Periodic and aperiodic consumer behavior

摘要

Various properties of nonlinear difference equations are analysed within the framework of a model of endogenous preference change. Theorems by Šarkovskii and Li and Yorke show that simple first order nonlinear difference equations exhibit a wide range of dynamical behavior: Stable points, a hierarchy of stable cycles, unstable cycles, and an uncountable set of aperiodic points. The economic analysis in this paper focuses in particular on the sequence of stable cycles and questions about rationality and consistent behavior over time within a structure of utility maximization.