Sophistication drives higher growth than navïeté in the Ak model with hyperbolic discounting: An exhaustive numerical exploration

Abstract

This paper examines the Ak endogenous growth model with naïve and sophisticated agents under hyperbolic discounting. The utility function is isoelastic, with an intertemporal elasticity of substitution less than one. We derive a simple condition to verify that the effective rate of time preference is lower — and, consequently, the growth rate is higher — when agents are sophisticated rather than naïve. An extensive numerical analysis suggests that this condition holds across the entire feasible parameter space.