.,
first period-) charge rate of approximately US-$425 per ton of nitrogen
fertilizer leading to an increase in price of more than 40% compared to the
current level. This figure, however, does not include the CO2-emissions
caused by the use of energy in the production of nitrogen fertilizer.
With respect to methane there are two main emission sources. The first
one is related to the digestive system of ruminants (i.e., cows, sheeps,
goats). 3~ Since the specific CH4-production per unit of livestock can hardly
be influenced by measures like changes in feeding (and since there exist no
end-of-pipe technologies), a 'poll-tax' on ruminants seems to be an appropriate method to tax the CH4-emissions from agricultural activities. Under
this regime the further assessment of the tax base is straightforward: For
example milk cows, which possess the highest 'emission coefficient' of all
kinds of ruminants, produce roughly 0.1 tons of CH 4 per year and unit of
cattle. In terms of the above presented scenario (see Table II) this would
imply an annual charge rate per milk cow which starts at about US-S51 and
increases up to a final level of about US-$716. 31
The second important source of man-made CH4-emissions is the deposition of solid waste. According to empirical evidence, about 0.125 tons of
methane are generated by the anaerobic decomposition of one ton of organic
Global Warming
73
substances (see Sauerbeck/Brunnert 1990: 43). Accounting for an organic
share of roughly one third this implies an emission coefficient of about
0.04 tons of CH 4 per ton of domestic waste. These emissions should be taxed
by a surcharge on the price for the collection and treatment of municipal
waste. 32 However, the assessment of the appropriate surcharge is complicated by the fact that some disposal sites may be equipped with end-of-pipesystems for the collection and treatment of the escaping gases. This implies
that the charge rate per ton of domestic waste is not uniform but has to be
adjusted to the technical standard of the respective disposal site. For example, in the scenario presented above the initial (first period-) surcharge per
ton of domestic waste amounts to about US-S10 if the used disposal site is
equipped with a end-of-pipe system which collects 50% of the escaping
gases.
Finally, it has to be emphasized that the proposed charge system should
not be implemented by one country alone. This is of particular importance
for carbon dioxide since such a national go-it-alone approach would significantly reduce the competiveness of energy-intensive commodities without
being able to secure a reduction in global CO2-emissions. In fact, this
approach could even lead to an increase in global CO2-emissions since it
would be conceivable that the production of energy-intensive commodities
would partially shift to other countries where the CO2-emissions per unit are
higher because of lower technical standards. Hence, in implementing the
proposed charge system a cooperative international solution is required.
7. Policy Implications
Although the model analysed above describes the respective economy-environment interactions in a considerably simplified manner, it illustrates that
the greenhouse problem is more than a CO2-problcm. Consequently, policies
adressing global warming should take account of these interactions. The
following policy conclusions can be drawn:
-- Policy measures against global warming should tackle not only the
emissions of carbon dioxide but also the emissions of methane, nitrous
oxide and the chlorofluorocarbons CFC H and CFC12. The implementation of a charge system on greenhouse gases is a reasonable way to
pursue an efficient combination of abatement activities.
-- The appropriate ratio between the charge rates regarding different
pollutants depends not only on the greenhouse potential and the atmospheric lifetime of the respective gases but also on the employed time
horizon and the discount rate. In particular, the relative price for the
emission of greenhouse gases which possess smaller disintegration rates
than carbon dioxide (e.g., nitrous oxide) is the higher the longer is the
employed time horizon.
74
Peter Michaelis
- - E v e n for a m o d e r a t e c h a r g e r a t e o n C O 2 the m o d e l p r e d i c t s c o m p a r a tively high charge rates for m e t h a n e , n i t r o u s o x i d e a n d c h l o r o f i u o r o c a r bons. M o r e o v e r , the m a g n i t u d e of the c a l c u l a t e d c h a r g e rates o n C F C s
i n d i c a t e s that a total b a n of these s u b s t a n c e s can b e r e c o m m e n d e d f r o m
an e c o n o m i c p o i n t of view since the rates w o u l d b e p r o h i b i t i v e in any
case.
