## Discrete Time Optimal Control Algorithm for Analysis of Long Run Timber Supply |

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acres harvested acres of trees age class age group April backwards recursion Bellman's optimality principle bordered Hessian change of subscripts Clifford concave concave function constrained maximization constraints control variables costate variables costate vectors D(Qj David Montgomery December define DEVELOPING COUNTRIES diagonal matrix discounted discrete time optimal DTOCP dynamic programming elements ENERGY ENVIRONMENTAL Equations 7a equations l3c feasible time path forest by age identify the direction initial conditions January July Kerry Smith Kopp Krutilla Kuhn-Tucker conditions L. P. Gianessi laws of motion Long Run Timber maximum principle Michael objective function October OPTIMAL CONTROL ALGORITHM Peskin present value principle minors PRODUCTION Raymond regeneration expenditures regeneration input RESOURCE Run Timber Supply Russell Sandra Glatt Sedjo September 1982 shadow prices shadow values single land class Smith and William solution stationary surplus Toman trees in age uj and wj uJ_1 Vaughan Watson William Ramsay Winston Harrington zero