Ecological Economics 32 2000 445 – 455
ANALYSIS
Natural capital and sustainability
Jan van Geldrop
a
, Cees Withagen
b,c,
a
Department of Mathematics and Computing Science, Eindho6en Uni6ersity of Technology, P.O. Box
513
,
5600
MB Eindho6en, Netherlands
b
Department of Economics, Vrije Uni6ersiteit Amsterdam and Tinbergen Institute, De Boelelaan
1105
,
1081
HV Amsterdam, Netherlands
c
Department of Economics, Tilburg Uni6ersity and Center, P.O. Box
90153
,
5000
LE Tilburg, Netherlands Received 31 March 1999; received in revised form 24 August 1999; accepted 25 August 1999
Abstract
This paper develops and rigorously analyses a model describing the optimal use of natural capital in a utilitarian framework. Natural capital is treated as an aggregate including exhaustibles, renewables and ‘environmentals’,
performing several functions. It is found that it converges to a steady-state in which it is kept constant by simultaneous investments and use. © 2000 Elsevier Science B.V. All rights reserved.
Keywords
:
Natural capital; Sustainability; Utilitarian framework www.elsevier.comlocateecolecon
1. Introduction
Keywords in any discussion on sustainability are
substitutability and
the second
law of
thermodynamics. The issue of substitutability was already promi-
nently present in early studies by Dasgupta and Heal 1974, Solow 1974a,b, Dasgupta and Heal
1979. These authors augmented Solow’s 1956 neoclassical growth model with a non-renewable
resource. In this simple setting sustainability was identified with the feasibility of maintained per
capita consumption. Together with reproducible capital the raw material from the exhaustible re-
source served as a factor of production in a neoclassical aggregate production function. The
class of production functions with constant elas- ticity of substitution between capital and the raw
material from the exhaustible resource received special attention. It was shown that aggregate
production over time is bounded from above even in the presence of Harrod neutral technical
progress and increasing returns to scale if the elasticity of substitution is smaller than unity. In
that case also total consumption is bounded from above and as a consequence sustainable develop-
Corresponding author. 0921-800900 - see front matter © 2000 Elsevier Science B.V. All rights reserved.
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ment is impossible. If the elasticity exceeds unity then the raw material is not a necessary input and
one could argue that there is no sustainability issue. The special Cobb – Douglas case where the
elasticity of substitution equals unity has therefore attracted special attention. Solow 1974a shows
that a necessary condition for sustainability, meaning sustained production at a level bounded
away from zero, is that the production elasticity of capital is larger than the production elasticity
of the raw material. Another necessary condition is that capital does not depreciate at least not at
a positive constant rate. The latter condition has not received much attention in the sustainability
debate. See Tisdell 1997 for an exception. Stiglitz 1974 allows for exogenous technical
progress, returns to scale and population growth as well as labour as a production factor in the
Cobb – Douglas framework. The necessary condi- tions for sustainability are to be modified. They
become slightly more complicated: increasing re- turns and technological progress are beneficial but
maintaining in this setting a constant rate of per capita consumption becomes more difficult be-
cause of population growth. Matters become sig- nificantly different when renewable resources are
introduced to the model. According to Solow 1974b, there exists ‘quite a lot of substitutability
between exhaustible resources and renewable or reproducible resources’. In the ‘Georgescu-Roe-
gen versus SolowStiglitz’ debate in this journal’s 1997 issue, at least this statement by Solow gets
Daly’s approval Daly, 1997a,b; Solow, 1997. If indeed there is a high elasticity of substitution
between materials from renewable and exhaustible resources then a positive rate of production can
be maintained in the framework set out above. It is sufficient to keep the input of the renewable
resource at a level that can be sustained indefin- itely by the natural growth process of the renew-
able resource. It should, however, be realised that the latter condition is jeopardised in reality, as
stressed by Clark 1997. Therefore, if substitution possibilities between renewable resources and
non-renewable resources are large enough at the production level, the substitution issue seems to
be resolved. However, this interpretation of sub- stitutability ignores that besides substitution in
production there might also be substitution, or rather complementarities, in preferences. If sus-
tainability does not only refer to material con- sumption but has a wider meaning including
well-being depending on amenity values corre- sponding to exhaustible resources, renewable re-
sources or biodiversity, then the original problem might arise again. This concern is expressed
clearly by Opschoor 1997. In the present paper we shall not address the issue.
