maximum amount of consumption that can be spent on consumption in one period without reducing real
consumption opportunities in future periods. This is sustainable by definition Daly, 1991. By con-
trast, the objective of strong sustainability is to maintain the ecological capital at the initial level.
This implies an astronomical value given to the environment in comparison with consumption. In
other words, in a strong sustainability framework, the environment can be said to be considered as
sacred capital Taylor, 1996. Finally, the objective of weak sustainability is to maintain the level of
social welfare. With respect to economic develop- ment and the environment, this is the total value
of instantaneous consumption and the environment in an area. Apparently, among the above concepts,
weak sustainability provides the most comprehen- sive approach to sustainable development. It allows
for trade-offs between consumption and environ- mental quality. Moreover, it integrates very weak
and strong sustainability as a special case. However, weak sustainability is not sufficient for sustainable
development, since the latter cannot exclusively be defined with reference to economic development and
the environment.
3. Extension to the social context
3
.
1
. Sustainability and social capital To comprehensively address the challenge of
sustainable development, the above framework must be extended to the social context of develop-
ment, and the terms of sustainability must be reformulated from an overall perspective:
The sustainability of a system should be judged on the whole system, not just part of it
Gowdy and O’Hara, 1997: 243. Again, questions must be addressed about the
objective and feasibility of sustainable development. In other words, sustainability must be defined with
respect to human-ascribed system goals objective, and the functioning of the overall system feasibil-
ity. This can only be assessed with respect to the ecological, economic and social capital of an area.
Ecological and economic capital, as well as related concepts of sustainability, are defined above. Yet,
the concepts of social capital and social sustainabil- ity are more elusive cf. Barbier, 1987; Tisdell, 1988;
Munasinghe, 1993; Berkes and Folke, 1994; Khan, 1995; O’Hara, 1995; McPhail and Jacobs, 1996;
Atkinson et al., 1997.
Munasinghe 1993 referred to socio-cultural sustainability as a concept which seeks to maintain
the stability of social and cultural systems, including the reduction of destructive conflict. This is consis-
tent with to the WCED 1987 definition of sustain- able development, which is primarily based on
ethical principles of social justice, including a concern for equity within and between generations
— especially the satisfaction of basic human needs and alleviation of poverty — as well as a concern
for peace and security. Moreover, as defined at the World Bank cf. McPhail and Jacobs, 1996, socio-
cultural sustainability would at least require main- taining some critical components of social capital.
In general terms, social capital socio-cultural capital, cultural capital refers to a society’s capa-
bility to deal with social, economic and environmen- tal problems and be active in shaping the
development of the overall system cf. Berkes and Folke, 1994. It consists of socio-cultural values and
norms, learned preferences, human capital and labor force, local knowledge of the environment,
social competence and institutions, human health and life expectancy, as well as cultural and social
integrity, and social cohesion.
Social capital is multifunctional. It embraces essential factors of economic production, provides
a basis for collective action within society,
1
and is in itself an essential input factor of social capital
accumulation, including health care.
2
Moreover,
1
In a general anthropological sense, ‘culture’ consists of a set of rules for a society, and implies commonality Berkes and
Folke, 1994.
2
Classical examples are described in economic models of learning and endogenous technical progress. Moreover, apart
from human capital and the labor force, the social system provides functions which contribute to the sustainability of the
economic system and production process. These sustaining functions are usually performed outside the boundaries of the
production process itself, in the so-called household sector and in human communities Gowdy and O’Hara, 1997.
