From a dynamic perspective, the existing literature on renewable resources in a Ramsey economy is puzzling. On the one hand, the central planner’s solution leads to the occurrence of limit cycles around the lower steady state (Wirl, J Econ Dyn Control 28, 2004); on the other hand, limit cycles arise in a market economy around the higher steady state (Bosi, Math Soc Sci 96, 2018). To reconcile these findings, we study the competitive equilibrium of a discrete-time Ramsey model with a renewable resource, where preferences are represented by two different utility functions with Constant Static Elasticity of Substitution (CSES) and Constant Intertemporal Elasticity of Substitution (CIES). In the CSES case, we recover the dynamics highlighted by Wirl (J Econ Dyn Control 28, 2004), while, in the CIES case, the ones obtained by Bosi, Math Soc Sci 96, 2018. Moreover, this conclusion is robust under two alternative regeneration processes for the resource (power and logistic laws). In other words, the dynamics seems to depend more on the preference structure than on the market structure (central planner versus market economy).