Singular optimal control model of stock dependent environmental policies

In many countries, forest policies consist of a system of various regulations, taxes and subsidies. In this article, we focus on those policies that regulate selective harvesting and study the example of Central Africa. We use a deterministic singular optimal control model of renewable resources to assess these policies with respect to a first best situation which integrates a social surplus or externality function. In particular, in contrast to earlier articles, we analyze a stock dependent tax, for which the objective function is piecewise differentiable. We use a theorem proposed by Hartl and Feichtinger to solve the mathematical problem. We show that this tax is the most flexible instrument with respect to fund collection.