Constant Sustainable Consumption Rate in Optimal Growth with Exhaustible Resources

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Abstract
The problem of optimal growth with an exhaustible resource deposit under R. M. Solow's criterion of maximum sustainable consumption rate, previously formulated as a minimum‐resource‐extraction problem, is shown to be a Mayer‐type optimal‐control problem. The exact solution of the relevant firstorder necessary conditions for optimality is derived for a Cobb‐Douglas production function, whether or not the constant unit resource extraction cost vanishes. The related problem of maximizing the terminal capital stock over an unspecified finite planning period is investigated for the development of more efficient numerical schemes for the solution of multigrade‐resource deposit problems. The results for this finite‐horizon planning problem are also important from a theoretical viewpoint, since they elucidate the economic content of the optimal growth paths for infinite‐horizon problems.

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