lies 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 adjustment when a different commodity is adopted as the standard commodity in the dynamic system. And finally, we shall discuss the usefulness of the generalized Hicks conditions in devising dynamical rules for the hyperstability of " policy systems."8 The illustrative examples are all taken from the theory of foreign exchange markets, but the results, of course, apply to any generalized system.
Our first task is to show that the Hicks conditions do, in a sense, correspond to the conditions of convergence of some dynamic systems. Let us take as an example a problem in devaluation theory. We can describe a closed static equilibrium system of n + 1 currencies with prices (exchange rates) expressed in terms of currency 0, denoted by p1, . . . pn, as follows:
where Bi is the balance of payments of the ith country. In equilibrium each Bi = 0, while near the equilibrium we can write the system (4) as follows:
after expanding Bi in a Taylor series and omitting nonlinear terms.
Now let us suppose that the exchange rat