The two sector overlapping generations model: A simple formulation

In this paper we provide a simple formulation of a two-sector overlapping generations model based on the social production function which characterizes the factor-price frontier associated with interior temporary equilibria. We first give a simple restriction for the existence of a long run equilibrium. Under gross substitutability, we show that such a steady state is locally indeterminate if the consumption good is sufficiently capital intensive, the elasticity of savings with respect to wage is low enough and the elasticity of savings with respect to the interest rate is large enough. We also exhibit a flip bifurcation giving rise to period-two cycles. When gross substitutability is violated, we prove that local indeterminacy may also occur when the investment good is capital intensive. However, when the consumption good is capital intensive, it requires the existence of at least two distinct steady state. Indeed, saddle-point stability is obtained as soon as uniqueness of the steady state holds. We also give conditions for the existence of complex characteristic roots and we exhibit a Hopf bifurcation giving rise to quasi-periodic cycles.