 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