APPENDIX TO CHAPTER VII
§ 1 (TO CHAPTER VII, § 2)
Money Substitutes Unlike Other Substitutes
Much reasoning has been based upon the assumption that the price determination of two commodities used as money is analogous to that of any other two commodities. It is clear, however, that two forms of money differ from a random pair of commodities in being substitutes. Two substitutes proper are regarded by the consumer as a single commodity. This lumping together of the two commodities reduces the number of demand conditions, but does not introduce any indeterminateness into the problem because the missing conditions are at once supplied by a fixed ratio of substitution. Thus, if ten pounds of cane sugar serve the same purpose as eleven pounds of beet-root sugar, their fixed ratio of substitution is ten to eleven; or if a bushel of India wheat can replace a bushel of Dakota wheat, the substitution ratio is unity. In these cases, the fixed ratio is based on the relative capacities of the two commodities to fill a common need, and is quite antecedent to their prices. Ten pounds of cane sugar can replace eleven pounds of beet-root sugar so long as human taste marks no other ratio. India and Dakota wheat have the same desirability or utility because they have the same relation to man's tastes. No change of market conditions, no change of price, could make a consumer regard one bushel of India wheat as equivalent to two of Dakota. The substitution ratio is fixed by nature, and in turn fixes the price ratio.
In the single case of money, however, there is no fixed ratio of substitution. In one age, ten ounces of silver may circulate as the equivalent of one of gold; in another, twenty ounces. No human taste or need will interfere. We have here to deal, not with relative sweetening power, nor relative nourishing power, nor with any other capacity to satisfy wants—no capacity inherent in the metals and independent of their prices. We have instead to deal only with relative purchasing power. We do not reckon a utility in the metal itself, but in the commodities it will buy. We assign their respective desirabilities or utilities to the sugars or the wheats before we know their prices, but we must first inquire the relative circulating value of gold and silver before we can know at what ratio we ourselves prize them. To us the ratio of substitution is identically the price ratio and therefore can have no influence in fixing that ratio. The case of two forms of money is unique. They are substitutes, but have no natural ratio of substitution, dependent on consumers' preferences.
The foregoing considerations are emphasized for the reason that they are overlooked by those writers who imagine that a fixed legal ratio is merely superimposed upon a system of supply and demand already determinate, and who seek to prove thereby that such a ratio is foredoomed to failure. This is the monometallist's favorite analogy. It is unsound, though its unsoundness does not necessarily involve the unsoundness of the monometallist's general conclusions. Gold and silver or any other two commodities which serve the purposes of money are not analogous to two ordinary and unrelated articles and are not completely analogous even to two substitutes, because, for two forms of money, there is no consumer's natural ratio of substitution. There seems, therefore, room for an artificial ratio. We shall see, however, that there are limits beyond which an artificial ratio will fail.
§ 2 (TO CHAPTER VII, § 2)
Limits for Ratios within which Bimetallism is Possible
A change of ratio is represented by a reconstruction of our reservoirs in new units, but we can, without the trouble of such a transformation, exhibit on the mechanism as it stands the limiting ratios between which bimetallism is possible. Suppose the film in Figure 7b to be forced, firstly to its extreme right limit, and secondly to its extreme left, and in each case permanent equilibrium to be attained. In the one case there is a premium on gold, in the other, a premium on silver. These premiums mark the divergences from the given ratio which are possible without destroying bimetallism. Thus suppose the legal ratio and that for which the mechanism is constructed is 32 of silver to 1 of gold and that, when the film is moved to the left limit, the level of gold will be below OO a distance 7/8 as great as the silver level, while at the right limit it will be 5/4. Then the ratio 32 to 1 can be varied between the factors 7/8 of 32 to 1 and 5/4 of 32 to 1 and bimetallism would succeed at any ratio between 32 × 7/8 to 1 and 32 × 5/4 to 1, i.e. between 28 to 1 and 40 to 1. A ratio below 28 to 1, such as the famous 16 to 1, would ultimately convert gold monometallism into silver monometallism, but would be inoperative in the opposite direction. A ratio above 40 to 1, such as 50 to 1, would ultimately convert silver monometallism into gold monometallism. A ratio between the two extremes would result in neither sort of monometallism but in bimetallism. The statistical determination of these limits is, of course, a problem which cannot with present knowledge be solved. The figures 28 and 40 are not intended as guesses, but purely as illustrations.