ON COMPOSITE CLASSICAL AND KEYNESIAN MICRO-DYNAMICAL PROCESSES

: This paper continues the investigation of Flaschel/Semmler(1988) on Keynesian dual and Classical cross-dual micro-dynamic adjustment processes. It analyzes further the range of stability of the dynamics which is obtained by an integration or composition of these two processes, where prices and quantities are each revised on the basis of two instead of only one principle, namely in response to supply/demand- as well as price/cost-discrepancies. The paper briefly shows that the procedures normally used to prove the stability of each separate case can be applied to this composite system only in a fairly limited way. Significant bounds on the adjustment speeds in the Classical domain have to be assumed 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 a composite system is then sketched and applied to this system. This approach takes into account the kind of composition of this extended dynamic system, i.e., its set of negative feedback mechanisms (the diagonal blocks of the complete structure) and the various interactions that can become established between these isolated and stable substructures. The findings in this paper are then 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 we have to assume certain limits for the strength of the Classical component to obtain a stable composite dynamics. In contrast to these theoretical results, no such (narrow) restrictions can be detected when the eigenvalues of numerical examples are calculated for a wide range of adjustment coefficients, even though - as we shall demonstrate - counterexamples to the general stability of this composite adjustment process do exist.