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IV: “Measuring” Changes in the Purchasing Power of the Monetary Unit - Ludwig von Mises, On the Manipulation of Money and Credit: Three Treatises on Trade-Cycle Theory 
On the Manipulation of Money and Credit: Three Treatises on Trade-Cycle Theory. Translated and with a Foreword by Bettina Bien Greaves,. Edited by Percy L. Greaves, Jr. (Indianapolis: Liberty Fund, 2011).
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“Measuring” Changes in the Purchasing Power of the Monetary Unit
All proposals to replace the commodity money, gold, with a money thought to be better, because it is more “stable” in value, are based on the vague idea that changes in purchasing power can somehow be measured. Only by starting from such an assumption is it possible to conceive of a monetary unit with unchanging purchasing power as the ideal and to consider seeking ways to reach this goal. These proposals, vague and basically contradictory, are derived from the old, long since exploded, objective theory of value. Yet they are not even completely consistent with that theory. They now appear very much out of place in the company of modern subjective economics.
The prestige which they still enjoy can be explained only by the fact that, until very recently, studies in subjective economics have been restricted to the theory of direct exchange (barter). Only lately have such studies been expanded to include also the theory of intermediate (indirect) exchange, i.e., the theory of a generally accepted medium of exchange (Monetary Theory) and the theory of fiduciary media (Banking Theory) with all their relevant problems.1 It is certainly high time to expose conclusively the errors and defects of the basic concept that purchasing power can be measured.
Exchange ratios on the market are constantly subject to change. If we imagine a market where no generally accepted medium of exchange, i.e., no money, is used, it is easy to recognize how nonsensical the idea is of trying to measure the changes taking place in exchange ratios. It is only if we resort to the fiction of completely stationary exchange ratios among all commodities, other than money, and then compare these other commodities with money, that we can envisage exchange relationships between money and each of the other individual exchange commodities changing uniformly. Only then can we speak of a uniform increase or decrease in the monetary price of all commodities and of a uniform rise or fall of the “price level.” Still, we must not forget that this concept is pure fiction, what Vaihinger termed an “as if.”2 It is a deliberate imaginary construction, indispensable for scientific thinking.
Perhaps the necessity for this imaginary construction will become somewhat more clear if we express it, not in terms of the objective exchange value of the market, but in terms of the subjective exchange valuation of the acting individual. To do that, we must imagine an unchanging man with never-changing values. Such an individual could determine, from his never-changing scale of values, the purchasing power of money. He could say precisely how the quantity of money, which he must spend to attain a certain amount of satisfaction, had changed. Nevertheless, the idea of a definite structure of prices, a “price level,” which is raised or lowered uniformly, is just as fictitious as this. However, it enables us to recognize clearly that every change in the exchange ratio between a commodity, on the one side, and money, on the other, must necessarily lead to shifts in the disposition of wealth and income among acting individuals. Thus, each such change acts as a dynamic agent also. In view of this situation, therefore, it is not permissible to make such an assumption as a uniformly changing “level” of prices.
This imaginary construction is necessary, however, to explain that the exchange ratios of the various economic goods may undergo a change from the side of one individual commodity. This fictional concept is the ceteris paribus of the theory of exchange relationships. It is just as fictitious and, at the same time, just as indispensable as any ceteris paribus. If extraordinary circumstances lead to exceptionally large and hence conspicuous changes in exchange ratios, data on market phenomena may help to facilitate sound thinking on these problems. However, then even more than ever, if we want to see the situation at all clearly, we must resort to the imaginary construction necessary for an understanding of our theory.
The expressions “inflation” and “deflation,” scarcely known in German economic literature several years ago, are in daily use today. In spite of their inexactness, they are undoubtedly suitable for general use in public discussions of economic and political problems.3 But in order to understand them precisely, one must elaborate with rigid logic that fictional concept [the imaginary construction of completely stationary exchange ratios among all commodities other than money], the falsity of which is clearly recognized.
Among the significant services performed by this fiction is that it enables us to distinguish and determine whether changes in exchange relationships between money and other commodities arise on the money side or the commodity side. In order to understand the changes which take place constantly on the market, this distinction is urgently needed. It is still more indispensable for judging the significance of measures proposed or adopted in the field of monetary and banking policy. Even in these cases, however, we can never succeed in constructing a fictional representation that coincides with the situation which actually appears on the market. The imaginary construction makes it easier to understand reality, but we must remain conscious of the distinction between fiction and reality.4
Attempts have been made to measure changes in the purchasing power of money by using data derived from changes in the money prices of individual economic goods. These attempts rest on the theory that, in a carefully selected index of a large number, or of all, consumers’ goods, influences from the commodity side affecting commodity prices cancel each other out. Thus, so the theory goes, the direction and extent of the influence on prices of factors arising on the money side may be discovered from such an index. Essentially, therefore, by computing an arithmetical mean, this method seeks to convert the price changes emerging among the various consumers’ goods into a figure which may then be considered an index to the change in the value of money. In this discussion, we shall disregard the practical difficulties which arise in assembling the price quotations necessary to serve as the basis for such calculations and restrict ourselves to commenting on the fundamental usefulness of this method for the solution of our problem.
