1. Natural resources and economic growth: towards a definition of sustainability

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1.1 Production and exhaustibility
1.2 Justifying a conservationist strategy
1.3 Sustainability and reproducibility
1.4 Sustainability and individual rationality
1.5 Conclusion

That the limited availability of natural resources may threaten economic growth has preoccupied economists since the birth of the discipline. Thomas Malthus, David Ricardo, John Stuart Mill, and other classical economists have paid so much attention to the limits to growth caused by finite natural resources that they have given these limits a central role in their analysis of the long-term dynamic evolution of market economies towards a stationary state. The gloomy conclusions reached by those early economists have received a modern formulation and further support in recent years with the works of G. Hardin and Baden, 1977; J. W. Forrester, 1971; and H. S. D. Cole et al., 1973.

1.1 Production and Exhaustibility

Modern economic theory allows us to distinguish between different characteristics of natural resources which are directly relevant to the problem in question. A resource is said to be exhaustible if one can find a pattern of use for this resource such that it will be depleted in finite time. Clearly, almost any natural resource, with perhaps the exception of solar energy, is exhaustible. A resource is said to be renewable if one can find a pattern of positive use such that its stock does not shrink over time. One can think of a fishery or of soil fertility as good illustrations of a renewable resource. Of course, if concern is about the issue of economic development and the possible constraints which natural resources may place on it, interest will naturally focus on the analysis of exhaustible and non-renewable resources which are essential. The definition of the latter concept is intuitive, though, as we shall see, it is not very useful: a resource is essential in production if 'the output of final goods is nil in the absence of the resource' (Dasgupta and Heal, 1974: 4). A similar definition can be used for a resource essential in consumption.

As pointed out by Stiglitz (1974), there are at least three ways to counterbalance the negative effects of essential resources on production: technical progress, increasing returns to scale, and substitution. The third factor needs to be examined in detail. Three different situations may again arise when one analyses the possibilities for substituting a reproducible input, say capital, to an increasingly scarce essential resource. The natural economic concept for measuring substitution possibilities is the elasticity of substitution (for a detailed exposition of what follows, see Dasgupta and Heal, 1974, 1979: 196-200). Let us focus on the class of CES production functions such as:

F(K,R,L) = (a 1K(s -1)/s +a 2R(s -1)/s +(1-a 1-a 2)L(s -1)/s ) (s -1)/s

where a 1, a 2, 1-a 1-a 2 > 0, and s > 0, s ¹ 1, K stands for reproducible capital, R for the flow of resources used in production, L for the labour force, and F for the final net output. If a > 1, F(K,O,L) > 0: the resource is not essential for production. If s < 1, the average product of the resource is bounded from above owing to the low degree of substitutability between R and K or L; therefore, if the resource stock is finite, it can only support a finite amount of output and, for infinite time, the only sustainable level of consumption is zero. In a way, the resource considered is trivially essential: no substitution allows the economy to escape the final doom. The really interesting case to analyse is that where s = 1. In such a case, as is well known, the above production function reduces to a Cobb-Douglas:

Y = Ka 1Ra 2L1-a 1-a 2

The question which arises is: does there exist a positive level of consumption which can be sustained for infinite time in this economy, assuming that there is no technical progress nor population growth?' The answer is 'yes', if the elasticity of output with respect to capital, a 1, exceeds that with respect to exhaustible resources, a 2. We normalize by setting L = 1, and assume that there is no depreciation of the capital stock. S0, the initial stock of resources, and K0, the initial stock of capital being given, the maximum constant consumption flow, C%, is given by:

Such a consumption programme can be sustained for infinite time, with the saving rate being set at a 2. It implies the following:


where t stands for time, starting at time zero. The programme defined by equations (3) to (6) above is worth examining in detail:

