Endogenous Time Preference and Strategic Growth

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

Essays on endogenous time preference and strategic interaction

Ankara : The Department of Economics, İhsan Doğramacı Bilkent Univ., 2013.Thesis (Ph. D.) -- Bilkent University, 2013.Includes bibliographical refences.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.Turan, Agah RehaPh.D

Strategic Interaction and Dynamics under endogenous time preference

International audienceThis paper presents a strategic growth model with endogenous time preference. Due to the potential lack of concavity and the differentiability of the value functions associated with each agent's problem, we employ the theory of monotone comparative statics and supermodular games based on order and monotonicity properties on lattices. In particular, we provide the sufficient conditions of supermodularity for dynamic games with open-loop strategies based on two fundamental elements: the ability to order elements in the strategy space of the agents and the strategic complementarity which implies upward sloping best responses. The supermodular game structure of the model lets us provide the existence and the monotonicity results on the greatest and the least equilibria. We sharpen these results by showing the differentiability of the value function and the uniqueness of the best response correspondences almost everywhere and show that the stationary state Nash equilibria tend to be symmetric. Finally, we numerically analyze to what extent the strategic complementarity inherent in agents' strategies can alter the convergence results that could have emerged under a single agent optimal growth model. In particular, we show that the initially rich can pull the poor out of the poverty trap even when sustaining a higher level of steady state capital stock for itself

Optimal Growth Strategy under Dynamic Threshold

International audienceWe consider an economy in which the technology exhibits nonconvexities due to fixed costs associated with production. Taking into account the incentives for investment to decrease fixed costs, we characterize the circumstances under which an underdeveloped economy can catch up with the developing ones. We show that it is optimal to get rid of the fixed costs inherent in production in finite time provided that the initial level of fixed costs are not too high and the technology for reducing fixed costs is sufficiently efficient. Indeed, we obtain that even though the income disparities may be very persistent and can be perceived as poverty traps, economies with not very high initial fixed costs and sufficiently efficient technology for reducing fixed costs would ultimately converge to the same steady state level of per capita income