Zero discounting and optimal paths of depletion of an exhaustible resource with an amenity value

Abstract

This paper studies the undiscounted utilitarian optimal paths of the canonical Dasgupta-Heal-Solow model when the stock of natural capital is a direct argument of well-being, besides consumption. We use a Keynes-Ramsey rule which yields a generalization of Hartwick's rule: if society has a zero discount rate but is ready to accept intertemporal substitution, net investment should not be zero as in the maximin case but should be positive, its level depending on the distance between the current and the long run bliss level of utility. We characterize solutions in the Cobb-Douglas utility and production case, and analyse the in ‡uence of the intertemporal elasticity of substitution on the time pro…le of the optimal paths. We show that, in the Cobb-Douglas case, the ratio of the values of the resource and capital stocks remains constant along the optimal path, and is independent of initial conditions. JEL: D9, Q01, Q3

Growth and long-run sustainability

“…Trade-off between current consumption and long-run consumption for constant growth rate development paths Sustainable growth in the DHS model corresponds to growth from an initial level of consumption c 0 lower than the maximin value m (S 0 , K 0 ). In this model, sustainable growth without limit is possible, for example when considering hyperbolic discounting (Pezzey, 2004) or following a constant saving rate rule, which can correspond to some undiscounted utilitarian optima (Asheim and Buchholz, 2004;Asheim et al, 2007;D'Autume and Schubert, 2008). As our purpose is to illustrate cases in which growth induces a catching up of the maximin value in finite time, we consider that society initially pursues consumption growth at a constant rate g > 0, a growth pattern that is not sustainable in the long-run without technological progress (Stiglitz, 1974;Llavador et al, 2011).…”

“…In the DHS model of an economy dependent on manufactured capital and an essential, non-renewable resource Heal, 1974, 1979;Solow, 1974), sustaining consumption at a constant level requires that investment in manufactured capital offset the depletion of the resource (Hartwick, 1977). A deviation downward from that possible constant-consumption path can allow for growth at a parametric rate through investment (Asheim et al, 2007;D'Autume and Schubert, 2008). The economy can choose from many different paths of sustained development.…”

“…Most of the literature focusing on the long-run aspects of sustainability relies on the definition of an optimality criterion and the study of the limiting behavior of the optimal path. In the tradition of Ramsey's model of undiscounted utility (Ramsey, 1928), some authors assume that growth leads the economy asymptotically toward an exogenous, bliss level of utility (Asheim and Buchholz, 2004; D'Autume and Schubert, 2008). The bliss level coincides with what is known as the green golden rule, which is the maximum level of utility that can ever be attained (Chichilnisky et al , 1995).…”

The zero discounting and maximin optimal paths in a simple model of global warming

“…2 We honor the memory of researcher Ken Stollery (1948Stollery ( -2005 who was struck down by illness at a tragically early age. 3 Hamilton and Ulph [1995] developed a somewhat di¤erent version of a Solow model with global warming independently of Stollery.…”

An environmental-economic measure of sustainable development

“…That level of effort is maintained so long as there is a net benefit to fishing. 4 The dynamics of the exploited resource becomeṡ…”