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Dott. Giuseppe Di Vita Italy

for Discussion Roundtables 1, 9, 11, 24, 25, 26, 28, 32, and 33

Table of Contents

Secondary Materials, Exhaustible Resources and Growth Rates

This paper presents a model of endogenous growth with an exhaustible resource, in which waste recycling increases the growth rate of total input. We show that technological change plays a central role in increasing the quantity of secondary materials produced.

In our model a double endogenous effect emerges: (i) a direct one through technological progress; (ii) an indirect one, by means of the discovery of the new techniques of waste recycling. One of the main findings is that the policy maker can increase the growth rate of the economy by promoting research activity.

Moreover, we demonstrate that total welfare increases, as a consequence of waste recycling, in industrialized countries and developing ones, but the production costs of secondary materials are lesser in the first. Finally, the principal results of our analytical framework are consistent with the empirical evidence.


After the Malthus and Ricardo debate, and since Hotelling's (1931) seminal paper, economic literature has paid more attention to the constraints imposed on growth by exhaustible resources.

The results of neoclassical growth models which consider this type of input have been quite optimistic. These models emphasize the existence of three economic forces offsetting the limitations imposed by exhaustible resources: technological change, the substitution of man-made factors of production for nonrenewable inputs and returns to scale (Stiglitz, 1974a). However, the effects of waste recycling on the exploitation of exhaustible resources and waste accumulation have not been considered.\footnote{% Stiglitz neglects this problem, affirming that the growth model with exhaustible resources and waste recycling is essentially the same as the model in which the effects of this process are neglected. See Stiglitz, 1974b, p. 151, footnote 1.}

The neoclassical growth models have treated technological change as exogenous to the system and costless. In recent papers the role of endogenous technological change in determining long-term economic growth is underlined (Romer, 1986, 1990, 1994). The dynamics of environmental preservation have been analyzed in endogenous growth models (Bovemberg and Smulders, 1995, Musu and Lines, 1995, Vellinga, 1995), also from the point of view of intergenerational equity (Olson and Knapp, 1997). There are endogenous growth models with exhaustible resources (see, for example, Kamien and Schwartz, 1978, Barbier, 1996), but there is no research on the effects of waste recycling upon the equilibrium path. However, economic literature has explored the issue of how the waste recycling process could help to sustain a development path compatible with a greater preservation of the environment (Baumol, 1977, Hoel, 1978, Smith, 1972). The difficulty in finding adequate landfill area to dispose of waste has prompted research for new productive processes that allow the re-use of waste (Anderson, 1987, Dinan, 1993, Highfill, McAsey and Weinstein, 1994). The recyclable waste itself becomes an input, deriving from the same productive process (closed loop) or from other sources such as other firms or households (open loop).

In this paper our analysis is focussed upon the waste recycling effects during transitional dynamics. We try to consider how the process considered could affect the growth rate of output and welfare. The findings of formal analysis suggest that there is a difference between costs in developing and developed countries in producing secondary materials. The conditions of convergence towards a stationarity growth path are shown, considering how the policy maker can influence the growth rate of total output. Those arguments, neglected in the previous literature, are of increasing interest with regard to welfare behavior.

In the analytical framework, we assume a closed economy. Waste can be recycled during the production process, serving as an input to obtain 'secondary materials'. The model considers an exhaustible natural resource and two types of waste: recyclable and non-recyclable. The first type is used to produce 'secondary materials', and its degree of recyclability is an increasing function of research activity. The second type of waste is discharged into the environment and is only indirectly considered in our analysis. The long-run costs of waste recycling are measured in terms of human capital and technology devoted to this aim.

Technological change is the result of private and public activity in the research sector, which is generated by rational agents that want to maximize their profits or social welfare. In our model, the knowledge is split into technology and human capital. The first one is a non-rivalry good, because anyone can use a new discovery. The second one is a rivalrous good, in fact the subjects that increase their human capital, incorporating technological improvement, cannot be in more than one place at the same time (Romer, 1990). Environmental concerns may be pushing the new scientific discoveries, as we understand by analyzing the non-renewable natural resource impact of a changing recycling technology. New ideas, embodied by the productive process and workers, allow us to reduce the costs of waste recycling, and increase the 'secondary materials' produced. Here we assume that human capital reflects the best current level of technology and has no depreciation rate. It can be used to produce final and intermediate goods like technology. The population and human capital are considered constant\footnote{% Assumptions similar to these were made in Romer (1990), pp. S79-80}. The flow of waste enters directly into the utility function with a negative marginal utility. Its presence may have an adverse effect on production as well. The waste stock reduction as a consequence of secondary material production increases the welfare of consumers. In the model strong long-run feedbacks of the waste management problem emerge, with regard to exhaustible resources and secondary material production.

The paper is organized as follows. The next section describes our model and derives the first order conditions, so as to show the effect of technological progress upon the waste produced and recycled. Section 3 shows the existence of an optimal stationary growth path, developing its diagrammatic analysis. Section 4 attempts to estimate the effects of waste recycling on the growth rate at which the economic system converges to the endogenous stationary growth path. We conclude with summary remarks. Algebraic details and demonstrations are given in the Appendix.

Large References

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Baumol, William J. 1977. ''On Recycling as a Moot Environmental Issue.'' \textit{Journal of Environmental Economics and Management} \textbf{4}:83-87.

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