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Topics in Classical Micro- and Macroeconomics pp 351–390Cite as

Composite Classical and Keynesian Adjustment Processes

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Abstract

This chapter attempts an integration of Keynesian dual and Classical cross-dual micro-dynamic adjustment processes in the framework of a standard Leontief model. It investigates why strategies which are capable of proving stability for each separate case cannot in general successfully be applied to the composite system, where both prices and quantities are each revised on the basis of two instead of only one principle, namely supply/demand – as well as price/cost – discrepancies. It will be shown that significant limits to the adjustment speeds in the Classical domain have to be postulated in order to prove stability for the composite dynamics by means of the standard tools of the Walrasian tâtonnement literature. In view of these results an alternative approach to the stability of such composite systems is then introduced and applied to this system. This approach takes explicitly into account the type of composition of our dynamic system, i.e., its set of negative feedback mechanisms and the various interactions that may in addition exist between such substructures, which makes this approach of great methodological interest.

Our central findings are that there exist three different ways which allow to prove stability for our composite Keynesian/Classical structure (diagonal dominance, quasi-negative definiteness and the above new approach with a two-level type of stability analysis). In each of these approaches, however, we have to assume relatively narrow limits for the strength of the Classical component to obtain a stable composite dynamics. In contrast, no such narrow restrictions can be detected when the eigenvalues of numerical examples are calculated for a wide range of adjustment coefficients, even though counterexamples to stability do indeed exist then as well in other cases (see the mathematical appendix, subsection 1).

The exact limits for the stability of our composite system therefore remain an open question in the present chapter. Their determination may, however, be subordinate to another problem, which is the need for a more developed analysis of Classical dynamics itself before the stability properties of its integration with Keynesian types of adjustments processes are discussed in more depth.

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Notes

  1. 1.

    This is an early example of a saddle-point instability, the now favored type of dynamics in approaches which make use of ‘rational’ expectations.

  2. 2.

    See Flaschel and Semmler (1987) for a more detailed analysis of the Classical dynamics.

  3. 3.

    Further useful references on this topic are Berussou and Titli (1982), Medio (1987), Michel and Miller (1977), and part I in Singh and Titli (1979).

  4. 4.

    e.g., the price reaction \(\dot{p}\) due to excess demand in its dependence on prices p.

  5. 5.

    See also the observations on Euler’s method in Ortega and Poole (1981, pp. 38 ff.), there with regard to models of predator-prey type.

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Authors and Affiliations

  1. Department of Business Administration and Economics, Bielefeld University, Universitaetsstrasse 25, 33615, Bielefeld, Germany

    Prof. Dr. Peter Flaschel

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  1. Prof. Dr. Peter Flaschel
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Flaschel, P. (2010). Composite Classical and Keynesian Adjustment Processes. In: Topics in Classical Micro- and Macroeconomics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-00324-0_16

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  • DOI: https://doi.org/10.1007/978-3-642-00324-0_16

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