Some Limitations of the Value Concept Quarterly Journal of Economics, volume 25 (1911) pp. 409-428. by Allyn A. Young Ever since the publication of "The Wealth of Nations" the notion of exchange value has remained the most fundamental and possibly the most consistently defined concept of economic science. Bickerings as to whether "power in exchange," "quantity received in exchange", or "ratio of exchange" best expresses this concept, as to whether exchange value is a quantitatively variable attribute or quality of a commodity or merely a disembodied ratio, have not been taken as seriously affecting the precision of the concept. It is possible that these differences, if consistently followed out, might have led to perceptible differences in doctrine at various points.(1*) But as it is, the essential points at issue between the advocates of conflicting economic theories have been born of other things than variant notions of the meaning of exchange value. Historically, if not logically, the differences alluded to have been verbal ones. It is not my purpose in the present paper to attempt the difficult and unprofitable task of suggesting any revision in an elementary concept which has worn well in actual service. I shall venture, however, to suggest certain limitations implicit in the value concept as commonly formulated. Failure to take account of these limitations has led to weaknesses in certain parts of the superstructure of theory that has been erected on the foundation of the theory of value. I The notion of exchange value is an abstraction. This much will be easily conceded, especially when the concept is carefully cleared of all entanglement with the really simpler concept of subjective value. As an abstraction it presents some superficial resemblance to such concepts of physical science as mass, extension, energy, and the like. Analogies based on this resemblance have been used freely in expositions of economic theory, especially in discussions of the "measure of value." Like value, these physical concepts are, in a quantitative sense, purely relative, - that is, mass, extension, or energy cannot be measured except in terms of units of mass, extension, or energy. Moreover, they too are abstractions, - properties or qualities of things, detached by analysis from the synthetic ideas given directly by human experience. This process of abstraction makes it possible and legitimate to neglect the other manifold and differing properties of things, and to conceive of the existing world in term of mass, volume, or potential energy. The method of abstraction has made it possible for science to find order and simplicity in an apparently complex universe. Furthermore, abstractions enter largely into all thinking which deals with general principles. These commonplaces of logic are rehearsed lest the trend of the present discussion should be taken to involve a general and necessarily futile argument against the use of abstractions in economic theory. The difficulties to be suggested spring from the fact that, as compared with the superficially analogous concepts of physical science, "exchange value" is an abstraction of a higher order and of a thinner sort. The concrete facts in the case are the exchanges of goods and services for money and money substitutes. Prices, not values, are the primary elements of the situation with which the economic theorist has to deal. And, as it happens, economic theory, at least of the more conservative sort, does concern itself very largely with the problem of price. The traditional theory of distribution deals with the forces determining the prices paid for the services of the factors in production. The theory of "normal value" is essentially a theory of price tendencies. The theory of market value is in general a demand and supply theory of prices. Modern refinements in the analysis of the forces living back of demand and supply have not altered the ultimate bearings of the theory. The formulating of equations between value and marginal utility on the one hand and marginal subjective costs on the other hand has of itself final significance only for a Crusoe economy. So far as the analysis of market forces is concerned, these modern developments of theory can scarcely be held to do more than to bring to light some of the principles which govern the choices made between the various alternatives open to buyers and sellers of commodities and services. In several representative modern treatises market prices are explicitly recognized as the pivotal facts in the situation, -- determining, as independent variables, the choices which individual producers and individual consumers make between the alternatives open to them, and at the same time determined, as dependent variables, by the aggregate selective process. But the real significance attached to the subject of price in pure economic theory has been in general much less than one would infer from its apparent prominence. For the notion of price has figured in large part as a convenient and workable substitute for the supposedly more general, though more cumbersome, concept of exchange value. In other words, so far as the pure theory of exchange has been couched in term of price, it has been felt that the procedure involved some sacrifice of scientific rigor, and was to be justified only on account of the simplicity gained in exposition.