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

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. • I consider the Ak -type endogenous growth model with hyperbolic discounting. • Agents can behave either naïvely or sophisticatedly. • Provide a simple condition to verify that effective discounting is lower with sophistication. • The growth rate would then be higher when agents are sophisticated than naïve. • Numerical simulations provide strong empirical support for this condition to hold.