Optimal Growth When the Stock of Resources is Finite and Depletable.

by Kent P. Anderson

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The implications of optimal growth when accounting explicitly for the depletion of nonreproducible resources, such as mineral deposits, fossil-fuel reserves, and geothermal energy. The problem is developed within the context of the familiar, neoclassical, one-sector economy in which the objective is to identify the path of capital accumulation that maximizes discounted per-capita consumption over a finite planning horizon, subject to endpoint conditions on the stocks of capital and resources. The mathematical analysis shows that when consumption of nonreplaceable stocks of resources is incorporated into an optimal economic growth model, the result is a tendency to postpone capital accumulation and to spend more time on turnpike growth paths where capital is used less intensively than it is in a model of the economy with unconstrained resources. In the extreme case, where the only feasible growth path is that of minimum resource use, all capital accumulation is postponed until the last possible moment. 22 pp. Ref.

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