(2*) That "price is value expressed in terms of money" is the common formula by which the transition from one concept to the others effected. Ignore changes in the general purchasing power of money and prices become accurate measures of exchange values and hence, in the analysis of the market, adequate substitutes for them. From this general trend of the systematic expositions of economic theory rather than from any unequivocal statement relating to the point at issue, it may be inferred, I think, that value is very generally thought of as logically antecedent to price. Value is the primary, price the derivative concept. This subordination of price to value puts aside the fact that concretely exchange values emerge only from the actual process of exchange (and there emerge as prices) as of minor import for the purposes of pure theory. The only logical excuse for this procedure which occurs to me is that value is the more general of the two concepts and hence has some claim to logical priority. But this greater degree of generality is purchased, I am inclined to think, at the expense of precision and reality. In most of the definitions exchange value falls into one or the other of two categories. In the one it appears as the general purchasing power or general ratio of exchange of a commodity, a notion which is vague and abstract in the highest degree. The makers of index numbers have had to explain repeatedly that they are dealing only with averages of the variations of particular prices; that a measure of the general purchasing power of money is not only impossible, but inconceivable. There is no way in which the imagination can blend into one concept the bushels of wheat, the tons of coal, and the yards of cloth a given amount of money will purchase. The notion of the "general purchasing power" of money or of a commodity is not simply loose and indefinite; it is meaningless. In the other class of definitions value appears, not as general purchasing power, but as any one of an aggregate of purchasing powers. In this sense a commodity is said to have not one but many values, corresponding to its specific ratios of exchange with all other commodities. Price, or money value, appears in this view merely as one species of a large genus. It seem fairly clear that this notion of value is really derived, by analogy, from the notion of price. Given the ratio at which each of two commodities exchanges for money and it is a matter of simple arithmetic to determine the "value" of each in terms of the other. Clearly here is something more tangible than is the notion of "general purchasing power." But this "generalized price concept" of value, as it might be called, is not free from difficulties of its own. Ostensibly it is not a mere derivative of the notion of price but shares in the general claim of the value concept to priority and independence. It leads to the hypothetical elimination of money as an essential part of the mechanism of the market, and to a view of the valuation process in which values are pictured as determined as though under a regime of pure barter. Money is brought in at the end of the process (for exposition's sake) as a register or common denominator of the values reached. Various objections to a view of valuation from which so many of the dominant facts of the actual market have been abstracted suggest themselves. That a state of pure barter is, even historically speaking, a sheer work of the imagination, is perhaps not a relevant objection, if it can be shown that the hypothetical projection of an idealized state of barter into the framework of our money economy really does add a substantial amount of simplicity to economic analysis. For a similar reason I am not disposed to attach much weight to the obvious objection that the complexity of the present system of division of labor and exchange renders a general system of barter altogether unthinkable. Of more cogency is Professor W.C. Mitchell's suggestion(3*) that the money concept itself has been an active factor in giving purpose, system, and rationality to economic activity. Modern business is conducted by men who have learned to think in terms of money, and the price-making process is largely in their hands. But this objection, like the others mentioned, presupposes a point of view quite different from that of current economic theory. Within the relatively narrow limits of scope and method which economic theory has set for itself can there be found substantial reason for questioning the legitimacy of the elimination of money in the general view of the valuation process? I believe that such ground of dissent exists, and that it is implicit in the very nature of the theory of exchange value itself. This theory, in whatever form it may be presented, is essentially a theory of the equilibrium of demand and supply. The values with which it deals are opposed to be those resulting from the effort of buyers and sellers to seek their own advantage, under conditions which leave them free to buy and sell such things as they please and to buy and sell more or less of these things. Back of all, the tendency toward the equilibrium of marginal satisfactions and marginal costs operates as a controlling factor. Moreover, the values which would be determined if equilibrium could be achieved are consistent one with another. That is, in order to ascertain the value of A in term of B, it would be sufficient to know the values of A and of B in terms of C. Now this fundamental postulate of value theory of a tendency toward a static equilibrium is thoroughly inconsistent with the other postulate of a hypothetical state of pure barter. In barter there is no efficient tendency toward a definite equilibrium. So far as the ratio of exchange between any two commodities is concerned an equilibrium point might conceivably be reached, but it would be only one of an indefinite number of possible points.