First of all it should be noted that there are various arithmetical means. Which one should be selected? That is an old question. Reasons may be advanced for, and objections raised against, each. From our point of view, the only important thing to be learned in such a debate is that the question cannot be settled conclusively so that everyone will accept any single answer as “right.”
The other fundamental question concerns the relative importance of the various consumer goods. In developing the index, if the price of each and every commodity is considered as having the same weight, a 50% increase in the price of bread, for instance, would be offset in calculating the arithmetical average by a drop of one-half in the price of diamonds. The index would then indicate no change in purchasing power, or “price level.” As such a conclusion is obviously preposterous, attempts are made in fabricating index numbers, to use the prices of various commodities according to their relative importance. Prices should be included in the calculations according to the coefficient of their importance. The result is then known as a “weighted” average.
This brings us to the second arbitrary decision necessary for developing such an index. What is “importance”? Several different approaches have been tried and arguments pro and con each have been raised. Obviously, a clear-cut, all-round satisfactory solution to the problem cannot be found. Special attention has been given the difficulty arising from the fact that, if the usual method is followed, the very circumstances involved in determining “importance” are constantly in flux; thus the coefficient of importance itself is also continuously changing.
As soon as one starts to take into consideration the “importance” of the various goods, one forsakes the assumption of objective exchange value—which often leads to nonsensical conclusions as pointed out above—and enters the area of subjective values. Since there is no generally recognized immutable “importance” to various goods, since “subjective” value has meaning only from the point of view of the acting individual, further reflection leads eventually to the subjective method already discussed—namely the inexcusable fiction of a never-changing man with never-changing values. To avoid arriving at this conclusion, which is also obviously absurd, one remains indecisively on the fence, midway between two equally nonsensical methods—on the one side the unweighted average and on the other the fiction of a never-changing individual with never-changing values. Yet one believes he has discovered something useful. Truth is not the halfway point between two untruths. The fact that each of these two methods, if followed to its logical conclusion, is shown to be preposterous, in no way proves that a combination of the two is the correct one.
All index computations pass quickly over these unanswerable objections. The calculations are made with whatever coefficients of importance are selected. However, we have established that even the problem of determining “importance” is not capable of solution, with certainty, in such a way as to be recognized by everyone as “right.”
Thus the idea that changes in the purchasing power of money may be measured is scientifically untenable. This will come as no surprise to anyone who is acquainted with the fundamental problems of modern subjectivistic catallactics and has recognized the significance of recent studies with respect to the measurement of value5 and the meaning of monetary calculation.6
One can certainly try to devise index numbers. Nowadays nothing is more popular among statisticians than this. Nevertheless, all these computations rest on a shaky foundation. Disregarding entirely the difficulties which, from time to time, even thwart agreement as to the commodities whose prices will form the basis of these calculations, these computations are arbitrary in two ways—first, with respect to the arithmetical mean chosen and, secondly, with respect to the coefficient of importance selected. There is no way to characterize one of the many possible methods as the only “correct” one and the others as “false.” Each is equally legitimate or illegitimate. None is scientifically meaningful.
It is small consolation to point out that the results of the various methods do not differ substantially from one another. Even if that is the case, it cannot in the least affect the conclusions we must draw from the observations we have made. The fact that people can conceive of such a scheme at all, that they are not more critical, may be explained only by the eventuality of the great inflations, especially the greatest and most recent one.
Any index method is good enough to make a rough statement about the extremely severe depreciation of the value of a monetary unit, such as that wrought in the German  inflation. There, the index served an instructional task, enlightening a people who were inclined to the “State Theory of Money” idea. Nevertheless, a method that helps to open the eyes of the people is not necessarily either scientifically correct or applicable in actual practice.
[1. ]The Theory of Money and Credit [(Yale, 1953), pp. 97ff.; (Liberty Fund, 1981), pp. 117ff.—Ed.].
[2. ][Hans Vaihinger (1852–1933), author of The Philosophy of As If (German, 1911; English translation, 1924).—Ed.]
[3. ]The Theory of Money and Credit [(Yale, 1953), pp. 239ff.; (Liberty Fund, 1981), pp. 271ff.—Ed.].
[4. ]Carl Menger referred to the nature and extent of the influence exerted on money/goods exchange ratios [prices] by changes from the money side as the problem of the “internal” exchange value (innere Tauschwert) of money [translated in this volume as “cash-induced changes”]. He referred to the variations in the purchasing power of the monetary unit due to other causes as changes in the “external” exchange value (aussere Tauschwert) of money [translated as “goods-induced changes”]. I have criticized both expressions as being rather unfortunate—because of possible confusion with the terms “extrinsic and intrinsic value” as used in Roman canon doctrine, and by English authors of the seventeenth and eighteenth centuries. (See the German editions of my book on The Theory of Money and Credit, 1912, p. 132; 1924, p. 104). Nevertheless, this terminology has attained scientific acceptance through its use by Menger and it will be used in this study when appropriate.
[5. ]See The Theory of Money and Credit [(yale, 1953), pp. 38ff.; (Liberty Fund, 1981), pp. 51ff.—Ed.].
[6. ]See Socialism [(Yale, 1951), pp. 114ff.; (Liberty Fund, 1981), pp. 97ff.—Ed.].