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 proposition holds, if the Hicksian perfect stability conditions are satisfied, when the shift of demand is interpreted as being from the dollar and all currencies whose exchange rates are kept fixed to the dollar. Note, however, that the Hicks conditions do not give us the sign of
so that we cannot specify, on the grounds of the Hicks conditions alone, whether a shift of demand from dollars to pounds raises or lowers the price of (say) the franc relative to the dollar.
But now we are in a position to see the narrow form of the mathematical implications of the Hicks conditions. Consider a shift of demand from the franc (currency j) to the pound (currency i). Then deltaBs / delta alpha = 0 for s not= i, j, while deltaBi / delta alpha = - deltaBj / delta alpha >0 in view of (16); with no loss of generality we can make deltaBi / delta alpha = - deltaBj / delta alpha = 1. Substitution in (13) then gives the change in the dollar price of the pound and the franc:
The Hicks conditions do not provide us with the sign of 