Efficient Endogenous Fluctuations in Two-Sector OLG Model

We consider a two-sector two-good two-periods overlapping generations model with inelastic labor, consumption in both period of life and homothetic CES preferences. There are two consumption goods, one pure (non-durable) consumption and one consumable (durable) capital good which can be either consumed or invested. Assuming gross substitutability and a capital intensive pure consumption good, we prove the existence of efficient endogenous fluctuations through a Hopf bifurcation if the share of the consumption of young in the composite good is low enough. We also show that some fiscal policy rules can improve welfare and prevent the existence of business-cycle fluctuations in the economy by driving it to the optimal steady state as soon as it is announced