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 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 how their nature in the presence of ‘well-behaved’ resource stock growth depends on the size of the intertemporal elasticity of substitution in consumption. If that elasticity is at least half, but not exactly one, steady states are saddle points. For the values of elasticity less that one half we use a parametric example to demonstrate the existence of stable equilibria (indeterminacy) and a subcritical flip bifurcation. These findings lie in conformity with empirics, which suggest that exploited fish populations exhibit not only the conventionally analyzed steady yields, but also cycles and irregularities.