Sustainable growth with environmental spillovers

Abstract

In this paper, we apply the approach of Ramsey and Koopmans to the problem of optimal and sustainable growth. Under plausible assumptions, intertemporal neutrality implies that the optimal growth path is sustainable without the contrivance of a sustainability constraint. The model is extended to cases involving environmental disamenities. The solutions equivalently solve the problem of maximizing net national product adjusted for depreciation in natural capital and environmental effects. Green net national product in this framework is constant over time, thus avoiding the paradox of declining sustainable income.

Introduction

In mainstream environmental economics, sustainable growth is modeled as a problem of maximizing an intertemporal utilitarian welfare function, subject to the constraint that the growth of consumption, utility, or social well-being cannot be negative (e.g. Asheim, 1999, Dasgupta, 2001). The constrained-utilitarian approach applies positive discounting of future utility, consistent with Koopmans's (1960) demonstration that there does not exist a utility function defined on all consumption streams that satisfies the usual axioms of rational choice and timing neutrality (i.e. without discounting). In an alternative approach (Beltratti et al., 1993, Beltratti et al., 1995, Chichilnisky, 1996),¹ social welfare is modeled as a weighted average of conventional growth and a concern for sustainability.

In what follows, we take a different tack, following the question posed by Anand and Sen (2000). Instead of incorporating a sustainability criterion as a side constraint, we incorporate the concern with intergenerational equity into the planner's objective function. We ask whether such a concern, in combination with a specification of interdependency between well-being and the natural environment, will lead to a sustainable consumption path. In particular, we employ the concept of intergenerational neutrality as proposed by Ramsey (1928) and Koopmans (1965). Ramsey (1928, p. 619) warned that the use of a positive utility discount rate is “ethically indefensible” and reveals “a weakness of the imagination”. Koopmans himself (1965, p. 240) noted “we welcome equally a unit increase in consumption per worker in any one future decade … Mere numbers cannot give one generation an edge over another …” Koopmans's (1965) solution to Koopmans's (1960) nonexistence problem relies precisely on the notion of “intergenerational neutrality” for a specific, non-empty subset of feasible consumption paths and is captured in turn by the zero utility discount rate.²

The first objective of the present paper is to examine optimal and intertemporally neutral growth with a nonrenewable resource that generates negative externalities such as acid rain and global warming. We suggest that assuming a backstop resource is plausible and that, under these conditions, optimal growth is sustainable, even without the imposition of a sustainability constraint. The second objective is to resolve the inconsistency between the sustainability requirement that consumption growth be non-negative and the finding that, in the standard model, maximizing sustainable income leads to eventually declining consumption. We show that this paradox does not arise under intertemporal neutrality.

In Section 2, we present the conditions for optimal and ethically neutral growth in a model with a non-renewable resource and a backstop technology. The maximum–minimum solution is shown to be a special case of this solution, albeit one which is unlikely to be preferred. In Section 3, we extend the model to include environmental disamenities associated with the use of non-renewable resources. In Section 4, we investigate the relationship between Ramsey–Koopmans optimal growth and sustainable income. Section 5 provides a brief summary and concluding remarks.