Competitive Equilibrium Cycles with Endogenous Labor

In this paper we study a two-sector optimal growth model with elastic labor supply. We provide a complete characterization of the production possibility frontier in terms of the capital intensity difference accross sectors. We show that the modified golden rule is saddle-point stable when the investment good is capital intensive. On the other hand, to characterize stability with a capital intensive consumption good, we focus on either additively separable or homothetic preferences. In the first specification, we compute the critical values for the elasticities of intertemporal substitution in consumption and leisure in correspondence to which the modified golden rule undergoes flip bifurcations and endogenous business cycles occur. At the same time, we show that within a utility linear in leisure the modified golden rule is always saddle-point stable. In the second specification for preferences, we show that the local dynamic properties of the optimal path depend instead on the shares of consumption and leisure into total utility. We also compute the flip bifurcation values for these parameters and we prove that endogenous fluctuations are even more likely with homothetic preferences.