social capital is a valuable asset as such. In partic- ular, human health, literacy and life expectancy,
cultural and social integrity, and social cohesion are components of human well-being cf. UNDP, 1990;
Atkinson et al., 1997. These components of social capital should be considered in a social welfare
function, in addition to environmental quality and per-capita income. Furthermore, objectives of
macroeconomic stability — such as full employ- ment, price level stability, and other economic goals
— are determinants of individual and social well- being. Correspondingly, we can represent social
welfare as an increasing function of aggregate income Y, macroeconomic stability M, social cap-
ital S, and ecological capital Q:
3
U = UY,M,S,Q with U
Y
, U
M
, U
S
, U
Q
\ 0,
U
YY
, U
MM
, U
SS
, U
QQ
1 This ‘socio-ecological-economic value function’
implies an extension of the above ecological-eco- nomic framework to the social and macroeconomic
context of human development. It enables formal analysis and definition of sustainability terms, going
beyond the original conception of weak and strong sustainability, which is exclusively based on objec-
tives of economic development and environmental preservation. The social welfare function Eq. 1
provides an integrated framework for addressing trade-offs across the various economic, social and
ecological system goals. In practice, these trade-offs must be evaluated through an adaptive process of
optimization for each location and each time Bar- bier, 1987.
3
.
2
. Defining sustainability from a socio-ecological-economic perspecti6e
Using the socio-ecological-economic value func- tion Eq. 1, we can formally define terms of weak
and strong sustainability. As illustrated below, weak sustainability requires keeping the aggregate
value U at least constant over time. But weak sustainability cannot exclusively be defined with
reference to income growth and environmental change. Social and macroeconomic change must
also be taken into account. Likewise, strong sustain- ability can no longer be restricted to issues of
maintaining some compartment of natural capital intact. Rather; it is respectively defined in terms of
economic, social and ecological sustainability:
weak sustainability: U: = U
Y
Y: + U
M
M : +U
S
S: + U
Q
Q: ] 0 2a
strong sustainability:
economic sustainability: U
Y
Y: + U
M
M : ]0
2b
social sustainability: S: ] 0
2c
ecological sustainability: Q: ] 0
2d economic de6elopment
with constant population: Y: ] 0
2e Minimum requirements for ecological and social
sustainability are non-decreasing stocks of ecolog- ical and social capital, respectively. Economic sus-
tainability requires that the aggregate value of income growth and change of macroeconomic
performance will not decrease over time. This represents the traditional trade-off among macro-
economic policy goals, namely, adequate income growth, full employment, and price-level stability.
This concept of economic sustainability is not equivalent to that of very weak sustainability. The
former requires macroeconomic stability including adequate income growth, while the latter repre-
sents the minimum requirement for economic devel- opment which is simply defined in terms of
per-capita income or, for constant population, aggregate income.
As a common feature, strong sustainability terms are defined within the realm of one partial system:
economy, society, or the environment. By contrast, the concept of weak sustainability is less restrictive
than any principle of economic, social, or ecological sustainability. It requires that the aggregate value
of economic, social, and ecological capital will be maintained intact over time, rather than to sustain
economic, social, and ecological capital separately.
4
4
The aggregation weights U
Y
, U
M
, U
S
and U
Q
correspond to the marginal value marginal social utility of aggregate
income and the current state of the economic, social and ecological system, respectively.
3
U
Y
and U
YY
etc. denote the first-order and second-order derivatives of U with respect to Y, etc.
3
.
