Endogenous Time Preference and Strategic Growth

Abstract

This paper presents a strategic growth model that analyzes the impact of Endogenous preferences on equilibrium dynamics by employing the tools provided by lattice theory and supermodular games. Supermodular game structure of the model let us provide monotonicity results on the greatest and the least equilibrium without making any assumptions regarding the curvature of the production function. We also sharpen these results by showing the differentiability of the value function and the uniqueness of the best response correspondence almost everywhere. We show that, unlike globally monotone capital sequences obtained under corresponding optimal growth models, a non-monotonic capital sequence can be obtained. We conclude that the rich can help the poor avoid poverty trap whereas even under convex technology, the poor may theoretically push the rich to her lower steady state.Lattice programming, Endogenous time preference