A simple endogenous growth model with endogenous fertility: Indeterminacy and uniqueness

Abstract.

This paper studies the equilibrium dynamics and indeterminacy of equilibria in an endogenous growth model with endogenous fertility choice. We characterize the conditions that give rise to an unique equilibrium as well as multiple equilibria. Whenever there exists a unique equilibrium, it will be globally determinate; when multiple equilibria arise, indeterminacy occurs. In particular, we find that two equilibria occur – one is associated with high fertility and low growth, while the other is associated with low fertility and high growth. A parameterized example is given to assess the empirical feasibility of our results. The validity of the neo-Malthusian relation between fertility and growth is then re-examined. Finally, we study the relation between growth and welfare and compare different balanced growth equilibria in terms of their lifetime-attained utility.

JEL classifications: O41, J13