Introduction Directory UMM :Data Elmu:jurnal:E:Ecological Economics:Vol34.Issue3.Sept2000:

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. PII: S 0 9 2 1 - 8 0 0 9 9 9 0 0 1 2 1 - 4 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