  1. The amount of resources used at time t, Rt, declines over time which does not cause the consumption flow to fall owing to the possibility of substituting the growing capital stock for the shrinking resources. In infinite time, the entire stock, S0, is depleted.
  2. As noted above, a, must be higher than a 2. Indeed, it can be shown that, if a 2 > a 1—the elasticity of output with respect to capital is low compared to that with respect to natural resources output will eventually decline to zero. As is the case when the elasticity of substitution is smaller than one, the resource is trivially essential: substitution possibilities do not allow a positive consumption flow to be sustained in infinite time.
  3. The programme defined above is intertemporally efficient: it can indeed be proved that there is no feasible programme which gives at least as much consumption in every period and strictly more in some (see Dasgupta and Heal, 1979: ch. 7).
  4. As shown by Solow (1974), it is also an optimal programme if the resource-managing authority follows the Rawlsian welfare approach to the intergenerational problem of optimal resource utilization by applying the maximin principle. Indeed, the interests of each succeeding generation are met when the minimum welfare which can be guaranteed to all of them is maximized.
  5. The amount of the resource used at time zero, R0, varies positively with S0 and negatively with K0. Comparing two economies, A and B. with the same amount of natural resources but where one of them, A, has a lower capital stock than the other, it can be shown that, to sustain the maximum constant consumption flow through time, A exhibits a higher initial rate of resource exploitation than B. Since both extraction paths must exhaust the resource stock over infinite time, the rate of extraction falls more rapidly in A than in B. and the extraction path curves cross once in the plane (Rt, t). Note also that, since A is poorer, the constant consumption flow it may enjoy is also lower. Finally, as given by equations (4) and (6), the accumulation of capital proceeds at a quicker pace in the capital-rich economy B. Diagramatically, these processes can be depicted as in Figure 1.1. It is therefore evident that high initial rates of resource exploitation are not incompatible with a development process characterized by a sustainable consumption flow. For LDCs which are comparatively resource-rich economies, high rates of extraction of environmental resources may be part of a sustainable development strategy, and should not necessarily be confused with destructive overexploitation.

Fig. 1.1 Constant consumption flows and extraction paths of a capital-rich economy, B. and a capital-poor economy, A

  1. If disembodied technical progress takes place, for instance at a constant rate l , the exhaustible resource, though essential, does not prevent a positive sustainable level of consumption, even if a 2 > a 1: one can always find a pattern of extraction Ri, such that , does not fall to zero. The same argument evidently holds for any production function if resource-augmenting technical progress is assumed to operate at a constant rate.
  2. We have not yet considered the possibility of an ever-growing level of consumption in the economy under concern. In the above model, it can be shown that such a growth path is actually possible if a constant level of consumption is feasible (that is, if a 1 > a 2): it just requires that capital is accumulated at a sufficiently high rate in the initial periods (see Dasgupta and Heal, 1979: ch. 10). To say that growing consumption is possible does not imply that it is optimal: 'A positive rate of impatience, no matter how small, implies that it is judged optimal to allow the economy to decay in the long run, even although it is feasible to avoid decay' (Dasgupta and Heal, 1979: 299).

1.2 Justifying a conservationist strategy

Up to now, we have examined the possibility for an economy to maintain a constant level of consumption over an infinite horizon with a given stock of a non-renewable resource which is essential in production. We have seen that, if a constant level of consumption is sustainable, then it requires that the resource stock is depleted at a decreasing rate. A fortiori, this also holds for a renewable resource: here, sustainability does not require the resource base to he preserved. Furthermore, it must be emphasized that in all the cases where the resource is not essential (in production), optimality may require its complete exhaustion in finite time. In other words, when technical conditions exist that render a resource (eventually) dispensable or superfluous, it may be quite sensible for a society to destroy it since, by doing so, it does not threaten future consumption and production possibilities.

Therefore, the conservationist view, following which the resource base is to be maintained, must be grounded elsewhere. There are at least four assumptions made in the model presented above which leave some space for a conservationist strategy to be vindicated. The first one is that of perfect information at the disposal of the decision-maker: anything relevant to the problem is known with certainty at the time of the decision. In the real world, however, information on natural resources is far from perfect. It is not at all clear, for example, that all future possible uses of the resource are correctly perceived today by the decision-maker: for instance, non-anticipated uses of the resource may be discovered some time in the future which will make its disappearance extremely prejudicial to the society. Under these conditions, it may be advisable to keep a minimum amount of a resource: in the words of Henry, 'the mere prospect of getting fuller information, combined with the irreversibility of the non-preservation alternative, brings forth a positive option value in favour of preservation' (Henry, 1974a: 90).

