In Gren 1997 it is shown that the consideration of these two spillover effects, instead of only one
as in most papers on transboundary pollutants, is likely to reduce the difference between outcomes
from coordinated and uncoordinated policies. However, in this paper we are mainly concerned
with the comparison of the value of marginal changes in the area of pollutant sinks. In subse-
quent analysis we will therefore abolish the first- order conditions for optimal choices of emission
reduction measures.
Coordinated minimization of total costs IC
for achieving a certain maximum pollutant load
target, L, is written as Min S
i N
[C
iR
R
i
+ C
iA
A
Li
] R
i
, A
Li
s.t. 1 − 2 S
i N
L
i
5 L
A
Li
5 A
Li
7 and the first-order conditions with respect to the
optimal choice of A
Li
is l
P
A
Li
i
− C
A
Li
i
= a
iIC
8 where l ] 0 is the Lagrange multiplier on the
pollutant load restriction, which measures the change in total costs from a marginal change in
the pollutant load restriction. Whether or not a
iIC
is positive depends on the cost and effectiveness of land as a pollutant sink as compared to abate-
ment options in all countries. The corresponding decision problems under na-
tional policies is written in the same way as Eqs. 6 and 7, except for the absence of summation
over all countries in the objective function. Under national minimization of costs, a restriction is
imposed only on the country’s pollutant load to the water body. The associated first-order condi-
tions under National maximization of net benefits
NB , is then written as
V
W
i
i
W
L
i
i
e
ii
P
A
Li
i
− C
A
Li
i
= a
iNB
9 The corresponding condition under National min-
imization of costs NC
is l
i
P
A
Li
i
− C
A
Li
i
= a
iNC
10 where the Lagrange multiplier, l
i
, measures the change in costs from a marginal change in the
pollution requirement L
i
which considers only the reduction options in the country. The multi-
plier on the overall reduction target, l, measures changes in total costs from a marginal change in
L where reduction options in all countries are taken into account.
3. Comparison of pollutant sink values
Assuming positive values of a marginal change in A
Li
, we can see from the first-order conditions Eqs. 6 and 8 – 10 that
a
iIB
= a
iIC
= a
iNB
= a
iNC
when S
j
V
j
W
j
W
j
L
j
e
ij
= l =
V
i
W
i
W
i
L
i
e
ii
= l
i
That is, the marginal sink values are the same when there are no transboundary impacts by the
water streams, when the efficient level of pollutant load reduction corresponds to the cost effective
level at the international and national decision levels, and when l = l
i
for all i = 1…,N countries. The last condition implies, in principle, that there
are no differences in pollutant reduction costs between the countries. It is very unlikely that
these three conditions are fulfilled, at least for relatively large international waters with several
surrounding countries. We then have the situation that the value of a marginal change in the area of
pollutant sink in a country depends on the deci- sion context and objectives, which is analysed in
the following section.
In order to compare the values under coordi- nated and uncoordinated actions, we take the
difference between the international and national values of a marginal change in land to be the
pollutant sink in country i under maximization of net benefits and minimization of costs, respec-
tively. The difference under the maximization of net benefits is then written as
a
iIB
− a
iNB
=
N j, j i
V
W
j
j
W
L
j
j
e
ij
P
A
Li
i
11 Obviously, we have a
iIB
\ a
iNB
as long as V
j
W
j
W
j
L
j
e
ij
\ where j i. That is, the
value of a marginal change in the area of pollu- tant sinks in country i is higher under coordinated
policies as long as there are any dispersion im- pacts of water quality and when positive valua-
tions of water quality improvements exists in at least one other country.
Under the cost effectiveness approach we have a
iIC
− a
iNC
= l − l
i
P
A
Li
i
12a Eq. 12a is positive or negative depending on the
relation between l and l
i
. These Lagrange multi- pliers are equal to the derivatives of the total and
national cost functions for changes in pollutant loads at L and L
i
, respectively, which implies that Eq. 12a can be rewritten as
a
IC
− a
NC
= − C
L
− C
L
i
i
A
io
, E
io
P
A
Li
i
, C = S
i
C
i
A
io
, R
io
12b and A
io
and R
io
denote the optimal choices of land use- and emission-oriented measures, respec-
tively. The relation between a
IC
and a
NC
is thus determined by the relation between the interna-
tional and national marginal costs for pollutant load reductions at the restrictions L and L
i
, respectively. Assuming negative and concave cost
functions in L and L
i
, respectively, the differ- ence between a
IC
and a
NC
is positive for marginal decreases in L and L
i
when the marginal cost of pollutant load reductions in country i is relatively
low as compared to other countries. Then, an increase in A
Li
implies cost savings in all coun- tries where pollutant reduction options are more
expensive than the cost of the increase in A
Li
. On the other hand, the national value of a marginal
change in A
Li
is higher when the national mar- ginal cost for pollutant reductions is relatively
high. When we instead focus on the role of informa-
tion provision, we take the differences between the values of marginal change in the area of
pollutant sinks between the efficient and cost ef- fective policies. This difference under coordinated
policies is written as
a
iIB
− a
iIC
= S
j
V
W
j
j
W
L
j
j
e
ij
− l P
A
Li
i
13 and under national policies we have
a
iNB
− a
iNC
= V
W
i
i
W
L
i
i
e
ii
− l
i
P
A
Li
i
14 Under both international and national policies for
maximizing net benefits we have that marginal benefits from pollutant reductions are equal to the
marginal cost. Since the Lagrange multipliers l and l
i
measure the marginal costs of pollutant load reductions at the cost effective load targets,
Eqs. 13 and 14 are both zero when the efficient level of pollutant load coincides with the cost
effective target. When the efficient loads are higher lower than cost effectiveness targets, the
differences in Eqs. 13 and 14 are negative positive. The values of sinks are then lower
higher under maximization of net benefits than when costs are minimized.
4. Application to the Baltic Sea
