Equilibrium existence in a discrete-time endogenous growth model with physical and human capital
This paper studies a discrete-time version of the Lucas-Uzawa endogenous growth model with physical and human capital in the presence of externalities. Existence of an optimal equilibrium is proved using tools from dynamic programming with bounded or unbounded returns. The proofs also rely on properties of isoelastic utility and homogeneous production functions and apply well-known inequalities in real analysis, seldom used in the literature, which significantly simplify the task of verifying certain assumptions that are rather technical in nature. Some advantages of adopting a parametric family of isoelastic utility functions, instead of the ad hoc formulation typically used, are also discussed.
econ.TH↗