Abstract
The central place of the concept of equilibrium in economic theory justifies the interest of economists in stability (a concept they employ in the same sense as mathematicians and physicists, as the quotations show). In fact, an equilibrium which (supposing that it has been hit upon by chance) is such that the slightest disturbance starts a movement away from it – i.e., an unstable equilibrium – is usually considered unmeaningful from an economic point of view. Besides, the comparative static and/or comparative dynamic analysis of an equilibrium, which are among the main tools of the trade, become useless if the equilibrium is unstable. The concern over stability, which dates back at least to Marshall (1879a) and Walras (1874; for a discussion of the priority problem see Jaffé’s note 5 to lesson 7, pp. 502–3 in his translation of Walras’s Elements), has led economists either to assume that equilibrium is stable (this involves the study of the necessary stability conditions and their use in comparative statics) or to search for ‘plausible’ conditions which ensure stability; these are usually sufficient stability conditions only (this is, for example, the approach taken in the study of the stability of general competitive equilibrium). However, in some cases, the presence of instability is an essential feature as, for example, in Hicks’s trade cycle model (1950). Therefore the epistemological question arises of whether stability is a good ontologically (and instability an evil) or not. This problem will be discussed in the last section.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Bibliography
Andronov, A.A., A.A. Vitt, and S.E. Khaikin. 1966. Theory of oscillators. London: Pergamon Press.
Bellman, R. 1953. Stability theory of differential equations. New York: McGraw-Hill.
Blatt, J.M. 1983. Dynamic economic systems – A post Keynesian approach. Armonk: Sharpe.
Coddington, E.A., and N. Levinson. 1955. Theory of ordinary differential equations. New York: McGraw-Hill.
Dore, M.H.I. 1985. On the concept of equilibrium. Journal of Post Keynesian Economics 7(2): 193–206, 1984–5.
Edgeworth, F.Y. 1881. Mathematical psychics. London: Kegan Paul. Reprinted, A.M. Kelley: New York, 1967.
Fisher, F.M. 1983. Disequilibrium foundations of equilibrium economics. Cambridge: Cambridge University Press.
Frisch, R. 1936. On the notion of equilibrium and disequilibrium. Review of Economic Studies 3: 100–105.
Gandolfo, G. 1980. Economic dynamics: Methods and models. Amsterdam: North-Holland.
Gandolfo, G. 1981. Qualitative analysis and econometric estimation of continuous time dynamic models. Amsterdam: North-Holland.
Gandolfo, G., and P.C. Padoan. 1980. A disequilibrium model of real and financial accumulation in an open economy. Berlin/Heidelberg/New York/Tokyo: Springer.
Goodwin, R.M. 1982. Essays in economic dynamics. London: Macmillan.
Hahn, F.A. 1982. Stability. In Handbook of mathematical economics, vol. II, ed. K.J. Arrow and M.D. Intriligator. Amsterdam: North-Holland.
Haken, H. 1983a. Synergetics – An introduction, 3rd ed. Berlin/Heidelberg/New York/Tokyo: Springer.
Haken, H. 1983b. Advanced synergetics. Berlin/Heidelberg/New York/Tokyo: Springer.
Hicks, J.R. 1939. Value and capital, 2nd ed. Oxford: Oxford University Press. 2nd ed., 1946.
Hicks, J.R. 1950. A contribution to the theory of the trade cycle. Oxford: Oxford University Press.
Hirsch, M.W., and S. Smale. 1974. Differential equations, dynamical systems, and linear algebra. New York: Academic.
Kaldor, N. 1934. A classificatory note on the determinateness of equilibrium. Review of Economic Studies 1: 122–136. Reprinted as Determinateness of static equilibrium. In Essays on value and distribution, ed. N. Kaldor. London: G.Duckworth, 1960.
Kalman, R.E., and J.E. Bertram. 1960. Control system analysis and design via the ‘second method’ of Lyapunov, Part I. Transactions of the ASME. Series D, Journal of Basic Engineering 82(2): 371–393.
Krasovskii, N.N. 1963. Stability of motion – Applications of Lyapunov’s second method to differential systems and equations with delay. Stanford: Stanford University Press.
LaSalle, J.P., and S. Lefschetz. 1961. Stability by Liapunov’s direct method with applications. New York: Academic.
Lotka, A.J. 1925. Elements of physical biology. Baltimore: Williams & Wilkins. Reprinted as Elements of mathematical biology. New York: Dover, 1956.
Marshall, A. 1879a. The pure theory of foreign trade. Privately published. 1879b. The pure theory of domestic values. Privately printed and circulated. Reprinted with Marshall (1879a) in one vol. in the London School of Economics Series, Reprints of Scarce Tracts in Economics and Political Science, No. 1, London: London School of Economics and Political Science, 1930.
Marshall, A. 1890. Principles of economics. London: Macmillan. 8th ed., 1920. 9th (Variorum) edn, ed. C.W. Guillebaud, 1961.
Medio, A. 1984. Synergetics and dynamic economic models. In Non-linear models of fluctuating growth, ed. R.M. Goodwin, M. Krüger, and A. Vercelli. Berlin/Heidelberg/New York/Tokyo: Springer.
Minorsky, N. 1962. Nonlinear oscillations. New York: Van Nostrand.
Newman, P. 1961. Approaches to stability analysis. Economica 28: 12–29.
Samuelson, P.A. 1947. Foundations of economic analysis. Cambridge, MA: Harvard University Press. Enlarged edn, 1983.
Sansone, G., and R. Conti. 1964. Non-linear differential equations. London: Pergamon Press.
Silverberg, G. 1984. Embodied technical progress in a dynamic model: The self-organization paradigm. In Nonlinear models of fluctuating growth, ed. R.M. Goodwin, M. Krüger, and A. Vercelli. Berlin/Heidelberg/New York/Tokyo: Springer.
Thom, R. 1972. Stabilité structurelle et morphogénèse. Trans. as Structural stability and morphogenesis. Reading: Benjamin, 1975.
Varian, H.R. 1981. Dynamical systems with applications to economics. In Handbook of mathematical economics, vol. I, ed. K.J. Arrow and M.D. Intriligator. Amsterdam: North-Holland.
Vercelli, A. 1982. Is instability enough to discredit a model? Economic Notes 3: 173–190.
Walras, L. 1874. Eléments d’économie politique pure. Lausanne: Corbaz et Cie. Definitive edn, Paris: Pichon et Durand Auzias, 1926. Trans. with notes and collation of editions by W. Jaffé as Elements of pure economics. London: Allen & Unwin, 1954.
Author information
Authors and Affiliations
Editor information
Copyright information
© 2018 Macmillan Publishers Ltd.
About this entry
Cite this entry
Gandolfo, G. (2018). Stability. In: The New Palgrave Dictionary of Economics. Palgrave Macmillan, London. https://doi.org/10.1057/978-1-349-95189-5_1678
Download citation
DOI: https://doi.org/10.1057/978-1-349-95189-5_1678
Published:
Publisher Name: Palgrave Macmillan, London
Print ISBN: 978-1-349-95188-8
Online ISBN: 978-1-349-95189-5
eBook Packages: Economics and FinanceReference Module Humanities and Social SciencesReference Module Business, Economics and Social Sciences