Optimal ergodic chaos under slow capital depreciation

Abstract

It has been known that, in a standard two-sector dynamic model, slow capital depreciation may result in a unimodal system with a kinked peak and that this system may be topological chaos, which is unobservable in Grandmont's sense. However, whether or not slow capital depreciation can cause observable chaos has not been examined in the existing literature. The present study demonstrates that slow capital depreciation may cause ergodic chaos, which is observable, by using a recent result of Sato and Yano (2012).

Ergodic chaos for non‐expansive economic models**

“…Although the increasing part has slope less than , it should be also possible to show ergodic chaos under a certain set of conditons. See Sato and Yano () for a proof. Other models with similar properties are studied by Khan and Mitra (, ), Fujio () and Yano and Furukawa (2010).…”