Abstract
Goodwin’s application of the predator-prey model from mathematical biology to theoretical economics has stimulated a considerable stream of follow-up work, including some of our own1). Of course, Goodwin was quite aware that his model was “starkly schematized and hence quite unrealistic” (Goodwin 1972, p. 442). While this statement provided ample opportunity for extensions and generalizations, the main stimulus for modifications should be based, at least in our view, on the basic cycle-generating mechanism of the model. In contrast to many earlier contributions by Goodwin to business cycle theory, this mechanism is not a Keynesian, but rather a Marxian one. This is because real wage increases are positively related to employment: whenever the rate of employment exceeds (falls short of) its ‘normal’ level, wage rises (declines) increase (decrease) the wage share in net product. On the other hand, accumulation and labour demand fall below (rise above) their ‘normal’ level, whenever the profit share does. This idea can be traced back to the ‘general law of capitalist accumulation’ (Marx 1974, pp. 574–606) which has also been discussed in more recent Marxist works (Bauer 1986, Sweezy 1942, Itoh 1980). However, it was not given a mathematical formulation until Goodwin combined the Marxian idea with Volterra’s (1931) predator-prey model from mathematical biology.2)
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Notes
See Goodwin (1972), Goodwin, Krüger, and Vercelli (1984), Glombowski, Krüger (1983a) and (1985).
Goodwin states: “It has long seemed to me that Volterra’s problem of the symbiosis of two populations-partly complementary, partly hostile-is helpful in the understanding of the dynamical contradictions of capitalism, especially when stated in a more or less Marxian form.” (Goodwin 1972, p. 445).
This effect has been considered in another paper. See Glombowski, Krüger, (1983b).
As the net product need not necessarily be sold completely, profits may partly exist in the form of inventories. Major theoretical problems are not necessarily involved here if, on the average, inventory growth does not outstrip product growth. Whether the latter condition is met depends, of course, on the solution of the model.
Underconsumptionists are invited to analyse the consequences of the opposite assumption.
In some European countries, e. g., Italy and the Netherlands, wage indexation has been practised for considerable periods of time. This may render a3 = 1 a realistic assumption.
Cf. Atkinson (1969).
References
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Glombowski, J., Krüger, M. (1987). Generalizations of Goodwin’s Growth Cycle Model. In: Batten, D., Casti, J.L., Johansson, B. (eds) Economic Evolution and Structural Adjustment. Lecture Notes in Economics and Mathematical Systems, vol 293. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-02522-2_11
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