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 discussion is not completely clear, however, and I am therefore inclined to interpret Hicks as actually intending to give full coverage to the numéraire but not completing the mathematical implications of doing so.
13 I have considered the problem of " optimum" currency areas in terms of its attributes for stabilization policy, optimum exploitation of the functions of money, and so on in Chapter 12; the present analysis suggests an additional criterion in terms of stability conditions.
14 Stability conditions should, in principle, be "invariants" in the sense that they are independent of the choice of units in which commodities are measured; this corresponds to Lange's "principle of invariance" (, p. 103). The above stability conditions are invariants only if, as is assumed in the case of the foreign exchange market analysis, the bij's are all measured in equivalent currency units.
In the general case, however, where prices respond to excess demands denominated in physical quantity units, the units in which bij( j