In this paper, we explore the link between cyclical and non-cyclical resource exploitation. As already shown (Wirl 1995) in the context of a two state-variable continuous control model, the form of the cost function is essential to explain the cyclical or non-cyclical nature of optimal solutions. We base our analysis on a one-state variable case. We present an impulse control model and study the impact of different cost functions on the type of solution. We show that the optimal harvesting behaviour derived from this model can either be cyclical or converge to a Most Rapid Approach Path solution, like the one in Clark's continuous control model (Clark 1990). We finally discuss the origin of the cost functions we studied and show that there are empirical underpinnings for the occurence of cyclical optimal harvesting solutions.