  We study a model for the exploitation of renewable stocks developed in Clark
et al. (Econometrica 47 (1979), 25-47). In this particular control problem, the
control law contains a measurable and an impulsive control component. We
formulate Pontryagin's maximum principle for this kind of control problems,
proving first order necessary conditions of optimality. Manipulating the
correspondent Lagrange multipliers we are able to define two special switch
functions, that allow us to describe the optimal trajectories and control
policies nearly completely for all possible initial conditions in the phase
plane.
