djustment 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 rate of one country, say the rth country, appreciates in proportion to its balance of payments surplus according to the law
while all other exchange rates adjust instantaneously to equilibrium. The solution of the differential system (6) is
and Deltarr is the cofactor (principal minor) of the element in its rth row and rth column.
For the dynamic process implied in (7) to be stable it is necessary and sufficient that Delta / Deltarr < 0. But this condition is precisely (for the analogous problem in the Walrasian system) the Hicksian condition of imperfect stability for the rth currency; and when the method is applied to each currency (in succession, not simultaneously), we have the complete Hicksian conditions of imperfect stability:
A similar analysis can help to show the usefulness of the Hicks conditions of perfect stability. Suppose that one exchange rate, say pi, is held constant (relative to the numéraire). This amounts to dropping the ith row and column from Delta, so that if the original experiment were repeated, this time with the ith exchange rate constant, we would get, instead of (7),
and the stability condition Deltaii / Deltaii,rr< 0, which is one of the Hicksian conditions of perfect stability. Proceeding along these lines, holding one or another set of prices constant, we get the complete Hicks conditions of perfect stability.
But does this dynamic process have any economic plausibility ? Are we not, as Samuelson argued, allowing "arbitrary modification of the dynamical equations of motion"? The answer is, in a sense, yes. But this can be the exact method needed in the theory of policy, where our purpose is to design stable dynamic systems.
As an example, we might be interested in examining aspects of the stability of an exchange-rate system such as that recently advocated by sixteen distinguished academic economists  -a sliding parity system (with widened exchange-rate margins).9 Is it not precisely a set of conditions such as the Hicks conditions that would be involved? We might ask, first, what would happen if, say, Britain (which we shall identify with country 1) adopted a sliding parity system while a subset of other countries (2, . . ., j) allowed their exchange rates to float, and the remaining countries, k, . . ., n, kept their rates pegged to, say, the U.S. dollar (the currency of country 0). Then, if we suppose that balances of payments of countries whose rates float adjust instantaneously while the pound adjusts slowly, the path of the pound over time would be
for which knowledge of the Hicks conditions would be directly relevant. Thus the particular form of the dynamic system adopted -which countries are left out and which are left in- would depend on which of the Hicks conditions are satisfied. The Hicks method does, therefore, have a role to play in dynamic aspects of the theory of economic policy.
The Hicks conditions, however, are not exactly what we need for the theory of economic policy, because, as we shall see, they are incomplete even in terms of Hicks' own method. In the experiments