66

SECTION III

MONEY

(H)

MEASUREMENT OF CHANGE IN VALUE OF MONEY

[THIS article consists of two papers, the first and third of three Memoranda which were presented to the British Association for the Advancement of Science in the years 1887, 1888, 1889 respectively. The three were prepared by the present writer acting as Secretary of a Committee appointed for the purpose of investigating the best methods of ascertaining and measuring Variations in the Value of the Monetary Standard. The second Memorandum dealing with a special aspect of the subject is reprinted as a separate Article, the second of the present section. The first and third Memoranda being in pari materia are here put together. The collocation of an originally somewhat diffuse disquisition with afterthoughts which occurred two years later does not form a model of order and unity. The composition is like the "scene of man," according to Pope, "a mighty maze "; but that it is not without a plan" may appear from the following résumé. The "natural method of calculating a measure of change," in the phrase of Mr. Flux (Journal of the Statistical Society, 1921, p. 175), is to determine the change in the money value of the articles consumed by the population under consideration. This standard is considered in the first section of the first Memorandum. The simplest form of this standard is "the comparative money-cost of a fixed schedule of articles" (Flux, loc. cit. Cp. N, below, p. 396). The most refined form of this standard compares the amounts of money required to procure the same satisfaction at different epochs (Cp. Sidgwick, Political Economy, Book I., ch. ii. § 3; Bowley, Journal of the Statistical Society, 1921, p. 351). Over against this Consumption-Standard is the Production- or Labour-Standard, which compares the amounts of money procured by the same "Real Cost" in the sense of effort-and-sacrifice. This standard is propounded in the last

section of the third Memorandum. Quantity of labour may not be a very distinct idea; as Adam Smith says, "the greater part of people understand better what is meant by a quantity of a particular commodity." There is, however, a very distinct difference between this and the first standard. Thus, if gold prices fall through increased production of commodities, as perhaps in the eighties of last century, according to the first standard there may appear a serious appreciation demanding correction; according to the second standard there may be no change in the "real value" (Marshall and Ricardo) of money, gold is behaving very well. These two standards may be regarded as species of a genus which may be described as subjective, or personal, in contrast with objective standards which are less directly adapted to definite human purposes. Such is the character of the " Indefinite Standard" consisting of a mere average, as propounded in Section VIII. of the first Memorandum, where it will be observed that some hypothesis involving sporadic dispersion of prices—before (with respect to standards of the first genus) repeatedly stated not to be implied-is now for the first time introduced. This may be considered as the first species of the objective genus. A second species is presented when we consider not only the fact of an average change in prices, but also as its cause the change in the relative quantity (and velocity) of circulation. This species may be identified with the second method of the third Memorandum; connected in 1889 with the name of Foxwell, and subsequently elaborated by Professor Irving Fisher. Within this species there is a variety which not only connects the change in prices with change in the quantity of circulation, but also considers as the cause of that cause change in the quantity of gold, or other primary money on which the circulation (cheques and notes) is based. The indefinite standard may also be divided into species of which one is irrespective of the quantities of commodities, the other takes account of quantities. The second species includes the variety just now mentioned (second part of Section IX., First Memorandum), and more generally cases in which the conditions of a perfect market are not realised in such wise as to render the first species appropriate (first part of Section IX.). A cross-division of the indefinite standard is formed by the use of different averages; in particular the Arithmetic Mean, the Median, the Geometric Mean and the Mode, the familiar four to which the character of objective and not directly adapted to special purposes principally appertains.

The genus index-number of prices may be defined so as to

include the measurement of differences between different places in the value of money (p. 290).

Another cross-division of the genus is formed by the limitation of the population or district to which the computations refer. The index-numbers examined on Sections III.-V. of the third Memorandum may perhaps be considered as thus referring to a particular interest, foreign trade.

Or these, like several of the remaining sections, may be considered as dealing with imperfect measures, symptoms and indications of one or other of the index-numbers above defined. Section III. of the first Memorandum is thus related to the Consumption-Standard of Section II. Section IV. and V. of the first Memorandum may be subordinated to the ProductionStandard of Section VII., third Memorandum. Section I. of the second Memorandum bears a similar relation to Section VI. Section I. of the second Memorandum might also be treated as an imperfect substitute for Section II. of that Memorandum (an abridgment in which account is not taken of the pull upon currency exercised by the repeated sale of a commodity). It is a question whether the Capital Standard proposed by Professor Nicholson should be treated as subsidiary or as a new substantive index-number.

There is finally an index-number subordinated not to one or other of the ends defined, but to several of them; adapted to secure the maximum of utility, regard being had to the different kinds of advantage described in the different sections. Such is the purport of the "mixed modes" in Section X. of the first Memorandum corresponding to Professor Wesley Mitchell's general purpose " index-number (see N, below, p. 387).

It may be asked, How does the indefinite standard enter into a compound of this sort? The answer that it contributes the important attribute of a "true mean" (Section VIII., First Memorandum, p. 233), a "good average" (Journal of the Statistical Society, 1923, p. 572). Such is the purport of that compromise between the principles of the Consumption-Standard and the more objective species which the British Association Committee seemed to sanction (Section X. of First Memorandum). The weighted Arithmetic Mean prescribed by the Committee would be proper in the absence of any hypothesis as to the dispersion of the data. But the formula may be used with more confidence when the hypothesis of sporadic distribution is known to be realised.

For further elucidations of the Memoranda the reader is

referred to two papers dealing with hostile criticism, viz. The doctrine of Index-numbers according to Mr. Correa Walsh, ECONOMIC JOURNAL, 1923, and the Calculation of Index-numbers by Mr. Correa Walsh, "Journal of the Statistical Society," 1923. Mr. Walsh makes a rejoinder in The Quarterly Journal of Economics, May, 1924.]

FIRST MEMORANDUM

CONTENTS.

PAGE

199

208

208

Introductory synopsis subsuming under three or four general heads the numerous varieties of the problem which are distinguished in the following sections :

SECTION

I. Description and division of the problem

Logical tree exhibiting the subdivisions

II.-VII. Cases in which no hypothesis is made as to the identity of the cause, or equality of the amount, of the given price-variations

II.-VI. Standards for deferred payments adapted to these cases
II. Standard based upon the items of national consumption, designed
to keep constant the value-in-use procured by money for the

Case where the proportions of the different commodities consumed
may be treated as constant

Modes of weighting the price-variations with the quantities con-
sumed
Subsidiary criteria of weight

Case where the proportions of consumption cannot be regarded as
constant. Professor Marshall's solution.

III. Standard adapted to the same purpose as the preceding, but con-
structed by a more summary method
IV. Standard based upon the national income per head as estimated by
the expenditure on articles of consumption
V. Standard based upon the income of producers as gauged by the
price of all kinds of articles (whether agents of production or
finished products)

221

Mathematical proof that almost any combination of the more

important articles is likely to be equally imperfect and equally
serviceable for the purpose in hand

226

VI. Standard based upon the amount of national capital, the value of
the "aggregate of purchasable commodities".

230

VII. Definition of the appreciation which it would be the object of bime-
tallism and similar projects to correct
Comparison in respect of remedial efficacy between standards for
deferred payments and bimetallism

VIII., IX. Case where it is assumed that a common cause has produced a general change of prices over the whole, or a considerable part, of the industrial world

Jevons' procedure, in so far as he takes a Mean not weighted by the
masses of commodities, is appropriate to this case