Applications of Distributed Optimal Control in Economics-The Case of Forest Management

This paper presents a theoretical model to find the optimal selective-logging regime of a size-distributed forest. The law of motion of the economic model is governed by a partial differential equation that describes the evolution of the forest stock over time. To find the solution of the resulting distributed optimal control problem, we propose a numerical solution technique known as "Escalator Boxcar Train" used in Biology, for the study of dynamics of physiologically structured populations. The empirical part of the paper determines the optimal selective-logging regime of a size-distributed forest, that is, the selective logging that maximizes the discounted net benefits from timber production of a stand of pinus sylvestris, over an infinite time horizon, and compares the selective logging with the clear-cutting regime.