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 canonicalDasgupta-Heal-Solow model when the stock of natural capital is a direct argument ofwell-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 acceptintertemporal substitution, net investment should not be zero as in the maximin casebut should be positive, its level depending on the distance between the current and thelong run bliss level of utility. We characterize solutions in the Cobb-Douglas utility andproduction case, and analyse the influence of the intertemporal elasticity of substitutionon the time profile of the optimal paths. We show that, in the Cobb-Douglas case, theratio of the values of the resource and capital stocks remains constant along the optimal path, and is independent of initial conditions.