t with respect to the numéraire we get instead
Imperfect stability requires that Deltaii /Delta < 0 for i = 1, . . ., n, whereas perfect stability requires that Deltaii,kk, ... ,nn / Delta kk ... ,nn < 0 for any subset of commodities k, ...,n, excluding commodity i. The Hicksian perfect stability conditions are thus
the first condition being the condition of imperfect stability.
5 It is slightly ironic that Marshall in his 1879 manuscript on foreign trade utilized the link between dynamics processes and stability, but not explicitly the link between stability and comparative statics, whereas Hicks utilized the link between stability and comparative statics but not the link between dynamics and stability. Samuelson used both links in his integration of dynamics and statics.
6 Actually, Metzler's example (p. 285) that the Hicks conditions are not sufficient for stability to be independent of the speeds of adjustment contains a numerical error that mars his demonstration [the second cubic of his footnote 12 should read lambda3 + 4lambda2 + 3.4lambda + 13.2 = 0 instead of lambda3 + 4lambda2 + 2.6lambda + 13.2 = 0 and in the first (correct) cubic the Routh conditions are satisfied]. But a slight adjustment to his counterexample can nevertheless demonstrate his point. If, for example, speeds are chosen so that, in his terminology, kl = k3 = 1, giving the cubic lambda3 + (2 + k2)lambda2 + (1+ 1.2k2) lambda + 6.6k2 = 0, the Routh conditions will not be satisfied for values of k2 somewhat less than 1.
7 In this connection Samuelson writes (, p. 554): "In principle the Hicks procedure is clearly wrong, although in some empirical cases it may be useful to make the hypothesis that the equilibrium is stable even without the 'equilibrating action' of some variable which may be arbitrarily held constant." Samuelson provides an example in connection with the Keynesian system later in his paper.
8 See, for example, Mundell  and the references there to the principle of effective market classification.
9 See page 111 for a list of 