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

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 influence of the intertemporal elasticity of substitution on the time profile 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.