-W i t h r e s p e c t to the situation in the F e d e r a l R e p u b l i c o f G e r m a n y a n d
c o m p a r a b l e i n d u s t r i a l i z e d c o u n t r i e s a p r a c t i c a l w a y to tax g r e e n h o u s e
gases s e e m s to b e a c h a r g e system including (1) a p r o d u c t c h a r g e o n fossil
fuels, (2) a p r o d u c t c h a r g e o n n i t r o g e n fertilizers, (3) a ' p o l l tax' o n
r u m i n a n t s a n d (4) an a p p r o p r i a t e s u r c h a r g e o n the p r i c e for the d i s p o s a l
o f m u n i c i p a l waste.
-Finally, the m o s t striking p o l i c y i m p l i c a t i o n of this m o d e l m a y b e that
efficient p o l i c y m e a s u r e s against g l o b a l w a r m i n g will n o t o n l y affect the
use of fossil fuels b u t will also i m p o s e a c o n s i d e r a b l e b u r d e n o n m o d e r n
agriculture specialising in livestock a n d in intensive f a r m i n g techniques.
This is d u e to the fact that these activities c o n t r i b u t e significantly to the
e m i s s i o n of the g r e e n h o u s e gases m e t h a n e a n d n i r o u s oxide. 33
Acknowledgements
I w o u l d like to t h a n k G e r n o t K l e p p e r w h o s e c o n t r i b u t i o n s have i m p r o v e d
the p a p e r c o n s i d e r a b l y . I also wish to t h a n k M a l t e F a b e r , J o h a n n e s Heister,
F r a n k J6st, E r n s t M o h r , M i c h a e l R a u s c h e r , A r m i n S c h m u t z l e r a n d t h r e e
a n o n y m o u s referees for helpful c o m m e n t s a n d suggestions.
Notes
1 Cf. e.g., Grubb (1989), Manne/Rmhels (1990), Mohr (1991), Nordhaus (1991) and Whalley/
Wigle (1991). A comprehensive overview on recent empirical work in this field is given by
Hoeller et al. (1990).
2 Mainly methane (CH~), nitrous oxide (N20) and the chlorofluorocarbons CFCI1 and CFC12
(cf. Section 5).
3 Strictly speaking, the cost incurred by the abatement of the first unit of all other greenhouse
gases must be higher than the cost incurred by the abatement of the last prevented unit of
carbon dioxide. For a formal treatment of such corner solutions see Michaelis (1991).
4 For a more detailed derivation of a diffusion function of this type see Faber et al. (1987:
Chap. 2).
5 Note that some of the greenhouse coefficients cited in the literature are calculated in such a
way that they already include the rate of natural degradation. This approach leads to
coefficients which depend on the time horizon. However, from a theoretical point of view, it
seems to be more appropriate to separate these effects by using constant greenhouse
coefficients in combination with an explicit consideration of the natural disintegration process.
6 Strictly speaking, the increase in temperature does not depend on the increase in s(t) but on
the increase in the concentration of the greenhouse gases. But nevertheless, for a given volume
of the atmosphere there is a constant relationship between the stock and the concentration.
7 Net emissions equal the emissions to the atmosphere minus the amount of greenhouse gases
Global Warming
75
that is disintegrated by natural processes during the respective period. Therefore, zero net
emissions imply that the stock s(t) remains unchanged.
8 Note that an interior solution (i.e., v,(t) > 0 for all i and t) is ensured by the assumption
c I = 0 for v~= 0.
9 However, this result crucially depends on the assumption that the abatement cost functions
do not change over time.
~0 Note that in the special case of equal disintegration rates (i.e., q, = qj) the interpretation of
(5a) is particularly simple: the "adjusted" marginal cost c~(v,)/a, should be equalized across
gases. This. of course, also implies that the ratio of marginal abatement cost remains constant
over tame.
~1 In the case of zero disantegration (i.e., q, = 0) this implies that the present value of marginal
cost should be equalized across periods.
~2 This assumption serves only for simplicity. The following argumentation can easily be
generalized on the case of multiple polluters.
~3 Note that another way to ensure efficiency may be the implementation of a hcense scheme
on greenhouse gases (cf. Helster/Michaelis 1992).