(4*) And it would be quite unreasonable to expect that there should be any mutual consistency between the ratios of exchange thus accidentally reached. The fact is that in treating exchange values as money prices in the analysis of supply and demand we are really doing more than availing ourselves of a convenient method of exposition. We are using a necessary and integral part of the analysis. The lucidity which the premising of a general medium of exchange adds to economic analysis (as in the theory of supply and demand at a price) is only a reflection of the precision and determinateness which the use of money gives to the actual operations of the market. Thus far I have dealt only with some of the logical aspects of the subordination of price to value. It is easily possible that the real explanation of this procedure is historical rather than logical. More specifically, I suggest that it may be a heritage of the interest which Adam Smith and his mediate followers took in the problem of "the real measure of value." (5*) Both the theory of national wealth and the theory of distribution seemed to demand a better measure of wealth than that afforded by money prices, with their continual fluctuations.(6*) From this source two divergent streams of theory have flowed. On the one hand we still seek for an "ultimate standard of value." But here the problem is an essentially practical one with distinctly ethical bearings. It is discussed in the literature dealing with index numbers and with the general problem of the standard of deferred payments. It has no direct relation to the pseudo-mechanical problem of economic equilibrium. And on the other hand we have continued to busy ourselves with the problem of the real measure of value in the sense of the exact measure of value. Here the marginal utility concept holds the field. But, as previously suggested, there is nothing in the marginal utility analysis that prevents a frank recognition of the dominance of the role played by money prices in the system of economic equilibrium. From utility, up though marginal utility, subjective value, and exchange value, to price, is a long and slippery road. Marginal utility, like price, may be said to be a relatively simple concept, derived from the concrete facts of experience. Value, on the other hand, is an abstraction of a very loose and indefinite sort. To pass directly from the analysis of demand to the analysis of price would reduce the dangers that spring from the ever present tendency to treat abstractions as realities.(7*) Moreover, frank recognition of the fact that the value concept is a derivative of the phenomena of price would be attended with no substantial modification of the general character of the theory of exchange. What now passes as a concession to the exigencies of exposition would stand forth without apology as a prime factor in the situation. This would, however, be a change of emphasis, and as such it would be wholesome.(8*) For there are indications that we have long since passed the point of diminishing returns, so far as added refinements in the general theory of economic equilibrium are concerned. What is needed is an analysis of the actual mechanism of the price-making process. There should be no room for such crudities as even an implied determination of prices by the comparison of the "values of commodities" and the (independently determined) "value of money." In short, such a change should make it easier for economics to assume the yet vacant place awaiting it among the positive sciences. II When we leave the pure theory of exchange and pass to that general group of problems and theories in which value figures as a measure of the existing stock of wealth or of any part of that stock we encounter difficulties of quite a different sort. Here economists have generally been content to speak of value in the sense of money value. This may be due to the practical difficulties in the way of any other procedure, or to a realization that the summation of "general purchasing power" is akin in principle to an attempt to determine the weight of the solar system. Yet even in this sense value is not equivalent to price. Prices emerge, as concrete facts, only in the process of exchange, and only in the process of exchange does money actually "measure value." Value, as applied to a stock of goods, is nothing more or less than imputed price.