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

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. Thi...

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Published inEconomic theory bulletin Vol. 12; no. 1; pp. 79 - 86
Main Author Uchiyama, Tomohiro
Format Journal Article
LanguageEnglish
Published Cham Springer International Publishing 01.06.2024
Springer Nature B.V
Subjects
Economic theory
Economic Theory/Quantitative Economics/Mathematical Methods
Economics
Economics and Finance
Game Theory
Macroeconomics/Monetary Economics//Financial Economics
Neoclassicism
Pollution
Public Finance
Research Article
Social and Behav. Sciences
Topology
Chaos
Neoclassical growth model
Externality
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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 et al. (J Econ Theory 201:Article 105446, 2022).
AbstractList 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 et al. (J Econ Theory 201:Article 105446, 2022).
Author Uchiyama, Tomohiro
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Cites_doi 10.2307/1884513
10.1007/BFb0084762
10.1016/j.jet.2022.105446
10.1090/ulect/067
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References Yorke, J.A., Yorke, E.: Chaotic behavior and fluid dynamics. In Swinney, H.L., Gollub, J.P. (eds.) Hydrodynamic Instabilities and the Transition to Turbulence (1985)
DayRHIrregular growth cyclesAm. Econ. Rev198272406414
RuetteSChaos on the Interval2017ProvidenceAmerican Mathematical Society10.1090/ulect/067
DengLKhanMAMitraTContinuous unimodal maps in economic dynamics: on easily verifiable conditions for topological chaosJ. Econ. Theory2022201Article 10544610.1016/j.jet.2022.105446
BlockLSCoppelWADynamics in One Dimension1992BerlinSpringer10.1007/BFb0084762
SolowRMContribution to the theory of economic growthQ. J. Econ.195670659410.2307/1884513
RH Day (264_CR2) 1982; 72
L Deng (264_CR3) 2022; 201
LS Block (264_CR1) 1992
RM Solow (264_CR5) 1956; 70
S Ruette (264_CR4) 2017
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SubjectTerms Economic theory
Economic Theory/Quantitative Economics/Mathematical Methods
Economics
Economics and Finance
Game Theory
Macroeconomics/Monetary Economics//Financial Economics
Neoclassicism
Pollution
Public Finance
Research Article
Social and Behav. Sciences
Topology
Title A necessary and sufficient condition for the existence of chaotic dynamics in a neoclassical growth model with a pollution effect
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