Growth and long-run stability
type: Item
instance of: scholarly article
title: Growth and long-run stability
zbMATH Open document ID: 0633.34047
DOI: 10.1007/BF00047540
author: Bjarne Sloth Jensen
author: Mogens Esrom Larsen
published in: Acta Applicandae Mathematicae
publication date: 1987-01-01T00:00:00Z
review text: The authors consider a scalar equation \(y'=f(y)\) where f is \(C^ 1\) and \(f>0\). Let \(\phi\) (t) be a fixed solution and let \(\psi (t)=\phi (t+h)\) be an arbitrary solution. The stability of f is called strong absolute if \(\lim_{t\to \infty}| \psi (t)-\phi (t)| =0\). Seven other kinds of stability were introduced. Conditions of f leading to each kind of stability (or instability) were obtained. Next, eight types of speed of growth of \(\phi\) were defined. For example, \(\phi\) is said to have unbounded growth if \(\phi '>0\) and \(\lim_{t\to \infty}\phi (t)=\infty\). The two concepts are roughly related by: the more rapid the growth, the less is the degree of stability. (See precise statement in the paper.) These results are then applied to the multiplier-accelerator growth model of Harrod and the neoclassical growth model of Solow in Economics.
Mathematics Subject Classification ID: 34D99
Mathematics Subject Classification ID: 34A34
Mathematics Subject Classification ID: 91B62
zbMATH DE Number: 4030018
zbMATH Keywords: economic dynamics
zbMATH Keywords: degree of stability
zbMATH Keywords: growth model
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf00047540
OpenAlex ID: W1990026424
description: scientific article; zbMATH DE number 4030018