(9*) The grounds and the purposes of the imputation vary. It may take the form of a merchant's appraisal of his stock on hand; it may result from the assessment of property for taxation, or its "valuation" for purposes of public control; it may arise from a statistician's efforts to reach an estimate of national wealth; finally, it may be implied in such economic theories as those in which "capital" is made to consist of all wealth, measured in term of money value. Leaving aside the cases in which the imputation is a judgment of "what price ought to be,"(10*) as involving an ethical rather than a purely economic problem, the general method of imputation may be said to consist of the establishment of hypothetical prices for all the units of a stock of goods on the basis of the current prices received and paid for similar units of similar goods. In the case of non-reproducible goods, and to a greater or less extent in the case of all non-standardized goods, the process of imputation necessarily involves varying degrees of estimate and guesswork. Moreover, as will be indicated presently, much depends upon the legitimacy of assuming that "similar units" as well as "similar goods" are to be dealt with. It may be objected that in fact other methods of valuation than the imputation of current prices to a stock are used. "Physical valuation," for purposes of public control might, for example, be cited. Physical valuation is assuredly not an attempt to get at the price of a business undertaking considered as a unit; nevertheless when it deals with "reproduction costs" it is an imputation of current prices to the separate parts of the material equipment of a business unit. When it deals with "the original cost of production" physical valuation is not valuation at all, but simply a measure of the investment of capital. Or, again, it might be urged, with apparently greater cogency, that the valuation of income-yielding goods is in essence a capitalization of the income yielded. This point has a direct bearing on the fundamental gumptions of certain latter day economic theories, and so deserves examination in some detail. That the method of capitalization is actually used as a method of imputation cannot be denied. But the essential question is whether this method affords, in a rigorous sense, a determination of value, or whether it is merely a convenient mode of reaching an estimate of value. I am inclined to take the latter view. In fact, if one holds that the value concept is a derivative of the notion of price, and that the value of a stock is a matter of imputed price, no other view seem possible. Among the things bought and sold in the market are securities and commodities that have more or less definite potencies in the way of conveying money income to their owners. The forces of the market tend to establish definite prices for such commodities and securities, and hence to establish definite ratios between incomes of given amounts and of given degrees of certainty, spontaneity, and futurity, and the prices of the income bearers. In the absence of evidence more directly to the point, the ratios or rates of capitalization thus established for the incomes from certain kinds of goods and securities may be used as the means of imputing price to similar goods and securities, not currently priced in the market, but with known or estimated income-yielding power.(11*) The possible objection that the "forces of the market" thus invoked are themselves in large part the resultants of the ratios at which individuals subjectively equate future incomes to present values is not to the point. For we are dealing with market values, which, so far as each individual is concerned, must be held to be objectively determined and objectively measurable. Considerations essentially similar to those outlined above hold, mutatis mutandis, with respect to the pseudo-capitalization of "psychic income."(12*) The value of a stock, then, as an economic concept, may be taken to be a derivative of the fact that particular units of the stock are exchanged or are estimated to be exchangeable at certain prices. The value of a homogeneous stock is got by multiplying the number of units in the stock by the price per unit. For the most part economists have not thought it necessary to mark a distinction between the price of the units exchanged and the value, or imputed price, of the units not exchanged. But Cournot (13*) and a few other writers have deemed it worth while to call attention to the simple and elementary fact that the maintenance of the 1evel of current prices is dependent on not overcrowding the market. Not all the units of any considerable stock, such as the stock of wheat, could be sold at one time at current prices, nor on the other hand, could buyers of any good substantially increase their purchases except at increased prices. The legitimacy of the notion of the value of a stock seem to hinge on the fact that presumably any one unit of the stock may be added to the amount sold without substantially affecting the price. The imputed exchange value seem to hold rigidly for the particular units of a stock, taken one at a time. If it were not that it would put an additional burden on an already hard-worked adjective, it might be insisted that exchange value, after all, is only marginal value. For all except the