3
. Indi6idual utility and social welfare Weak sustainability is defined above as a com-
prehensive concept that entails strong sustainabil- ity principles as special cases, and allows one to
take into account trade-offs across the various system goals. It implies consideration of social
values of income, macroeconomic stability, social capital, and environmental quality. This is a pre-
requisite for socially optimal resource allocation, which demands that resources should be allocated
to their highest-valued uses. For free-market economies, the values used for making such judg-
ments are assumed to be those of private con- sumers,
while social
optimality involves
a statement about the desired distribution of re-
sources and resource rights. Moreover, defined as non-decreasing social welfare, weak sustainability
implies a principle of intertemporal equity; a prin- ciple which has been discussed extensively, and
which must logically be extended to interpersonal equity, or distributive justice, in order to be con-
sistent with the core idea of sustainable develop- ment. This does not necessarily imply an equal
treatment principle. Rather, we can reformulate the social welfare function 1 as a weighted sum
of individual utilities:
U =
N i = 1
g
i
·u
i
y
i
,M,S,Q 3
For each individual i i + 1,...,N, utility u
i
is defined as a function of individual income y
i
as well as the economic, social, and ecological system
conditions M, S and Q, that are the same for all inhabitants of a neighborhood or region. For the
aggregation, individual utility weights, g
i
, are used. These weighting factors are fundamental for
determining a social optimum which integrates economic efficiency and social equity require-
ments. They constitute a normative element which is made explicit in Eq. 3, and which is implicit in
a conventional economic framework of general market equilibrium cf. Negishi, 1960. While
practical difficulties may be involved with the task of establishing utility weights, it seems, for ethical
reasons, more appropriate to use explicit rather than implicit utility weights. This is particularly
justified in the presence of poverty and distribu- tional concerns.
5
On the basis of the Bergson-type social welfare function Eq. 3, we can redefine the formal
condition for weak sustainability. It requires that the value of social welfare U does not decrease
over time. For constant population N, weak sus- tainability is defined in terms of intertemporal
welfare change, this is the weighted sum of in- tertemporal change of individual utility u;
i
, plus an additional term which results from conceivable
change of utility weights: U: =
N i = 1
g
i
·u;
i
+
N i = 1
g; ·u
i
] 4a
By contrast, indi6idual impro6ement requires non- decreasing individual utility u:
u;
i
= u
i
y
i
·y;
i
+ u
i
M ·M
: + u
i
S ·S: +
u
i
Q ·Q: ] 0
4b Weak sustainability requires that the total value
of social welfare should be maintained intact over time. It does not necessarily imply improvement
for all individuals. Rather, weak sustainability requires that individual losses are balanced by
adequate improvements for other individuals, such as the aggregate value of social welfare will
not decrease over time. In contrast, if effective compensation is required for social stability, then
Pareto improvement will be necessary for sustain- able development. Thus, both criteria of weak
sustainability and individual improvement of all must be satisfied.
3
.
4
. Population growth, economic de6elopment, and sustainability
Up to this point, I have abstracted from popula- tion growth, though this is generally seen as major
threat to sustainable development. Yet, popula- tion growth implies more pressure on natural
capital, resulting from land use change and re- source consumption. Moreover, under considera-
5
The assessment of such weights may be based on an empirical analysis of democratic decision processes voting,
questionnaires, interviews, or group decisions in a participa- tory process.
tion of population change, terms of economic development and weak sustainability need to be
reformulated. In simple terms, economic development can be
referred to as growth of per-capita income. The latter is defined as total income Y divided by
population N, while total income is the sum of individual incomes y
i
: total income:
Y =
N i = 1
y
i
5a average per-capita income:
y = Y
N 5b
Correspondingly, economic
de6elopment growth of per capita income requires that the
growth rate of aggregate income must exceed the population growth rate:
y; = y· Y:
Y −
N: N
n
] 6
This is only an imperfect proxy for economic development, even if properly defined in the Hick-
sian sense, and thus sustainable by definition. Based on a measure of average income, it is not
sensitive to distribution inequality and lack of macroeconomic stability. By contrast, the concept
of weak sustainability embraces distributional concerns in an integrated framework with trade-
offs across economic, social and ecological system goals.