The second law of thermodynamics implies that in a closed system the total amount of useful
energy and materials decreases over time. Hence, in a closed system, aggregate production over
time cannot be adequately described by the type of neoclassical production function discussed
above, even if there is easy substitution between renewables and non-renewables. However, Ayres
1997, 1998 argues that the earth is not a closed system because of the inflow of solar energy.
Moreover, in spite of the fact that material de- grades, it can be recycled to a large degree with
the use of external energy. This argument then restores the validity of the theoretical exercises on
sustainability and substitution.
In the present paper we take the issues raised above into account by studying a simple growth
model on a high level of aggregation. It is a widely accepted view that the environment per-
forms several economic functions such as the sup- ply of resources, the assimilation of waste, the
provision of intrinsic beauty and biodiversity. Be- cause these functions are rather diverse and are
executed by different constituent parts of the envi- ronment, an analysis on a disaggregate level seems
to be most appropriate. However, strong aggrega- tion may sometimes have an advantage, in partic-
ular when conceptual issues on a global scale such as climate change and ozone depletion are to be
discussed. In this paper we will concentrate on one example of the latter approach, namely, the
issue of natural capital and sustainability of eco- nomic systems. In some parts of the literature
sustainability is more or less identified by main- taining the so-called natural capital stock see e.g.
Pearce and Turner, 1990. This presumes the exis- tence of a single number measuring the perfor-
mance of nature with respect to the functions
mentioned above, and we see no problem in mak- ing this assumption for expository purposes. As a
matter of fact, it facilitates the analysis of several issues that are, in our opinion, pertinent to sus-
tainability. First of all, natural capital is a factor of production. Production can be used for con-
sumption purposes and also for investments, di- rected towards improving the quality of natural
capital, or for enlarging the available stock by exploration or for the build-up of backstop tech-
nologies or for the preservation of biodiversity see on the latter Weitzman, 1998. On the other
hand, excessive use of natural capital decreases its ‘value’ but may increase instantaneous welfare
here the examples of water and exhaustible re- sources come to mind. So, there is a trade-off
between natural capital as a factor of production and alternative uses. The question arises which is
the optimal use of natural capital. With a Rawl- sian objective will correspond constant instanta-
neous
‘happiness’ over
time, whereas
it is
generally argued that with a utilitarian criterion with discounting, natural capital will decrease
over time and future generations are doomed or are at least victimised by the greediness of the
present generation. We will show that the latter statements are incorrect in their generality. More
specifically, it will be shown that under a utilitar- ian regime natural capital will steadily increase
over time if it is small initially; furthermore, if initial natural capital is large it will decrease, but,
and this is perhaps surprising, on this trajectory there will nevertheless be investments in improv-
ing natural capital. Hence, the initial abundance of natural capital does not justify only exploiting
it. It is necessary from the beginning to manage it properly by investing in it. The intuition behind
this result is that investments in natural capital increase its capability to produce desirable com-
modities and are therefore to be undertaken un- less natural capital is extremely abundant. The
policy recommendation following from these ob- servations is that even in a ‘neoclassical’ perspec-
tive natural capital should be managed carefully by investing in it. Natural capital as an aggregate
has certain properties of a backstop technology.
Before proceeding to the analysis we wish to mention two serious caveats of our approach.
First we assume that natural capital as such does not have an amenity value: only consumption
yields utility. We therefore abstract from issues such as beauty of, for example, mountains and
forests. Second, working with an aggregate ig- nores that certain constituent parts are possibly
subject to irreversible processes. Exploitation of a given mine is irreversible, loss of biodiversity is
irreversible and many other examples can be given. However, the neglect of irreversibilities
strengthens our result: even if they do not exist a careful management of natural capital is necessary
along an optimum.
The outline of the paper is as follows. The model is presented in Section 2. There we also