Characterizing the sustainability problem in an exhaustible resource model

We provide a general condition under which consumption can be sustained indefinitely bounded away from zero in the continuous time Dasgupta-Heal-Solow-Stiglitz model, by letting augmentable capital substitute for a non-renewable resource. The assumptions made on the production function are mild, thus generalizing previous work. By showing that Hartwickʼs rule minimizes the required resource input per unit of capital accumulation, and integrating the required resource input with respect to capital, we obtain a complete technological characterization without reference to the time path. We also use the characterization result to establish general existence of a maximin path.