marginal units the imputed value is purely hypothetical, subject only to the limits set by the existing potential demand and existing potential supply. As Jevons suggested,(14*) the theory of demand and supply is properly a theory of rate of demand and rate of supply. A slender stream of goods flows though the market from sellers to buyers, and at the point of exchange this flow is equated (in terms of price) to the stream of money (and money substitutes) flowing in the opposite direction. The vague outlines of a dynamic theory of price are easily imaginable. Such a theory might analyze the forces controlling the volumes and rates of flow of particular kinds of commodities, and the volumes and rates of flow of the parts of the money stream to which these are equated in the market. It could not be expected that such a theory would lead to conclusions substantially different from those reached by the analysis of the forces tending to static equilibrium, and it would be decidedly more cumbersome. But the use of the static method has tended to falsify our view of the facts in some particulars. Seizing a moment when the two streams are running smoothly and steadily (corresponding to the condition of static equilibrium) we image them, in effect, to be suddenly congealed. Then, with this tactical advantage, we devote ourselves to a painstaking analysis of the proximate factors determining the prices of the goods which happened to be thus arrested at the very moment when they were passing though the narrow channel of exchange. But to be satisfied with this achievement would be to fall short of the opportunity for system making. So we examine the upper reaches of the congealed stream of goods, imputing value to everything we find, on the basis of the price units discovered at the point of exchange. Going still farther back we subject to the same Midas-like touch the upper reservoirs of goods that are usually only drawn upon when the stream is running dry. And finally, by a supreme tour de force, we convert into value units those outlying pools of intimate personal belongings, not customarily thought of in terms of money value, even by those who prize them most, and from which normally only a thin rivulet trickles to join the stream of goods passing though the market place. In short, for system's sake, the whole material equipment of human living is recast in molds fashioned after the notions of catallactics. This view of things is implicit in a large part of the body of systematic economics. But I wish frankly to say that in my opinion the symmetry and logical completeness of the systems of Professor Fetter and Professor Fisher are due in no small part to the fact that they have gone farthest on this road. III If the value of a stock is a matter of imputed price, and if this is in reality an accurate measure only for the marginal units of a stock, the size of unit to be employed in the imputation becomes a matter of some importance. The value got by dividing the stock into the smallest possible units will be the maximum; the value got by considering the whole stock one unit will be a minimum. This suggestion should not be confused with the objections urged by Mr Hobson and others against the theories of marginal productivity and of marginal utility on the fallacious ground that the results reached depend upon the size of the units chosen. For these theories deal with changing ratios (of utility to quantity or of product to labor) and in whatever form they are stated there is implied in them the mathematical notion of a limiting ratio.(15*) There is no implication of this sort in the ordinary conception of the value of a stock of goods. Here we have to deal with the imputation of market prices to concrete units of definite size. An example taken from actual experience may serve to make the matter clear. A forty-acre tract of land on the outskirts of a small village was assessed for taxation on the basis of an actual value of $8000, or $200 per acre. Half of one acre was subsequently sold as a building lot, and assessed at $400, or $800 per acre. As the building lot was not taken from the best located part of the tract, its owner made complaint of over-assessment. A little investigation showed that though several more building lots of the same size could be sold at or near a price equivalent to $800 per acre, the tract as a whole could not be sold for much more than $200 per acre. Any one acre, taken by itself, was worth $800; yet to have multiplied this amount by the number of acres would have given the absurdly high total value of $36,000. What, by the method of price imputation, was the total value of the tract? The foregoing illustration involves more than the principles implied in the imputation process, i.e. that the market must not be overcrowded and that the rate of supply is supposed to be normal. The fact seems to be that the price of building lots and the price of the tract as a unit were affected by and adjusted to entirely different conditions of demand. The example is probably an extreme one. But that the total value of a tract of land depends in part upon the way in which it is subdivided is an unquestionable fact of real estate operations. The field of corporation finance furnishes similar