I have defined weak sustainability as non-de- creasing social welfare. For constant population,
this is represented in Eq. 4a as the weighted sum of intertemporal change of individual utility, and
the aggregate welfare change as a result of possi- ble alteration of distribution weights. In the case
of population growth, this expression must be extended. An additional term appears, which is
equal to the product of population growth times social welfare:
6
weak sustainability with population growth: U: =
N i = 1
g
i
·u;
i
+ g;
i
·u
i
+ N:
N ·
N i = 1
g
i
·u
i
] 7
Using Eq. 4b and the subsequent set of definitions
U
Y
=
N i = 1
g
i
· u
i
y
i
· y;
i
y; =
N i = 1
g
i
· u
i
y , U
M
=
N i = 1
g
i
· u
i
M ,
U
S
=
N i = 1
g
i
· u
i
S ,
U
Q
=
N i = 1
g
i
· u
i
Q 8
we can reformulate the equation on the left, as follows:
U: =
N i = 1
g
i
· u
i
y
i
·y6;
i
+ u
i
M ·M
: + u
i
S ·S: +
u
i
Q ·Q:
+ g;
i
·u
i
+ N:
N ·U
= U
Y
N·y; + U
M
·M : +U
S
·S: + U
Q
·Q: +
N i = 1
g;
i
·u
i
+ N:
N ·U
9 Under consideration of
N i = 1
y; = N·y; = Y: − N:
N ·Y
10 we finally get a modified condition for weak
sustainability: U: = [U
Y
Y:. + U
M
M : +U
S
S: + U
Q
Q:] +
N i = 1
g;
i
·u
i
n
+ N:
N ·U − U
Y
Y
n
] 11
The first term in square brackets corresponds to the original expression for weak sustainability
with constant population, equal utility levels and equal utility weights for all individuals. The sec-
ond bracket represents the change of social wel- fare due to a conceivable change of utility
weights. For practical reasons, we may assume constant weights, at least for short-term compari-
sons on an annual base. In this case, the second bracket term would vanish.
6
Remember that social welfare is defined as U =
i = 1 i = N
g
i
u
i
, and compare the special case with equal individuals equal
weight and equal utility: U = Ngu [ U: = Ngu; + g;u + N:gu = Ngu; + g;u + N:NU.
The third pair of square brackets contains the expression for intertemporal welfare change as a
result of population change. Under the assump- tion of decreasing marginal utility of aggregate
income U
Y
\ 0 and U
YY
B 0 and growing popu-
lation, this expression is positive: N:
N ·U − U
Y
Y =
N: N
· U
Y −
U Y
·Y ]
0 for N: ] 0 B
0 for N: B 0 By contrast, for declining population this ex-
pression would be negative. Thus, weak sustain- ability is not easily defined, if population and
distribution weights change. However, some gen- eral rules can be proposed.
For decreasing
population, the
rule is
straightforward: N: B 0:
U
Y
Y: + U
M
M : +U
S
S: + U
Q
Q: ]
− N:
N ·
U Y
− U
Y
·Y
n
] 13
Since the expression in square brackets is nega- tive, the term on the right is positive. In this case,
the value of intertemporal change of the total capital must exceed some positive value. This is
determined by the absolute value of the popula- tion decline rate, times the difference between
society’s average and marginal utility of income, times aggregate income.
By contrast, in case of population growth, the sign of this term changes; it is negative. This
means that the welfare of the original population could decrease, while the outcome would be
judged as aggregate welfare improvement, and thus considered weakly sustainable. Yet, as
proposed above, Pareto improvement may be necessary for sustainable development. Corre-
spondingly, a rule is required which is more re- strictive. For this purpose, I suggest, as an
approximation for practical uses, that the original weak sustainability rule Eq. 2a can be applied
as a ‘safe’ criterion in the case of population growth:
N: ] 0: U
Y
Y: + U
M
M : +U
S
S: + U
Q
Q: ] 0 14
In other words, the original value principle of weak sustainability, which calls for maintaining
the total value of capital intact over time, is a ‘safe minimum rule’ for cases with population
growth and constant distribution weights. We may use this approximation Eq. 14 with the
qualification that the social welfare function Eq. 3 is defined as the weighted sum of individual
utilities, and that the set of definitions in Eq. 8 applies for the marginal social values of aggregate
income, macroeconomic stability, social capital, and environmental quality.
4. A ‘sustainability-based social value function’
