v = u × E.
The relatively fixed value of the precious metals has made it possible for the unity of value to be determined on and easily represented by means of a certain quantity of metal, and the actual monetary system is the result, the value of all things having been henceforth expressed by means of the monetary unity identifying itself with the unity of value determined on. But it may in consequence be remarked in looking closely into this, and it is important to do so, that this result has been reached not because the thing: «metal money», has made its appearance, but because thanks to it, a common denominator of the value of things in general has been employed which did not exist before.
Now, as we shall see, this common denominator does not of necessity remain invariably tied to the thing, money, or more generally to any sort of material support which has served to define it at a given moment. Once fixed it may be considered independently of this support; becoming thus a permanent quantity in time and space, taking in consequence the character of a common measure of the transactional value of things and being employed as a unity of measure of that value[C].
In reality this hypothesis could only be made when there was no such thing as money, and a system of barter exclusively prevailing, those engaged in making transactions might have said to themselves. «Let us choose a common denominator of the value of things that we may write down our transactions, and not be any longer obliged to carry on the exchange of usable things when we do not want them, let us take for example the value of a kilogram of wheat here at ... to day, the ... as common denominator and let us calculate directly the value of all other things by this unity.
»Evidently every other thing would be worth as many times this unity as we see men would give kilograms of wheat to possess it, and thus the numerical value of things would be easily established.
»Let us agree further in future always to express the value of things by this initial value of the kilogram of wheat, a value which has only existed during the preceding operation, and which strictly can only have existed for an indefinitely short time, but which can be considered as absolutely permanent, and apart from any necessity of occupying ourselves with the variation of value undergone in time and space by the kilogram of wheat itself.»
It will result that if v' is the value of a thing at any period and at any place of which the originally fixed value was v, the relations will be:
| v = u × E | v' = u × E | ||
| whence: | v'/v = E'/E | and | v' = v × E'/E |
that is the value v of a thing at any time and place is equal to its initial value simply multiplied by the proportion of the terms which represent the conditions of the supply and demand at the two periods under consideration.
Let us note, that, as it should do the formula v'/v = E'/E shows that the unity is eliminated when the point in question is the estimate of relative values.