problem. The sum of the value of the disintegrated parts of a corporation's material equipment together with the value of its franchise, if this can be sold separately, is one thing; the price which the corporation's assets as a whole would bring under the hammer is another thing; and the total value of the outstanding securities of a corporation may be yet another thing. Here again the essential thing in the situation is the fact that the equities in the corporation's property may be subdivided in different ways, and that the field of demand varies with the method of subdivision. Take, for example, the problem of the value of a corporation's securities. Here, as in the case of some railroad corporations, the bulk of the stock and bonds may be securely held for purposes of investment and control. The value imputed to these is derived from the prices of the relatively small part of the securities which happen to figure actively on the stock exchange. Disregarding the element of control, which is an abnormal peculiarity under American railroad conditions and hence negligible for the present reasoning, and assuming that the rate of supply is not under any circumstances apt to be extremely high, this method of imputation may be said to give fairly precise results in such cases. For such securities are distinctly marketable goods, and their market is highly organized and elastic. But the fact remains that the total value of the equities in a corporation depends on the way in which they are subdivided. Bonds of small denominations find a market not open to bonds of larger denominations. Moreover, in a complexly capitalized corporation, the classification of securities is such that it offers to buyers of incomes a carefully graded assortment of risks. This maximises the selling or capital value of a corporation's income-earning power. Different levels of demand are tapped and the result is better than if the curve of diminishing buyers' prices for any one level were followed too far. Preferred stocks may sell readily when bonds are a drug in the market. That changes in total value are affected by a skilfully conducted railroad reorganization (even when no new capital is invested and net earning power is not increased) is well known. All these considerations may have some bearing on practical problems of assessment and of public valuation. It is possible that they deserve some consideration in connection with any theory which deals with the notion of "total wealth measured in terms of money value," altho I am disposed to regard them as of relatively less significance than the more general views suggested in the second division of this paper. There remains the problem of the bearing of the general limitations of the value concept on the statistical problem of the measurement of national wealth. If value is not additive, of what significance is the statistical summation of the wealth of a country?(16*) It might be thought that the validity of the statistical undertaking stands or falls with the validity of the theoretical notion of total wealth measured in terms of value. But over and beyond the fact that we should expect to find in our theoretical notions a degree of precision not attainable in statistical practice, the statistical undertaking stands on firmer ground. The total wealth with which it deals is avowedly only the sum of the wealth of individuals. An individual's wealth includes generally only a small fraction of the stock of any commodity, and the difficulties to be taken into account are mostly of the relatively minor kind encountered in the assessment of property for purposes of taxation. Income statistics being lacking, an individual's wealth constitutes the only available index of his economic well-being. The station of wealth for the nation, divided by the number of families, gives a roughly accurate notion of the general diffusion of well-being. The estimate of national wealth would be justifiable, even though it meant nothing in itself, since it leads roughly to a result that does mean something. Taken by itself it gives us merely the sum of the imputed prices of individual property rights. NOTES: 1. It may be noted that these differences have an important bearing on the problem of the measurement of changes in the general level of prices. that Jevons's explanation of the ground of his choice of the geometric average for this purpose is hazy has come to be a generally accepted statement. But in fact the matter seems to be rather simple. Jevons, like Cournot (Mathematical Principles of the Theory of Wealth, Eng. transl. ch. ii), came naturally and unhesitatingly to the conclusion that changes in prices are only changes in ratios, and hence should be averaged geometrically. Later, the criticisms of Laspeyres suggested to him that a change in the value of gold is, after all, a change in its purchasing power, and that the arithmetic average had therefore some claim to consideration. Jevons continued to defend the use of his geometric average (for his purposes) but his former unquestioning confidence in it was gone. Compare his Investigations in Currency and Finance, new edition (1909), pp. 19-21 and 113-115. 