sses, and (b) the assumption of stability. Acceptance of (b) is the essence of the correspondence principle, but how are we to determine (a)?
Consider, for example, the following alternative expressions for dynamical systems:
To each of these systems there will correspond a different set of stability conditions. System (1) is a version of that used by Samuelson to prove that the Hicks conditions are neither necessary nor sufficient for stability. Yet, as he himself noted, more complete generalizations such as (2) and (3) can be developed with different consequences for comparative statics. There is, therefore, an element of arbitrariness in the specification of dynamic systems in the absence of empirical information and there may on these grounds be a pragmatic justification for Hicks' method of developing " stability conditions " that are "timeless." The Samuelson criterion is completely general and is an appropriate methodological approach, but for purposes of yielding practical results generality often implies emptiness.
The purpose of this chapter is to show that the Hicksian stability analysis is a useful contribution to the integration of statical and dynamical theory. First, we shall show that the perfect and imperfect stability conditions do correspond to the dynamic stability conditions of some dynamic processes, irrespective of the pattern of signs of the price-matrix. Second, we shall argue that, despite their usefulness in the form Hicks presented them, the perfect stability conditions are not completely general, since they do not yield the information obtained by extending his method to the commodity "adopted" as the standard commodity. Third, we shall show that generalized conditions can be obtained by interpreting his device of holding subsets of prices constant with respect to the standard commodity as an arbitrary method of forming various composite commodity groupings. Further, we shall show that dynamic systems that fail to satisfy the generalized conditions will be unstable at some speeds of a