The argument about incomplete information may however be turned the other way round: at the time of decision-making, information is not necessarily available on the possible appearance of perfect substitutes for the resource or on the exact size of the resource stock, which may render too conservationist a strategy uneconomical. For instance, from 1907 to 1957, the services rendered by a ton of coal have increased tenfold because of reductions in the energy required for mining, transport, and electricity generation and transmission (Fisher, 1981: 95). Or, from 1947 to 1972, the estimated world oil reserves also increased tenfold (see Fisher, 1981: 93). The effect of uncertainty may therefore be ambiguous. However, it is clear that irreplaceable assets, for which no close substitute exists, should be given some value per se, so as to prevent their complete destruction when this outcome can be avoided (see e.g. Krutilla, 1967; Henry, 1974a, b). This is probably the argument which underlies propositions to classify as world patrimony geographical zones of particular ecological interest (for instance, the Antarctic and, presumably, in the near future, part of the Amazonian forest) or to maintain a minimal biodiversity by protecting endangered biological species.

The second assumption made in the above model is that the resource in question is of no value except as a productive input. Exhaustible resources, such as places of natural beauty, pure air, or unpolluted rivers, may however be directly valuable to the consumer. As expressed by John Stuart Mill:

A world from which solitude is extirpated, is a very poor ideal. Solitude, in the sense of being often alone, is essential to any depth or meditation of character; and solitude in the presence of natural beauty and grandeur, is the cradle of thoughts and aspirations which are not only good for the individual, but which society can ill do without. Nor is there much satisfaction in contemplating a world with nothing left to the spontaneous activity of nature; with every rood of land brought into cultivation, which is capable of growing food for human beings; every flowery waste or natural pasture ploughed up, all quadrupeds or birds which are not domesticated for man's use exterminated as his rivals for food, every hedgerow or superfluous tree rooted out, and scarcely a place left where a wild shrub or flower could grow without being eradicated as a weed in the name of improved agriculture.... If the earth must lose that great portion of its pleasantness which it owes to things that the unlimited increase in wealth and population would extirpate from it, for the mere purpose of enabling it to support a large, but not a better or happier population, I sincerely hope, for the sake of posterity, that they will content to be stationary, long before necessity compels them to it. (Mill, 1848: 115-16).

At some point therefore, it makes sense also to consider natural resources as consumer goods, a positive utility being associated with their mere presence, or their degree of purity. There is therefore a possible trade-off between their contribution as a productive input and the utility they bring when left unused. By analogy with a resource essential in production, exhaustion of a resource essential in consumption will never be optimal. Note also that it has been repeatedly suggested in the literature that environmental resources, as consumer goods, are superior goods: their demand is likely to have a very high income elasticity. Therefore, one may expect that, with the growth in income following from economic development, a demand for higher environmental standards will also develop. This must be taken into account in the decision process when, for instance, irreversible changes are to be brought about in the natural environment. Of course, if one does not know with certainty how preferences will be shaped in the future, then, as explained above, an option value must be given to the resource, that is, conservation is to be favoured. For instance, some may think that, in the future, environmental resources will be highly valued, while others may argue that people in the future will be satisfied with an almost entirely artificial world. Irreversibility implies that, in current decisions, more attention should be given to the former than to the latter possibility, even if one may think that both scenarios are equally likely: for the choice to be optimal, it must be biased towards preservation by taking into account the option value of the natural resources (for more details and a formal proof, see Henry, 1974a).

A third assumption made in the above models is that one can always substitute capital for environmental resources in the production functions. In the real world, technical conditions do not involve such possibilities for smooth substitution between these two factors, making unlimited growth in the presence of exhaustible resources a less likely outcome.

As for the fourth assumption, it lies in the smoothness of technical processes: it is indeed assumed that changes brought about by an optimal exploitation of the resource are slowly cumulative (there is no discontinuity). Though such an assumption may appear reasonable when it concerns resources such as fossil energy, it is hardly appropriate for natural resources involving ecological processes: just think of land, forests, pure air, or clean water. For these types of resources, there may well be threshold levels of Exploitation beyond which the whole system moves in a discontinuous way from one equilibrium to another.

