But such a definition does not advance us much, as the following illustration will show. As it happens, our forbears in antiquity have left us the interesting piece of information that the construction of the Propylaea on the Acropolis in Athens cost a little more than 2,000 gold talents. Was this dear or cheap? Naturally, the talent is not negotiable on the exchanges of our day, but on the basis of its gold content we can establish that a sum of 2,000 talents would be equivalent to about 4,000,000 gold dollars. But was the purchasing power of the 2,000 talents equal to that of 4,000,000 gold dollars? We must admit that we are completely in the dark about this. It is possible that in ancient Athens, bread and eggs were much cheaper than they are today in New York or London; on the other hand, some things were probably more expensive than they are today, some, indeed, infinitely more expensive—things which all the gold in antiquity could not buy for the simple reason that they did not exist. Such were the radio, the telephone, electricity, and other goods upon which we moderns place such great value. Since the composition of demand has completely changed, we lack the means of comparing the purchasing power of money of those times with that of our own. Moreover, comparisons of purchasing power cannot be made unless we know the relative importance of each item in that average or typical “bundle” of goods of which we have spoken, and this relative importance of the different items varies in the course of the years. Hence, historical comparisons of purchasing power are always matters of conjecture, more or less. Furthermore, since the relative importance of each commodity varies not only from century to century but also from country to country, comparisons of the value of money are exceedingly difficult to make not only in time but also in space. True, we hear talk of expensive countries and cheap countries, and there is no denying that with an equal sum of money a traveler may be better off in one country than in another. But it is only with serious qualifications that we can accept the flat assertion that four German marks have the same purchasing power as one United States dollar.* Many who have spent longer periods of time in the one and in the other country, and whose scales of preferences differ, may rightly question the validity of such parities, proving once again how questionable are all such calculations of average purchasing power.
The extremely problematical character of such average estimates may be seen in an analogous kind of measurement. Every skier knows that meteorological data describing the snow as being of a depth of so and so many inches will often be unreliable; violent winds or a hot sun may have left his favorite slopes bare of snow. The practice of announcing the average fall of snow is not, for all that, devoid of utility. But if we would really like to establish what the average fall is, we should eventually have to measure the depth of the snow in all locations and to reduce to an average these numerous particular data. But even then we would have omitted to consider a fact of especial interest to skiers, namely, that though some slopes may be superbly covered, there will be others completely denuded of snow. Measurement of the snowfall in all places is patently impossible, but another possibility remains. We can content ourselves with measuring the fall of snow in fifty places, and with these partial measurements estimate the average fall, taking into account the area covered at a given height by the snowfall. In other words, we use a practicable number of particular measurements and then “weigh” the results according to their importance. This is exactly the way in which we attempt to estimate the average level of prices (and the variations from it) : we ascertain this level by means of so-called index numbers. We are now aware, however, that there is a certain arbitrariness which enters into all such calculations.14 This arbitrariness, we may add, is limited in its effects, being of less importance the greater is the change in the value of money. For example, during the German inflation, the crudest index numbers still served their purpose. Vice versa, a change in the value of money can be unambiguously determined only when the change is one of large degree.
If the concept of the purchasing power of money is problematical, the supposed connection between the purchasing power of money and the quantity of money, of which we have already made mention, is equally so. It does not detract from the fundamental truth of the quantity theory of money to add that there are features of this theory which are, to say the least, highly problematical.15 As it is hardly possible to give here even a brief description of the more doubtful aspects of the quantity theory, we shall content ourselves with two important observations. We should note, in the first place, that the quantity of money is not the sole determinant of its purchasing power. It is clear that if the quantity of money remains the same while the quantity of goods offered for sale varies, the purchasing power of money will vary correspondingly. Secondly, it is clear that it is not simply the quantity of money which determines purchasing power but only that fraction of it which is actually spent in a given period. If the rate at which money is expended (velocity of circulation) increases, the effects on the purchasing power of money will be the same as those caused by an increase in the quantity of money, velocity remaining unchanged.16 Thirdly, particular attention should be directed to the fact that the connection between the quantity of money and its purchasing power is less and less problematical the greater is the change in purchasing power. The greater the degree of monetary depreciation, the simpler becomes the analysis of its causes. In the macroscopic proportions of the great German inflation (192023), even the crudest form of the quantity theory which attributed the depreciation of the mark only to the gigantic increase in the money supply fitted the facts immeasurably better than those explanations which sought to ascribe the blame to other factors, in particular to Germany’s then “passive” (unfavorable) balance of payments.