The optimal management of the environment is becoming increasingly important with our
growing awareness of the problems of loss of biodiversity and overconsumption of natural
capital stocks. We used perturbation theory to provide simple feedback rules to compute
optimal yields and depletion rates for many different types of renewable resources and to
find the optimal steady state. The model is arbitrary in the state variable, stock, and quadratic
in the control variable, yield. A quadratic objective function includes downward sloping …

The optimal management of the environment is becoming increasingly important with our
growing awareness of the problems of loss of biodiversity and overconsumption of natural
capital stocks. We used perturbation theory to provide simple feedback rules to compute
optimal yields and depletion rates for many different types of renewable resources and to
find the optimal steady state. The model is arbitrary in the state variable, stock, and quadratic
in the control variable, yield. A quadratic objective function includes downward sloping …