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International Economics, Robert A. Mundell, New York: Macmillan, 1968, pp. 298-317.
Robert A. Mundell
The stability analysis introduced by Hicks has been one of the most successful failures in economic theory. Originally developed to integrate statical and dynamical general equilibrium theory, it was used by Hicks (, p. 62) as a bridge between dynamics and comparative statics:
The laws of change of the price system, like the laws of change of individual demand, have to be derived from stability conditions. We first examine what conditions are necessary in order that a given equilibrium system should be stable; then we make an assumption of regularity; that positions in the neighbourhood of the equilibrium position will be stable also; and thence we deduce rules about the way in which the price-system will react to changes in tastes and resources.
But the stability conditions were not founded on an explicitly formulated dynamic system. Hicks had defined stability along conventional lines:
In order that equilibrium should be stable, it is necessary that a slight movement away from the equilibrium position should set up forces tending to restore equilibrium....
but concluded that stability requires that
. . . a rise in price makes supply greater than demand, a fall in price demand greater than supply.
This is indeed the stability condition corresponding to a dynamic system in which excess demand causes a rise in price, but, as Samuelson pointed out, the proposition is not explicitly derived as the condition of convergence of such a dynamical system. The problem may be considered trivial in the case of a single market,3 but it raises difficulties in analysis and interpretation in the case of multiple exchange (exchange of more than two commodities), as Hicks foresaw (, p. 66):
What do we mean by stability in multiple exchange ? Clearly, as before, that a fall in the price of X in terms of the standard commodity will make the demand for X greater than the supply. But are we to suppose that it must have this effect (a) when the prices of other commodities are given, or (b) when other prices are adjusted so as to preserve equilibrium in the other markets?
To resolve the difficulty Hicks introduced his concepts of perfect and imperfect stability. He noted first that it was necessary to distinguish a series of conditions-that a rise in the price of X will make supply greater than demand (1) all other prices being given, (2) allowing for the price of Y being adjusted to maintain equilibrium in the Y market, (3) allowing for the prices of Y and Z being adjusted, and so on, until all prices have been adjusted. He then defined as imperfectly stable a system in which a rise in price of a commodity causes excess supply for the commodity after all repercussions are allowed for, and as perfectly stable a system in which a rise in price causes excess supply regardless of how many other prices are adjusted to attain equilibrium values in their respective markets.4
Samuelson  criticized Hicks' concept of stability on the grounds, as stated above, that "stability conditions are not deduced from a dynamic model, except implicitly." Hicksian stability is not equivalent to "true" dynamic stability, and the Hicks conditions are neither necessary nor sufficient for the convergence of the dynamical system implicit in Hicks' dynamics, that is, the dynamic system Samuelson postulated as the "natural extension" of the Walrasian system. True dynamic stability requires that the roots of the characteristic equation of the dynamic system have negative real parts, and this requirement is not equivalent to the Hicks conditions.5
Samuelson's criticism undermined the logic of Hicks' method. But the conditions of stability produced by that method retained an important place in the literature. Samuelson had already observed that the Hicks conditions were equivalent to the conditions of "true" dynamic stability in the symmetrical case. Metzler showed that they were equivalent in the case of gross substitutes, and also necessary 