A necessary and sufficient condition for the existence of chaotic dynamics in a neoclassical growth model with a pollution effect

TL;DR

This paper establishes a precise condition for chaos in a neoclassical growth model affected by pollution, analyzing how pollution intensity influences chaotic dynamics using recent mathematical results.

Contribution

It provides the first necessary and sufficient condition for chaos in a pollution-affected growth model, applying recent chaos theory to economic dynamics.

Findings

Chaos occurs under specific pollution conditions

The chaos condition varies with pollution strength

Application of recent chaos theory to economic models

Abstract

In this paper, we study a neoclassical growth model with a (productivity inhibiting) pollution effect. In particular, we obtain a necessary and sufficient condition for the existence of a topological chaos. We investigate how the condition changes as the strength of the pollution effect changes. This is a new application of a recent result characterising the existence of a topological chaos for a unimodal interval map by Deng, Khan, Mitra (2022).