A clarification of the Goodwin model of the growth cycle

Abstract

We show that there is a difficulty in the original Goodwin model which is also found in some more recent applications. In it both the labour share and the proportion employed can exceed unity, properties which are untenable. However, we show that the underlying dynamic structure of the model can be reformulated to ensure that these variables cannot exceed unity. An illustrative example extends the original model, and we argue it is both plausible and satisfies the necessary unit box restrictions. r 2005 Elsevier B.V. All rights reserved.JEL classification: E32

Two-Population Social Cycle Theories

“…For instance, Mehrling (1986) added game-theoretic foundations to the original model, while Desai et al (2004) fix some problems in the mathematics that had allowed wages to be over 100% of output and employment to rise over 100%, and Sportelli (1995) seeks to eliminate the instability in Goodwin's original model.…”

Unemployment, income distribution and debt-financed investment in a growth cycle model

“…also Chiarella et al, 2000, p. 25 In this contribution, Chiarella and co-authors present the dynamic multiplier as a 'conventional' assumption of Keynesian macrodynamics. For the present model, in order to take into account the exogenous trend growth rate g n and the assumption that all wages are consumed, we adjust this basic principle as follows (cf., e.g., Glombowski and Krüger, 1988;Chiarella and Flaschel, 2000, p. 286…”

Giuseppe Palomba and the Lotka-Volterra equations

“…Dynamic systems that are such as not to vary in their essential features for a small variation of the form of the differential equations are called structurally stable. More formally, consider the modified system d y 1 dt = (a 1 − b 1 y 2 − py 1 ) y 1 = (a 1 − b 1 y 2 ) y 1 − py 2 1 , d y 2 dt = − (a 2 − b 2 y 1 + qy 2 ) y 2 = − (a 2 − b 2 y 1 ) y 2 − qy 2 2 ,…”

“…(2) Consider now the two species living together: the coefficient characterizing the rate of increase of the first species will no longer be a constant, but will be decreased owing to the existence of the extermination process (proportional to y 2 , the number of individuals of the second species), since fishes of the first species are eaten by fish of the second species. Thus, instead of a 1 , we have a 1 = a 1 − b 1 y 2 .…”

“…This seems a complicated way of saying that it is necessary to save (reduce consumption) in order to invest and increase the capital stock 2. Palomba does not specify what gives rise to this growth.…”