Abstract We incorporate a renewable resource as a factor of production and store of value into an overlapping generations model. We characterize dynamics and stability of steady state equilibria by introducing the concave resource growth function. The nature of equilibria in the presence of ’well-behaved’ resource stock growth depends on the size of the intertemporal elasticity of substitution in consumption. If it is at least half, but not exactly one, steady states are saddle points. For intertemporal elasticity less than one half we use a parametric example with logistic growth to demonstrate the existence of stable equilibria (indeterminacy) and a subcritical bifurcation.