Qualitative analysis of the Goodwin model of the growth cycle

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216305%3A26510%2F17%3APU132807" target="_blank" >RIV/00216305:26510/17:PU132807 - isvavai.cz</a>

Výsledek na webu

<a href="https://www.upo.es/revistas/index.php/RevMetCuant/article/view/2694" target="_blank" >https://www.upo.es/revistas/index.php/RevMetCuant/article/view/2694</a>

DOI - Digital Object Identifier

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Jazyk výsledku

angličtina

Název v původním jazyce

Qualitative analysis of the Goodwin model of the growth cycle

Popis výsledku v původním jazyce

Goodwin's model is a set of ordinary differential equations and is a wellknown model of the growth cycle. However, its four constants require an extensive numerical study of its two differential equations to identify all possible unsteady state behaviors, i.e. phase portraits, which corresponds to infinitely many combinations of numerical values of the constants. Qualitative interpretation of Goodwin's model solves these problems by replacing all numerical constants and all derivatives by trends (increasing, constant and decreasing). The model has two variables - the employment rate V, and the labour share U. A solution of the qualitative Goodwin's model is a scenario. An example of a Goodwin's scenario is - V is increasing more and more rapidly, U is decreasing and the decrease is slowing down. The complete set of all possible 41 Goodwin's scenarios and 168 time transitions among them are given. This result qualitatively represents all possible unsteady state Goodwin's behaviours. It is therefore possible to predict all possible future behaviours if a current behaviour is known/chosen. A prediction example is presented in details. No prior knowledge of qualitative model theory is required.

Název v anglickém jazyce

Qualitative analysis of the Goodwin model of the growth cycle

Popis výsledku anglicky

Goodwin's model is a set of ordinary differential equations and is a wellknown model of the growth cycle. However, its four constants require an extensive numerical study of its two differential equations to identify all possible unsteady state behaviors, i.e. phase portraits, which corresponds to infinitely many combinations of numerical values of the constants. Qualitative interpretation of Goodwin's model solves these problems by replacing all numerical constants and all derivatives by trends (increasing, constant and decreasing). The model has two variables - the employment rate V, and the labour share U. A solution of the qualitative Goodwin's model is a scenario. An example of a Goodwin's scenario is - V is increasing more and more rapidly, U is decreasing and the decrease is slowing down. The complete set of all possible 41 Goodwin's scenarios and 168 time transitions among them are given. This result qualitatively represents all possible unsteady state Goodwin's behaviours. It is therefore possible to predict all possible future behaviours if a current behaviour is known/chosen. A prediction example is presented in details. No prior knowledge of qualitative model theory is required.

Druh

J_SC - Článek v periodiku v databázi SCOPUS

CEP obor

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OECD FORD obor

50202 - Applied Economics, Econometrics

Projekt

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Návaznosti

S - Specificky vyzkum na vysokych skolach

Rok uplatnění

2017

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Revista de Metodos Cuantitativos para la Economia y la Empresa

ISSN

1886-516X

e-ISSN

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Svazek periodika

neuveden

Číslo periodika v rámci svazku

23

Stát vydavatele periodika

ES - Španělské království

Počet stran výsledku

11

Strana od-do

223-233

Kód UT WoS článku

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EID výsledku v databázi Scopus

2-s2.0-85021742327