One of the problems is that we do not know what lies ahead. Our knowledge of the real processes at work is simply too poor. As expressed by Broeker, 'we play Russian roulette . . . [and] no one knows what lies in the active chamber of the gun' (quoted in Chakravarty, 1990: 70). To take an example, the global warming-up resulting from the greenhouse effect will cause an increase in the mean global temperature estimated from 1.5 °C to 5 °C in the next fifty years (and from 3 °C to 10 °C for the next ninety years) (Schokkaert, 1992). In the present state of our knowledge, we are not able to predict more accurately the global warming-up, not to speak of its global consequences, even though it is clearly an issue to which an impressive amount of scientific work and a lot of attention from political authorities have been devoted in recent years. In general, one can surmise that, if there exists a threshold level beyond which complete disaster is a possibility, it is never optimal to go beyond it.

1.3 Sustainability and Reproducibility

The aforementioned arguments in favour of conservation rest on the idea of irreversibility: irreversibility is indeed at the heart of the problem. That the use of a mineral or of fossil energy in a production process is irreversible is quite obvious, total recycling never being possible (according to the second law of thermodynamics). The same holds true when there are use thresholds beyond which a global and irreversible change occurs in the ecosystem (e.g. desertification of the Sahelian area) or when destruction of a place of natural beauty (e.g. Hells Canyon—see Krutilla and Cicchetti, 1972; Fisher, 1981: 139-63—the Forest of Fontainebleau, or the Garibaldi pine tree in Rome) is contemplated. It nevertheless bears emphasis that many natural resources are, within given limits, renewable. Pure air or clean water are renewable resources and their use does not necessarily bring about irreversible changes.

Every ecosystem is characterized by a carrying capacity, a notion which can be defined in the present context as the amount of the natural resource that can be exploited without endangering the reproduction of the ecosystem. Reproducibility or conservation are directly related to the notion of carrying capacity: a level of production making use of a natural resource is reproducible if it lies within the upper limit set by the carrying capacity of the ecosystem within which it takes place. In other words, reproducibility refers to 'the ability of a system to maintain its productivity when subject to stress and shock, where the former is "a regular, sometimes continuous, small and predictable disturbance, for example the effect of growing soil salinity" . . . and the latter is "an irregular, infrequent, relatively large and unpredictable disturbance, such as is caused by a rare drought or flood or a new pest". The key is to reduce resource degradation and the associated stresses and shocks to a level where the natural processes and functions of the agro-ecosystem can counteract them' (Barbier, 1989: 441).

This concept of reproducibility or conservation should be carefully distinguished from the concept of sustainability: as shown above, sustainability (of a consumption level, or of a development process) may require the ultimate destruction of a resource or a change in the ecosystem. Reproducibility is a more stringent criterion in that it requires the resource base to be preserved. When using the concept of sustainability, we are concerned about whether a level of well-being (or of production. or of con gumption) can be maintained over an infinite horizon, whereas, when referring to reproducibility, we are not only concerned with the possibility of sustaining a level of well-being but also with the way this can be done since we require the stability the ecosystem within which human intervention takes place. The concept of reproducibility has a definite advantage over that of sustainability, namely that, in some instances, it has an operational content (the resource base cannot be destroyed) which is lacking in the concept of sustainability: whether a development process is 'sustainable' or not is, in general, unverifiable. On the other hand, though the concept of reproducibility helps to characterize human intervention in an ecosystem, it says nothing about its desirability (or optimality), except under ultraconservationist views considering the current status quo as preferable to anything else. The weakness of the latter concept is clear enough when the current ecosystem is itself the result of former non-reproducible human interventions, such as the conversion of wild forests into arable land, or when the resource base would disappear in the absence of direct human intervention to sustain it. In the words of Brookfield, 'it does no violence to sustainability to point out that conversion of a forest into well-managed agricultural land is not degradation if the product of the new use is of greater total utility to people, and can be maintained through time' (Brookfield, 1991: 48).

