he second point to notice about (44) is that " Britain" should attach less weight to the balance of payments of other countries' currencies than to her own balance if currencies are all substitutes for one another; this follows because every ratio Deltaji / Deltaii < 1 for j not= 1.19
Leaving now the special case of the gross substitutes to return to the more general case represented by equations (42), we can find immediate implications of the Hicks conditions. First, if the Hicks conditions are satisfied, " normal" adjustments are implied in the sense that, ceteris paribus, a deficit in a country's balance of payments suggests depreciation and a surplus appreciation; this follows because every kii = Deltaii /Delta > 0 given the Hicks conditions of imperfect stability and alpha i< 0.
But more than this can be said. The following identities have to hold, from our definitions and Jacobi's ratio theorem:
the inequality following at once from the Hicks conditions of perfect stability. Proceeding to the last term we have
More generally, if the basic matrix [bij] is Hicksian, the matrix of the speeds required for hyperstability must satisfy the conditions that every principal minor be positive, that is,
Analogous conditions hold for the extended Hicks conditions if the system is to be hyperstable regardless of the currency used as the key currency. In this sense the Hicks conditions alone are sufficient to establish in a weak sense the correctness of exchange rate policies directed at correcting "own" balances of payments.
These developments conform to the conclusions of economic intuition indeed, they may be interpreted as bringing the mathematical treatment of the subject closer to the level of common sense. They nevertheless suggest that the Hicksian stability analysis is not lacking in significance for the integration of dynamical and statical theory.20, 2l
1 Adapted from: a forthcoming article in Essays in Honor of Sir John R. Hicks (N. Wolfe, ed.).
2 I am happy to acknowledge many helpful conversations on the sub