Essays on endogenous time preference and strategic interaction

Abstract

This thesis includes three self contained essays on the existence and qualitative properties of equilibrium dynamics under endogenous time preference. In the Örst essay, we reconsider the optimal growth model proposed by Stern (2006). We prove the almost everywhere di§erentiability of the value function and uniqueness of the optimal path, which were left as open questions and show how a small perturbation to the price of future oriented capital qualitatively changes the equilibrium dynamics. Almost none of the studies on endogenous time preference consider the strategic interaction among the agents. In the second essay, by considering a strategic growth model with endogenous time preference, we provide the su¢ cient conditions of supermodularity for dynamic games with open-loop strategies and show that the stationary state Nash equilibria tend to be symmetric. We numerically show that the initially rich can pull the poor out of poverty trap even when sustaining a higher level of steady state capital stock for itself. Lastly, in the third essay, we consider the socially determined time preference which depends on the level of Ösh stock and characterize the basic Öshery model under this setup. We provide existence of collusive and open-loop Nash equilibria and compare the e¢ ciency and qualitative properties of them.