Management of renewable resources, such as animal population and forests, and the concept of reproducibility can be illustrated with the help of a well-known diagram first developed to analyse fisheries (see Dasgupta and Heal, 1979: 113-17; Fisher, 1981: 79-86). The crucial feature of a renewable resource is the natural growth law according to which the growth of a resource is a function of its stock. For the sake of simplicity, we shall assume that the latter is the only variable affecting the growth of the resource. Furthermore, the relation between growth and stock is not monotonic. Indeed, the environment has a carrying capacity for the resource, a maximum level of population beyond which the growth of the resource is negative. Before this point, however, the growth-population curve takes on the form of a logistic curve. The relation can be represented as in Figure 1.2.

In this diagram, Xc represents the maximum population the environment can sustain, i.e. the carrying capacity. X0 represents the minimum population size below which the growth of the population is negative: the population dies out. For many natural resources, X0 = 0. However, for some animal species, X0 can be strictly positive, either because, below this level, the population is too scattered to assure its reproduction (whales or elephants might be examples), or because it lacks the necessary genetic diversity. Between X0 and Xc, the growth curve takes on a bell-shape, with a maximum in Xm. This level is often called 'maximum biological yield. Let us now introduce human intervention in the form of fishing efforts resulting in fish catches. Since it has the effect of changing the population size, it is measured on the vertical axis as shown in Figure 1.3.

Fig. 1.2. Biological growth law

FIG. 1.3. Catches and biological growth

The curve can be straightforwardly derived from the growth-population curve. It represents the relation between the stock of population and the maximum amount of fish which can be caught while keeping this stock constant. We shall refer to this level of catches as the equilibrium level. A given level of catches is compatible with a conservationist objective and is called reproducible if it is located on the catch-population curve: any level of fishing effort or catches in that area allows the population stock to be maintained. An amount of catches located below the curve allows the population stock to grow (as indicated by the arrows) and is also compatible with a conservationist objective. A given level of catches is called sustainable if it lies beneath the shaded area: despite the changes in population that it may bring about, the level of catches can be maintained for ever. Note also that, as soon as there is human intervention, the equilibrium stock is lower than it would have been if the level of catches were nil (see Xc. in Figure 1.3).6

A last application of the distinction between reproducibility and sustainability can be found in the recent proposals for the reform of conventional methods of national accounting. In the recent literature on environmental economics (see e.g. Dasgupta and Heal, 1979: 245-6; Weitzmann, 1976; Dasgupta and Mäler, 1990; Chakravarty, 1990), it has indeed been repeatedly suggested that conventional national accounting approaches should be modified to better reflect the environmental costs brought about by the processes of income creation. The basic idea is to extend conventional measures of net national income by adding measures of changes in the stock of natural resources. 'In the simplest of cases, where current well-being depends solely on current consumption, real net national product reduces to the sum of the social (or shadow) price of an economy's consumptions and the social (or shadow) price of the changes in its stocks of real capital assets' (Dasgupta and Mäler, 1990: 9), it being understood that capital assets include manufactured capital as well as natural resources. The most important implication of the approach adopted by Dasgupta and Mäler, is that, if an economy simply exchanges natural resources against consumer goods on foreign markets but does not produce anything, it will exhibit a net national product equal to zero. This is because the increased consumption flow is bought at the price of a proportionate reduction of the nation's nature-made capital. Such a result is in total contrast with the conventionally measured national income which may be quite high and even grow if resources are depleted at an increasing rate. The measure gives a more sensible description of the real income generated by oil exports or destruction of tropical forests, when the proceeds of the sales involved are not invested in building up national productive capital. To take another example, compare two economies where the sole production sector is fishing. The first economy 'produces' (at no cost) and consumes the sustainable yield from its resource base while the second economy 'produces' and consumes in one period the entire stock of its resource. According to conventional national accounting practice, the NNP of the second economy in that period would of course be much greater than that of the first economy. According to the practice advocated by Dasgupta and Mäler, however, the reverse would hold true since the NNP of the second economy would just be nil.

The relevance of the new accounting method is particularly evident in the case of developing countries, as suggested by Chakravarty: a look at the world at large would suggest that for the majority of inhabitants on the earth the precariousness of their daily existence has not been significantly reduced by the development process even where there have been increases in per capita GNP.... Neither new technology nor investment in material capital have enabled them to substitute for the loss of their environmental capital stock which has been substantially eroded. The situation has been rendered more difficult by the imitation of an alien life-style especially by the elite in these countries. (Chakravarty, 1990: 70)