l conditions are not satisfied.
The general conditions are necessary conditions for a system to be stable regardless of the currency (commodity) chosen as key currency (standard commodity) and regardless of how quickly the various exchange rates adapt to disequilibrium. This proposition is perfectly general in the sense that it is valid in the n-currency case.16
I shall conclude this book by showing how the Hicks conditions, extended as above, can be useful in devising dynamic mechanisms that are "strongly stable." The problem could be approached from the direction of the correspondence principle, which, in a narrow version of it, suggests that we apply to comparative statics the conditions that the characteristic equation of the systems have negative real parts. The justification for this narrow version lies in the observation that the systems we know are not characterized by instability. But there is no reason, in principle, why stronger conditions could not be applied. We could, following Hicks (and Samuelson), require that the system be stable no matter which subsets of market variables are held constant. Alternatively, we could use conditions that the roots be real or complex according to whether we observe cycles in the system under investigation.17 If, for example, we observe an absence of cycles in the real world, we know at once that the Hicks conditions are sufficient conditions for dynamic stability.
In the theory of policy (under incomplete information) the problem is often to choose among different dynamic systems, or different degrees of centralization of a given dynamic system; this is often expressed in terms of allocating, dynamically, instruments to targets (the problem of effective market classification), and we may want to construct strongly stable systems: first, because systems near the borderline of stability may become unstable if disturbed by outside shocks; second, because the cost of adjustment may be higher if the system, even though stable, oscillates in its approach to equilibrium; t