A Dynamic Optimization Model of Depletable Resources

This article develops a dynamic optimization model to describe the supply of a depletable resource within an economy. An implementable version of the model is applied to the dynamic allocation of coal supply to the U.S. energy sector for the period 1979-2000. Several primary energy sources, including coal, oil, gas, and nuclear power, are considered in a linear programming process model of the energy-producing sector. The supply of coal appears to be particularly sensitive to the future pattern of nuclear power capacity escalation, and less so to escalations in oil import prices. The latter observation depends, however, on the rate of substitution of coal for oil and gas to process heat and petrochemicals.