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.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Notes
- 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.
See Flaschel and Semmler (1987) for a more detailed analysis of the Classical dynamics.
- 3.
- 4.
e.g., the price reaction \(\dot{p}\) due to excess demand in its dependence on prices p.
- 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.
References
Aoki, M. (1977). Dual stability in a Cambridge-type model. Review of Economic Studies, 44, 143–151
Arrow, K., Karlin, S. & Suppes, P. , (Eds.). (1960). Mathematical social sciences. Stanford: Stanford University Press
Berussou, J. & Titli, A. (1982). Interconnected dynamical systems: stability, decomposition and decentralisation. Amsterdam: North Holland
Drazen, A. (1980). Recent developments in macroeconomic disequilibrium theory. Econometrica, 48, 283–306
Duménil, G. & Lévy, D. (1987a). The dynamics of competition: A restoration of the Classical analysis. Cambridge Journal of Economics, 11, 133–164
Duménil, G. & Lévy, D. (1987b). The stability of long-term equilibrium in a general disequilibrium model. Paris, Mimeo: CEPREMAP
Flaschel, P. & Semmler, W. (1986). The dynamic equalization of profit rates for input–output models with fixed capital. In W. Semmler (Ed.), Competition, Instability, and Nonlinear Cycles. Berlin: Springer, 1–34
Flaschel, P. & Semmler, W. (1987). Classical and neoclassical competitive adjustment processes. The Manchester School, 55, 13–37
Franke, R. (1987). Production prices and dynamical processes of the gravitation of market prices, Bern: Peter Lang
Fukuda, W. (1975). The output adjustment mechanism in a multisectoral economy. Kobe University Economic Review, 21, 53–62
Gantmacher, F. R. (1970/1). Matrizenrechnung I, II. Berlin: VEB Deutscher Verlag der Wissenschaften
Goodwin, R. M. (1953). Static and dynamic general equilibrium models, In R. M. Goodwin (Ed.), Essays in linear economic structures. London: Macmilan, 75–120
Goodwin, R. M. (1970). Elementary economics from the higher standpoint. Cambridge: Cambridge University Press
Goodwin, R. M. (1983). Essays in linear economic structures. London: Macmillan
Goodwin, R. M. (1988). Essays in nonlinear economic dynamics. Bern: Peter Lang
Goodwin, R. M. & Punzo, L. F. (1986). The Dynamics of a Capitalist Economy. Cambridge: Polity
Gordon, R. J. (1983). A century of evidence on wage and price stickiness in the United States, the United Kingdom and Japan. In J. Tobin (Ed.), Macroeconomics, prices and quantities. Washington D.C.: Brookings Institutions, 125–147
Hahn, F. (1982). Stability. In K. J. Arrow & M. D. Intrilligator (Eds.), Handbook of mathematical economics. Amsterdam: North Holland, 45–67
Hicks, J. (1965). Capital and growth. Oxford: Oxford University Press
Jorgenson, D. W. (1960). A dual stability theorem. Econometrica, 28, 892–892
Kaldor, N. (1985). Economics without equilibrium. New York: M.E. Sharpe
Kemp, M. C & Kimura, Y. (1978). Introduction to mathematical economics. Heidelberg: Springer
Lancaster, P. (1969). The Theory of Matrices. New York: Academic Press
Lancaster P. & Tismenetsky, M. (1985). The Theory of matrices. New York: Academic
Leijonhuvud, A. (1968). On keynesian economics and the economics of keynes. Oxford: Oxford University Press
Marshall, A. (1947). Principles of economics. London: Macmillan
Marx, K. (1967). Capital, Vol.III. New York: International Publishers
Mas–Colell, A. (1986). Notes on Price and Quantity Dynamics. In H. Sonnenschein (Ed.), Models of economic dynamics, Heidelberg: Springer, 86–112
Medio, A. (1987). A multisector model of the trade cycle. In D. Batten, J. Casti & B. Johansson (Eds.), Economic evolution and structural adjustment (pp. 291–313). Heidelberg: Springer
Michel, A. N. & Miller, R. K. (1977). Qualitative analysis of large scale dynamical systems. New York: Academic
Morishima, M. (1960). A reconsideration of the Walras-Cassel-Leontief model of general equilibrium. In K. Arrow, S. Karlin, & Suppes, P. (Eds.), Mathematical social sciences. Stanford: Stanford University Press, 156–177
Morishima, M. (1976). The economic theory of modern society. Cambridge, UK: Cambridge University Press
Morishima, M. (1977). Walras’ economics. Cambridge, UK: Cambridge University Press
Ortega, Y. M. & Poole, W. G. Jr. (1981). An introduction to numerical methods for differential equations. Marshfield, Mass: Pitman
Ricardo, D. (1951). Principles of political economy and taxation. Cambridge: Cambridge University Press
Semmler, W. (1984). Competition, monopoly and differential profit rates. New York: Columbia University Press
Semmler, W., (Ed.). (1986). Competition, instability and nonlinear cycles. Lecture Notes in Economics and Mathematical Systems. Heidelberg: Springer
Siljak, D. D. (1978). Large-Scale dynamic systems. Stability and structure. New York: North Holland
Singh, M. G. & Titli, A. (Eds.). (1979). Handbook of large scale systems. Engineering applications. Amsterdam: North Holland
Smith, A. (1974). The wealth of nations. Middlesex: Pinguin
Sonnenschein, H., (Ed.). (1986). Models of economic dynamics, Heidelberg: Springer
Tobin, J., (Ed.). (1983). Macroeconomics, prices and quantities. Washington D.C.: Brookings Institutions
Walras, L. (1977). Elements of pure economics. Fairfield, New Jersey: Kelley
Woods, J. E. (1978). Mathematical economics. London: Longman
Zurmühl, R. (1964). Matrizen und ihre technischen anwendungen Heidelberg: Springer
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2010 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
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
Download citation
DOI: https://doi.org/10.1007/978-3-642-00324-0_16
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-00323-3
Online ISBN: 978-3-642-00324-0
eBook Packages: Business and EconomicsEconomics and Finance (R0)