nerally, the Hicks conditions on the left correspond to Hicksian adjustments when each currency (commodity) is treated in isolation; the adjacent conditions to their right are the Hicksian conditions when in the ith and ith goods move in the same proportion; and so on. The entire set of conditions are needed if the logic of Hicks' method is carried out to the bitter end.14
An important implication of the general conditions is that a system satisfying the Hicks conditions, but not the general conditions, will be stable or unstable depending on which currency is adopted as the key currency.15 Consider, for example, a world of three currencies, dollars (currency 0), pounds (currency 1), and francs (currency 2), and suppose that the balances of payments of the three countries are related to exchange rates according to the equations
where the exchange rates are defined in, and the Bi are expressed in, an abstract unit of account (IMF par value units). (Equilibrium exchange rates are unity or any multiple of unity, as the system is homogenous of degree 0.)
Let us consider a dynamic system in which the dollar is constant with respect to its par value so that the dollar becomes the effective numéraire. Let the par values of the pound and franc adjust in proportion to B1 and B2, respectively. We then have the following dynamic system:
In this system, the Hicks conditions of perfect stability, narrowly interpreted, are satisfied (since b11 = -2 < 0, b22 = -1 < 0), and
and the system is dynamically stable regardless of the (positive and finite) values of kl and k2 .
Consider, however, a system in which the par value of the franc is fixed so that it becomes the "key currency " instead of the dollar. The dynamic system then becomes
for which the Hicks conditions are not satisfied, It is dynamically stable or unstable according to whether k0 >< 4kl .
This result could be predicted at once by applying the general conditions as given in the stability triangle (32). The sum of the coefficients in (34a) are positive, so the genera