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 Hicks conducts to derive his stability conditions he accords the numéraire -the standard commodity- a special role. In this section we shall consider the precise deficiencies in the statical information provided by the Hicks conditions. This is best established by considering the comparative statics theorems implied by the Hicks conditions. Consider the equilibrium system
where, again, the Bi's are balances of payments, the p's are exchange rates, and alpha is a parameter.
Differentiation of (11) with respect to alpha yields
and the solutions for the exchange-rate changes are
Now consider an increase in demand for the currency of country i such that deltaBi / delta alpha > 0; while the excess demand for every other currency, at given exchange rates, is unchanged (deltaBj / delta alpha = 0 for i not= j). Then, instead of (13), we have simply
By the Hicks conditions of imperfect stability Deltaii /Delta < 0, so deltaBi / delta alpha > 0 implies dpi / d alpha > 0. Thus an increase in demand for the currency of the ith country raises the price of that currency after adjustment of all other exchange rates has been allowed for.
Similar implications follow from the conditions of perfect stability if we hold various subsets of other exchange rates constant relative to the numéraire. If, for example, the exchange rates of countries k, . . ., n are held constant, we get, instead of (14), the equation
the inequality being an implication of one of the conditions of perfect stability.
How can an increase in demand occur in a closed system ? Clearly only at the expense of other commodities (currencies) in the system. Cournot's law (or Walras' law in the context of the Walrasian system) ensures that
where the summation, it should be emphasized, extends over all the commodities. The interpretation of (14) is therefore that an increase in demand for (say) pounds (the currency of country i) at the expense of dollars raises the dollar price of the pound. Now if other exchange rates are held constant relative to the dollar, the pro