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 economists who signed the petition.
10 This is perhaps apparent immediately, since the Hicks conditions can be expressed in terms of the commodity chosen as numéraire, the excess demand for which is never allowed to go to zero. On this point (but without apparent recognition of its implications) see Lange (, p. 92).
11 More compactly, we can state the conditions as requiring that every first minor of B be "Hicksian." Not all the conditions are independent, however, since B00 = B11 = Bnn in view of the characteristics of B.
12 One might think that Hicks really intended his conditions to extend over the entire range of excess demand coefficients (including the numéraire), this would be incorrect since the last (augmented) determinant is singular. Alternatively, it might be thought that Hicks intended the conditions to apply no matter what commodity were taken as numéraire. The latter interpretation seems to be fortified by a footnote which states ( p. 75): " [this] can be seen at once if we adopt the device of treating X (momentarily) as the standard commodity, and therefore regarding the increased demand for X as an increased supply of the old standard commodity m ...." If this device were adopted to derive the Hicks conditions it would indeed result in conditions equivalent to the above stability conditions. Yet this interpretation would conflict, not only with all subsequent interpretations of the Hicks conditions by other writers on stability, but also with Hicks' own explicit statement in the Mathematical Appendix (p. 315), which specifies that the conditions must hold "for the market in every Xr (r = 1, 2, 3, . . ., n-1)"; that is, the market for the numéraire (the nth commodity) is omitted, In any case his discussion on pages 68-71 fails to make the point clear, while his third graph in Figure 16, which he asserts is stable, is actually totally stable only if the line along which there is zero excess demand for the standard commodity (not drawn in his figures) is inelastic referred to the abscissa. The discu