On the Least Upper Bound of Discount Factors that are Compatible with Optimal Period-Three Cycles

In this study, we derive, in the standard class of optimal growth models, the least upper bound of discount factors of future utilities for which a cyclical optimal path of period 3 may emerge.1 On the one hand, Nishimura and Yano (1994) and Nishimura et al. (1994) construct examples in which a cyclical optimal path of period 3 emerges for discount factors around 0:36. On the other hand, Sorger (1992a,b, 1994), demonstrates that if such a path emerges in an optimal growth model of the standard class, the model’s discount factor cannot exceed 0:5478.

[1]  J. Scheinkman.  On optimal steady states of n-sector growth models when utility is discounted☆ , 1976 .

[2]  An Exact Discount Factor Restriction for Period-Three Cycles in Dynamic Optimization Models , 1996 .

[3]  Karl Shell,et al.  Do Sunspots Matter? , 1983, Journal of Political Economy.

[4]  L. Montrucchio.  Dynamic complexity of optimal paths and discount factors for strongly concave problems , 1994 .

[5]  On the minimum rate of impatience for complicated optimal growth paths , 1992 .

[6]  J. Yorke,et al.  Period Three Implies Chaos , 1975 .

[7]  Gerhard Sorger.  Minimum impatience theorems for recursive economic models , 1992 .

[8]  Kazuo Nishimura,et al.  Ergodic chaos in optimal growth models with low discount rates , 1994 .

[9]  Gerhard Sorger.  Period Three Implies Heavy Discounting , 1994, Math. Oper. Res..

[10]  A. N. Sharkovskiĭ.  COEXISTENCE OF CYCLES OF A CONTINUOUS MAP OF THE LINE INTO ITSELF , 1995 .

[11]  Tapan Mitra,et al.  Periodic and chaotic programs of optimal intertemporal allocation in an aggregative model with wealth effects , 1994 .

[12]  L. McKenzie,et al.  Optimal economic growth, turnpike theorems and comparative dynamics , 1986 .

[13]  L. McKenzie,et al.  Turnpike theory, discounted utility, and the von Neumann facet , 1983 .

[14]  L. Montrucchio,et al.  On the indeterminacy of capital accumulation paths , 1986 .

[15]  F. P. Kelly.  Bounds on the Performance of Dynamic Routing Schemes for Highly Connected Networks , 1994, Math. Oper. Res..

[16]  Michele Boldrin,et al.  Sources of Complex Dynamics in Two-Sector Growth Models , 2021, Cycles and Chaos in Economic Equilibrium.

[17]  W. Brock,et al.  Global Asymptotic Stability of Optimal Control Systems with Applications to the Theory of Economic Growth , 1976 .

[18]  M. Yano,et al.  Nonlinear Dynamics and Chaos in Optimal Growth: An Example , 1995 .

[19]  D. Cass,et al.  The structure and stability of competitive dynamical systems , 1976 .

[20]  M. Yano,et al.  Optimal chaos, nonlinearity and feasibility conditions , 1994 .