On knife-edge conditions with unbounded growth

Dariusz Bugajewski , Piotr Maćkowiak


Imagine an economic process modeled with help of ordinary differential equations with some fixed initial conditions and suppose that a solution to the system under consideration, for some reason, should enjoy desired conditions. It appears that small changes in the system describing the modeled process may have devastating effect on the fulfillment of the desired conditions by solutions of the perturbed system. Such a feature of a system is called a knife-edge condition in the literature on economic growth and it has recently found some deeper interest in that literature. However, the available results seem to be unclear and not correct – this paper shows how to correct and improve these results, creating consistent mathematical foundations of that theory. The main contribution of the paper is that knife-edge conditions are present whenever long-term unbounded growth of an economic variable is required as (or implied by) a desired regularity condition.
Author Dariusz Bugajewski - Adam Mickiewicz University (UAM)
Dariusz Bugajewski,,
, Piotr Maćkowiak (WIiGE / KEM)
Piotr Maćkowiak,,
- Department of Mathematical Economics
Journal seriesJournal of Macroeconomics, ISSN 0164-0704, (A 25 pkt)
Issue year2015
Publication size in sheets0.5
Keywords in EnglishKnife-edge condition, Long-term growth, Perturbation of system of differential equations, Regular growth
ASJC Classification2002 Economics and Econometrics
Languageen angielski
Score (nominal)25
Score sourcejournalList
ScoreMinisterial score = 20.0, 18-12-2019, ArticleFromJournal
Ministerial score (2013-2016) = 25.0, 18-12-2019, ArticleFromJournal
Publication indicators WoS Citations = 0; Scopus SNIP (Source Normalised Impact per Paper): 2015 = 0.955; WoS Impact Factor: 2015 = 0.714 (2) - 2015=0.922 (5)
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