Saddles, Indeterminacy and Bifurcations in an Overlapping Generations Economy with a Renewable Resource
We incorporate a renewable resource into an overlapping generations model with standard, well-behaved utility and constant returns to scale production functions. Besides being a factor of production the resource serves as a store of value. We characterize dynamics, efficiency and stability of steady state equilibria and show that the nature of steady state equilibrium depends on the value of the intertemporal elasticity of substitution in consumption. In particular, if that elasticity is at least half, but not exactly one, stationary equilibria are saddle points. The stationary equilibrium is stable when the intertemporal elasticity of substitution is unity. For smaller values of that elasticity we use a parametric example to demonstrate the existence of stable equilibria (indeterminacy) and a subcritical flip bifurcation. Hence, an overlapping generations economy with a renewable resource can display cycles and indeterminacy even in the absence of externalities or imperfect competition.
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