2. Even Marshall, whose theory is cast more consistently in terms of price than that of any other writer since Cournot, explains (Principle of Economics, 5th ed., p. 62) that in his treatise "the price of anything will be taken as representative of its exchange value relatively to things in general, or in other words as representative of its general purchasing power." A more explicit statement is that of Pareto (Manuel d'Economie Politique, p. 209): "The general notion of the price of one commodity in terms of another is useful in economic science because it eliminates money. In practice the prices of all commodities are stated in terms of one of them, which is called money, so that it is difficult to avoid speaking of price in this sense when one is discussing concrete phenomena. Even in theory it is very useful to introduce this notion at the first. This, of course, anticipates the theory of money, which ought to come after the general theory of economic equilibrium, but there is no great harm in this, especially if the increased lucidity in exposition which the use of this concept gives is taken into account." 3. In his paper, The Rationality of Economic Activity, Journal of Political Economy, vol. xviii, pp. 208 and ff. 4. For the proof of this statement the reader is referred to Marshall, Principles of Economics, 5th ed., Appendix F. 5. See on this subject, T.S. Ashton, Index Numbers and the Standard of Value, Journal of Political Economy, vol. x, especially pp. 13 and 14. 6. This statement is not offered as a complete explanation of the preoccupation of the early economists with the problem of the real measure of value. It seems probable that, as various writers have suggested, the general trend of yet earlier economic thought (running back, very likely, to the analysis of money as a "recognized representative of demand" and a "universal standard of measurement" in Aristotle's Nichomachean Ethics, book V, ch. ix), the philosophical and juristic preconceptions of the economists themselves, and the influence of the dominating principles of the physical science of the day must all be taken into account. It may be noted in this connection that the thing sought was not a "real measure of value" in any but a transcendental sense. 7. An admirable example of the possibilities of this direct form of treatment may be found in Mr Wicksteed's recent book, The Common Sense of Political Economy, ch. i-vi. On the general logical difficulties arising from the hypostatising of abstractions see H.A. Aitkins, Logic, ch. v. 8. In 1900 the Railway World obtained the opinions of a large number of economists on the question whether there could be said to a distinction between "real prices" and "nominal (or money) prices" corresponding to the common distinction between "real wages" and "nominal wages". the majority of the answers were in the affirmative. Professor C.W. Mixter went so far as to imply that money prices were "apparent" and "real prices" were actual. This seems to me to be transcendental metaphysics of an extreme sort. On the point at issue I find myself in absolute accord with Professor H.J. Davenport, that "to talk of real as against nominal prices is terminological nonsense." and with Professor D.R. Dewey, who said, "The question is absurd. The is but one kind of prices." The distinction does not even have pragmatist's justification, for, as Professor T.S. Adams suggested, the problem at hand (the possible justification of increasing railway rates on account of the rise in the general price level) should have been approached in another way. See the pamphlet on Depreciated Currency and Diminished Railway Rates, Philadelphia, 1909. 9. Professor Irving Fisher's definition of value restricts it to this particular usage. "The value of goods is the product of their quantity multiplied by their price." See The Nature of Capital and Income, p. 336. 10. Corresponding to the definition of value which President Hadley prefers. See his Economics, p. 92. 11. Such, for example, was precisely the method followed by the exports employed by the Interstate Commerce Commission and the Bureau of the Census in estimating the commercial valuation of the railways of the United States. See Bulletin 21 of the Bureau of the Census, 1904. 12. The foregoing discussion is, I think, in essential harmony with the thesis maintained by Professor H.J. Davenport, in his paper on Capitalization and Market Value, Yale Review, vol. xix, p. 132 (Aug. (1910). 13. "Under this conception [a sum of exchangeable values] wealth has doubtless only an abstract existence; for, strictly speaking, of all the things on which we set a price, or to which we attach a value in exchange, there are none always exchangeable at will for any other commodity of equal price or value." -- Mathematical Principles of the Theory of Wealth, Eng. transl., p. 9. 14. Theory of Political Economy, 3rd ed., p. 64. 15. All of which is explained in non-mathematical fashion and with painstaking lucidity in Wicksteed's The Common Sense of Political Economy, book I, ch. ii. 16. Disregarding the well-known practical difficulties of the undertaking. On some of the aspects of the question suggested in the text one may consult with profit Emile Chatelain, De l'Evaluation du Capital National, revue d'Economie Politique, vol. xxi, pp. 361 and ff.