Abstract
In recent neoclassically and classically oriented literature on competitive processes several models have been presented which work not only with the ‘law of demand’ but also with the ‘law of profitability’. In such dynamical models a cross-dual process is stylized in which price changes are initiated by imbalances in supply and demand and changes of outputs are caused by profitability differentials. Such cross-dual dynamics can now be found in neoclassical tradition (Morishima 1976, 1977; Mas–Colell 1974, 1986) and in classical tradition. In classical tradition the analysis of such a cross-dual adjustment process was initiated particularly by some recent publications of Nikaido (1978, 1983, 1985) who questioned the stability of classical competition. In comparison to his results it is the purpose of this article to show that the classical approach to the dynamics of competition may be able to produce stability results which are of at least comparable interest to those of neoclassical stability theory.
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Notes
- 1.
We thank V. Caspari, K. Dietrich, G. Duménil, D. Foley, R. Franke, M. Glick, D. Lévy and A. Shaikh for helpful comments on an earlier version of this chapter.
- 2.
We should stress however that there also exists an established body of literature which dispenses with this type of anonymous market price adjustment by allowing individuals to set prices (see Hahn 1982; Fisher 1983 for details). Yet from a classical perspective, the interaction between natural and market prices was the important one, which is the reason why we neglect this part of the literature on the stability of market economics.
- 3.
This, for reasons of simplicity, is used to denote the corresponding theories of Smith, Ricardo and Marx as well as their followers.
- 4.
Though in our chapter the proofs of the stability properties of the proposed dynamical systems are provided by referring to the equilibrium or natural profit and growth rate R ∗ , computer simulations have shown that the results are not invalidated if the average profit and growth rate R(x, p) = pBx ∕ pAx instead of R ∗ is used as benchmark in our dynamical systems (see Flaschel and :̧def :̧def Semmler 1986a, 1986b). This actual rate, of course, constitutes the more important benchmark and should be used for this purpose in the end (see Steedman 1984, p. 135, for a related observation).
- 5.
Since our classical-oriented model in prices and quantities still (1) abstracts from the role of non-reproducible inputs, inventory and financial constraints, and (2) formulates demand functions (for a growing system) in a preliminary way, our cross-dual competitive process does not yet present a dynamical process in ‘real time’. As discussed above, similar complications also have led Walras to describe his process of groping in a production economy not as a process ‘as it takes place effectively’. Our proposed cross-dual process however, lends itself to two possible interpretations. First, the suggested cross-dual dynamics allows an application to the Taylor–Lange iteration to an equilibrium in a planned economy, see also the remarks of Mas–Colell (1986, pp. 60) on the iterative determination of an equilibrium in a planned economy by means of the ‘indirect’ Walrasian instead of the ‘direct’, more Keynesian, method. Second our proposed dynamics provides a framework for comparing corporate quantity, price and financial planning with classical competitive adjustment processes (see, in this regard also the remarks of Clifton 1983, pp. 30/31 on ‘dynamic tâtonnement’ and corporate planning, and also Semmler 1985, Chap. 6). In fact, the actual pricing procedures of large multi-plant and multi-product firms can be viewed as two stage procedures where first, ‘base prices’ including a normal rate of return on investments are computed to be modified flexibly in a second stage by responding to changing market conditions (capturing the imbalances in the markets where the firms operate).
- 6.
See Fisher (1983, Appendix) for further details on quasi-global stability.
- 7.
According to Fujimoto (1975), the natural rate R∗ is uniquely determined, because of our assumption p ∗ > 0.
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Flaschel, P. (2010). Classical and Neoclassical Competitive Adjustment Processes. In: Topics in Classical Micro- and Macroeconomics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-00324-0_15
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