Renewable resources in an overlapping generations economy without capital

We incorporate a renewable resource into an overlapping generations model without capital and with quasi-linear preferences. Besides being an input for production the resource serves as a store of value. We characterize the dynamics, efficiency and stability of the steady state equilibria. The stability properties are sensitive to the type of the resource growth. For constant growth there is only one steady state equilibrium which is stable and efficient. In the general case of the concave growth function there are usually at least two steady state equilibria, one of which is stable and the other one unstable. The unstable steady state is efficient, but the stable one may or may not be. We study the robustness of our results by assuming a logarithmic periodic utility function. We show that for the Cobb-Douglas production function the steady state is unique and stable regardless of whether the equilibrium is efficient or inefficient. Our analytical results are illustrated by numerical calculations.