Stability

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.