14 In the following pollutant Gj may indacate carbon dioxide. Note that this also implies
a ~ = 1.
~5 Note that the magnitude of the basic level, a~[(1 - q,)/(1 - ql)] r - 1, degenerates to 1 in the
case of carbon dioxide (i = 1).
~6 This implies that the relative price for the emission of greenhouse gases which possess
smaller disintegration rates than carbon dioxide -- e.g., nitrous oxide (cf. Section 5) -- is the
higher the longer is the employed time horizon,
17 In the literature (e.g., Faber/Proops 1990) this planning procedure is frequently labelled as
'rolling myopic planning'. However, as Schmutzler (1991) points out, this expression may be
misleading since the term 'myopic' usually indicates some kind of economic shortsightedness,
lake, e.g., maximizing short-term payoff.
is It should be noted that the original motivataon of such planning procedures is to cope with
uncertainty and the emergence of novelty (see, e.g.. Faber/Proops 1990). In contrast to this we
assume that the problem at hand is completely deterministic but the process of decision
making itself is deficient in dealing with sufficiently long time horizons.
~9 For a theoretical analysis of the properties of time paths resulting from such an overlapping
planning procedure, see Schmutzler (1991: Chap. 4).
20 For diagrammatic reasons in Figure 1 contanuous instead of discrete time is used.
2~ Tropospheric ozone (O3), which also contributes significantly to global warming, takes a
special position because it is not directly emitted from anthropogenic sources but is created by
highly complex and non-linear atmospherical processes that involve nitrogen oxides, methane,
carbon monoxide and other trace gases. Therefore, an unambiguous assignment of tropospheric ozone to an individual polluter is not possible and hence nobody can be charged for
emissions.
22 The greenhouse coefficients mentioned in Table I indicate only the gases' relative potential
to prevent anfrared rays from escaping the earth's atmosphere. As already mentioned in Note
5 this figures should not be confused with other greenhouse coefficients (also published by the
IPCC) which are calulated in such a way that they already include the rate of natural
disintegration.
23 According to (8) an increase in the disintegration rate q~ would ceterls paribus cause an
increase of the basic charge levels regarding all other greenhouse gases.
_~4 Some empirical studies indicate that a charge rate of more than US-S200 per ton would be
necessary to achieve a reduction in emissions of 50~ which would be required to stabilize the
greenhouse effect (see Hoeller et al. 1990: 40).
2s This effect becomes the more important the longer is the considered time horizon. For this
reason, and because of the problems discussed in Section 4, the scenario presented above is
restricted to a comparatively short time horizon. In contrast to this, some recent empirical
76
Peter Michaelis
studies on reducing CO 2 employ time horizons of more than 100 years (see Hoeller et al.
1990).
26 To gwe a first clue to the impact of such a charge on CFCs it may be noted that a
customary refrigerator contains about 250 grams of CFC 11 and 150 grams of CFC12. In terms
of the scenario presented above this implies an initial increase in price per unit of about US$86.
2v Note that the charge rates in Table II cover only the greenhouse effect of chlorofluorocarbons but not their harmful effect on the ozone layer.
28 In particular, there are differences regarding the main emission sources between countries
of the northern and the southern hemisphere. In the latter, deforestation and the cultivation of
rice contribute significantly to the emission of greenhouse gases.
29 Note, however, that this relationship depends on the completeness of the combustion and
the absence of end-of-pipe technologies.
30 For the FRO the annual emission of C H 4 caused by ruminants is estimated to the about 1
million tons (cf. Sauerbeck/Brunnert 1990: 38).
31 Based on an average milk production of 6000 litre per year this implies a charge rate per
liter of milk which starts at US-S0.00 85 and increases up to US-S0.12.
32 It should be noted, however, that most German municipalities apply fiat rates with respect
to the collection and treatment of waste. In this case, a surcharge will induce no incentive for
reducing waste.
33 Of course, the charge o n C H 4 and N20 will only be a part of the burden. Since modern
farming is an energy intensive activity the impact of the CO2-tax on fossil fuels must be added
to assess the total costs imposed on agriculture by an effective greenhouse policy.
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