 the dollar and the other currencies pegged to it as a composite currency. By analogy the price of the pound should rise when demand shifts from a currency other than the dollar, say, the franc, while other currencies (for example, the mark) are pegged to the franc.
Thus consider a shift of demand, at constant exchange rates, among three currencies i, j and k, such that
and every other deltaBr / delta alpha = 0. Then, from (13), we have
Applying the restrictions that and setting
we can deduce the change in price of the pound relative to the mark and franc.
where A is the sum of the cofactors of the elements in the following matrix:
The cofactor of, say, the element Deltajk can be related to the second cofactors of Delta by Jacobi's ratio theorem,
so that A /Delta can be written entirely as the sum of second cofactors, and (24) can be rewritten
The inequality sign should hold if an increase in demand for one country's currency occurs at the expense of any other country, one other currency price remaining constant relative to that country. But the mathematical information is not given to us by the Hicks conditions. The reason is that the mathematical implications of the Hicks method have not been developed with respect to the currency adopted as numéraire.l0
When we do extend Hicks' method to make it " symmetrical " with respect to the numéraire (appreciating, say, the pound relative to, say, the franc, allowing various subsets of other currency markets to adjust), we get, of course, a set of conditions that specifies the signs of terms like those in (20) and (25). Along with the Hicks conditions, which can be written
[The next term requires that the ratio of the denominator of the second ratio and the sum of sixteen third minors be negative, and so on for successive ratios. The last term in the conditions of (27) specifies that the sum of the (n-l)th minors (n2 in number) be negative. But the (n-l)th minors are equivalent to the elements in the original determinant, so the last condition simply requires that the s