A ‘sustainability-based social value function’

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’

Population growth will have impact on the opportunity space, and thus the feasibility set of sustainable development. The boundaries of the opportunity space for sustainable development are determined by economic, social, and environ- mental system capacities, and critical limits of capital beyond which the system could not re- cover from stress or shocks. Altogether, this im- poses limitations upon human activity in the long-run that need to be anticipated for sustain- able development. Correspondingly, an adequate value function must not only integrate individual and social values, but also account for limits of criticality, namely, ecosystem resilience and the satisfaction of basic human needs Hediger, 1999: 1. Sustainable development is a normative princi- ple that calls for meeting basic human needs. The latter are conventionally defined in terms of adequate supply of food, water, health care, shelter, and minimum education WCED, 1987; Moon, 1991. These minimum standards of development are physical, but also cultur- ally and economically determined Chichil- nisky, 1977, and cannot be traded off against each other and against market commodities Pearce and Turner, 1990. In an aggregate form, this can be defined in terms of a ‘mini- mal’ level of consumption or income, and rep- resented by a poverty line cf. Atkinson et al., 1997. 2. Another minimum requirement for sustainable development is compliance with environmental capacities. This does not necessarily imply preservation of current assimilation and regen- eration capacities of the ecosystem. Rather, as Perrings 1996 pointed out, ‘the best that can be achieved through environmental manage- ment is the stabilization of the system at sus- tainable levels of activity, and this is the same as the protection of system resilience.’ Corre- spondingly, thresholds of ecosystem resilience must be considered in any viable concept of sustainable development cf. Holling, 1973; Common and Perrings, 1992. This has also been referred to as a concept of ‘critical natu- ral capital’ Pearce et al., 1994. So far, I have introduced minimum conditions of ecological and economic sustainability that re- strict the opportunity space for sustainable devel- opment. These constraints limits of criticality are defined in terms of thresholds of ecosystem resilience and minimum income to satisfy basic human needs, Q c and Y c , respectively. Yet, to comprehensively address the challenge of sustainable development, critical levels of social capital and macroeconomic performance must also be included. As mentioned above, social sus- tainability refers to a concept which seeks to maintain the stability of social and cultural sys- tems. Correspondingly, ‘critical social capital’ S c may usefully be defined as minimum level of social cohesion beyond which the social system risks collapse. In a similar form, one may imagine maximum levels of unemployment and inflation, M c , above which the socio-economic system may abruptly change. Thus, to coherently address is- sues of sustainable development, critical levels Q c , Y c , S c , and M c must be taken into ac- count with reference to environmental quality, basic needs, social capital, and macroeconomic stability. Using the social welfare function Eq. 1, as simplification of the more adequate form Eq. 3, we can define the opportunity space for sustainable development. It is restricted by the current social indifference curve, U = UY ,M ,S ,Q , which is historically determined by the present state of development Y , as well as present levels of macroeconomic stability M , so- cial capital S , and environmental quality Q , as well as the critical levels Y c , M c , S c , and Q c . As illustrated in the economy-environment sphere of Fig. 1, the consideration of these critical levels leads to a sustainability frontier that is broken into three parts. For given levels of macroeconomic stability M \ M c and social capital S \ S c , and for any level of aggregate income Y \ Y c and environmental quality Q \ Q c , it is equal to the social indifference curve U which is based on individual preferences. By con- trast, for Y = Y c and Q = Q c , the sustainability frontier lies on the boundaries imposed by Q c and Y c , respectively; while for any Y B Y c or Q B Q c , no terms of sustainability and sustain- able development can be defined. In other words, if the starting conditions are not in the interior of the maximum sustainability space {Q \ Q c , Y \ Y c , M \ M c , S \ S c }, sustainable devel- opment is not feasible. Rather, a process of transi- tion is required to enter the opportunity space of sustainable development. The boundaries of this opportunity space are crucial for sustainable development analysis. Any modification of the system across these boundaries of ecosystem resilience, basic needs, critical social capital, or critical levels of unem- ployment and inflation, could impose irreversible change. In economic terms, this means that such alterations would significantly reduce the variety of possible choices for a long time into the future Henry, 1974, and would be infinitely costly to reverse Arrow and Fisher, 1974. This involves a fundamental problem for decision making and the Fig. 1. The opportunity space for sustainable development and the sustainability-based social value function evaluation of alternative development paths within the opportunity space of sustainable devel- opment. Along the original indifference curve U , which is part of the sustainability frontier in Fig. 1, irreversibility would not be anticipated. But irreversible change would suddenly appear when the system reaches either limit Q c or Y c . This may not in general be socially desirable. Rather, a social value function should be conceptualized so as to anticipate potentially irreversible effects at the boundaries of the sustainability space. Proposition: A sustainability-based social 6alue function matches values based on aggregate indi- vidual preferences, the current state of develop- ment of economy, society and the environment Y , M , S , Q , and socio-ecological-economic system requirements of sustainability critical lim- its Y c , M c , S c , and Q c , and anticipates po- tentially irreversible changes at the boundaries of the opportunity space for sustainable development: W = WY, M, S, Q, Y , M , S , Q 15 for Y \ Y c , M \ M c , S \ S c , Q \ Q c with W Y , W M , W S , W Q \ 0, W YY , W MM , W SS , W QQ B lim Y “ Y c W Y Y, M, S, Q, Y , M , S , Q = , lim M “ M c W M Y, M, S, Q, Y , M , S , Q = lim S “ S c W S Y, M, S, Q, Y , M , S , Q = lim Q “ Q c W Q Y, M, S, Q, Y , M , S , Q = WY , M , S , Q = UY , M , S , Q W Y Y , M , S , Q = U Y Y , M , S , Q , W M Y , M , S , Q = U M Y , M , S , Q W S Y , M , S , Q = U S Y , M , S , Q , W Q Y , M , S , Q = U Q Y , M , S , Q This function is defined for Y \ Y c , M \ M c , S \ S c and Q \ Q c , only. It is based on a system perspective, and, apart from current devel- opment Y , M , S , Q , different from the indif- ference curve U . The new value function W does asymptotically approach the minimum standards Y c , M c , S c and Q c , and implies equivalent combinations of Y, M, S and Q that are above those of the original value function U which is exclusively based on individual preferences. Cor- respondingly, the sustainability-based social value function W does not intersect the preference- based social value function U . This is illustrated in Fig. 1 for given M and S , and the indifference curves U and W . An important feature of the sustainability- based social value function is the implicit balance across different approaches. Given the current state of development Y , M , S , Q , aggregate preference maximization is given priority for the evaluation of marginal changes, while more con- servative approaches will be dominant if the sys- tems moves toward any boundary of the sustainability space. The W-function implies an anticipation of potentially irreversible changes at the boundaries of the opportunity space for sus- tainable development. It is more sensitive to mod- ifications of the overall system than the original welfare function U. In other words, from an integrated sustainability perspective, which is rep- resented by the social value function W, the trade- offs among the different system goals are higher valued than in a weak sustainability framework, which is based on the individualistic value func- tion U. This implies that, for society to be indif- ferent in the course of development, income growth that would be required to compensate for the degradation of social and ecological capital is higher in an integrated sustainability framework than an aggregate value function based on indi- vidual preferences would suggest. In like manner, any sacrifice of income would need to be compen- sated by an improvement of the overall system to an extent which is higher than traditional welfare concepts would suggest.

5. Conclusion