The Purchasing Power of Money PDF
The Purchasing Power of Money PDF
The Purchasing Power of Money PDF
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THE PUECHASING POWER OF MONEY
THE MACMILLAN COMPANY
NEW YORK BOSTON CHICAGO
SAN FRANCISCO
MELBOURNE
THE MACMILLAN CO. OF CANADA, Ltd.
TORONTO
THE PURCHASING POWER
OF MONEY
ITS DETERMINATION
AND RELATION TO CREDIT
INTEREST AND CRISES
BY
IRVING FISHER
PBOFEBSOK OP POLITICAL ECONOMY IN TALE UNIVBKSITT
ASSISTED BY
HARRY G. BROWN
INSTRDCTOK IN POLITICAL ECONOMY IN TALE UNIVEKSITT
PROPERTY OF LIF^^fARY
SIMON NEWCOMB
OBEAT SCIENTIST, IHSFIBING EBIEND,
"SOCIETABY CIBCTOATIOBT"
F5"
PROPERTY OF LIBPARY
W-^ YOHK STATE r''^^ 57^
1110- frIU Al mM fsELAIIONS
CORNELL UNIVERSITY
PREFACE
The purpose of this book is to set forth the principles
determining the purchasing power of money and to
apply those principles to the study of historical changes
in that purchasing power, including in particular the
recent change in " the cost of living," which has aroused
world-wide discussion.
If the principles here advocated are correct, the pur-
chasing power of money or its reciprocal, the level of
prices depends exclusively on five definite factors
(1) the volume of money in circulation
; (2) velocity its
of circulation (3) the volume of bank deposits subject
;
Pkimart Definitions
FAQB
i
1. "Wealth and exchange 1
I
2. Exchangeable goods 4
i
3. Circulation of money against goods 6
CHAPTER n
FuBCHASiNO Power of Monet as eeiated to the Equation
OF EXCEU.NGE
i
1.
2.
The various circulating media ....
The equation of exchange arithmetically expressed
8
14
( 3. The equation of exchange mechanically expressed 21
The equation of exchange algebraically expressed
I
i
4.
CHAPTER in
iNFtlTENCB OP DEPOSIT CuBBENCT ON THE EQUATION
AND THEBEFOBE ON PuBCHASINa POWEB
CHAPTER IV
distubbance of equation and of fubchabino powbb oubino
Transition Febiods
CHAPTER V
Indibeci Influences on Fubchasino Poweb
Influence of conditions of production and consumption on
1.
2.
trade and therefore on prices
Influence of conditions connecting producers
. . ...
and consumers
74
CHAPTER VI
Indieect Influences (Contimied)
.... 99
104
CHAPTER Vn
Influence op Monbtabt Systems on Purchasing Powbb
1. Gresham's Law
f
)
Cases when bimetallism fails immediately
2.
sumption ,,
\
4. The limping standard the gold-exchange standard '.
'.
;
' 127
15. Bimetallism in France 1'52
ANALYTICAL TABLE OF CONTENTS xvii
PAGE
i
6. Lessons of French experiment 135
The limping standard in India
i
i
7.
8.
9.
The limping standard in the United States ....
General description of system in the United States . . .
138
140
143
CHAPTER Vni
Ihpluence of Quantitt op Monet and Otheb Factobs on
PuBCKASiNG Power and on Each Otheb
CHAPTER IX
The Disfebsion of Prices makes necessart an Index ov
PuROHASiNO Power
1.
2.
3.
Consequently other prices must over-respond ....
Some prices cannot respond readily to price movements . .
from Sp to FT 194
4. Summary 196
CHAPTER X
The Best Index Numbers of Furchabino Fowbb
CHAPTER XI
Statistical Vbbipication. Gknekai, Histoeioal Review
PAGE
The last thousand years .
234
237
2. The last four centuries .
CHAPTER Xn
Statistical Veeification. Recent Teabs
1- Professor Kemmerer's statistics, 1879-1908 276
2. New estimates for JIf and W,
1896-1909 280
3. New estimates for MV
and V, 1896-1909 282
4. New estimates for MY and V, 1896-1909 285
5. Estimates for T and P, 1896-1909 . 290
P directly and indirectly calculated
6.
7.
8.
Correcting discrepancies
The final results
.... 292
298
304
9. The comparative importance of price-raising causes 307
,10. Influence of antecedent causes such as tariSs, etc. 311
11. Results and by-products of Chapter Xn 315
CHAPTER xni
The Pbobleu of making Fubchasing Power mobe Stable
1. The problem of monetary reform 319
2. Bimetallism as a solution 323
3. Other proposed solutions 328
4.The tabular standard 332
5.The writer's proposal 337
6. Summary and conclusion 848
APPENDICES
Appendix to Chaftek II
1
2
(to Ch. n, 3).
(to Ch. II, 5).
The concept of an average
The concept of velocity of circulation
.... . .
PAOE
349
352
3 (to Ch. II, 5). "Arrays" otp's, Q's, andpQ's . . .355
4 (to Ch. II, 5). " Arrays " of e's, m's, and F's . . .358
5 (to Ch. II, 5). The coin-transfer concept of velocity and the
concept of time of turnovei 362
6 (to Ch. II, 5). Algebraic demonstration of equation of ex-
change 364
7 (to Ch. II, 5). P must be a specific form of average in order
to vary directly as M and F and inversely as the 's, . . 864
Appendix to Chapter m
1 (to Ch. ni, 2). "Arrays" of ft's and r's . . . .367
2 (to Ch. in, 4). Algebraic demonstration of equation of ex-
change including deposit currency 368
Appendix to Chapter V
1 (to Ch. V, 5). Effect of time credit on equation of exchange 370
Appendix to Chapter VI
1 (to Ch. VII, 2). Money substitutes unlike other substitutes . 376
2 (to Ch. VII, 2). Limits for ratios within which bimetallism
is possible 378
Affbkdix to Chaptbb X
PASS
1. Each form of index number for prices implies a correlative
index number for quantities 385
2. Index numbers for prices occur in arithmetical pairs as also
do index numbers for quantities 390
3. General meanings of p's and Q's 392
4. Beview of 44 f ormulse, heading table columns . . . 393
5. Review of 8 tests, heading table rows 400
6. The interior of the table column 11 in particular
; . . . 408
7. The 44 formulae compared 418
8. Reasons for preferring the median practically . . . 425
9. Summary 428
page 479 by inserting 1910, 160, 113, 162, 154 (the extension of column
: ;
given do not imply that the items opposite are in all cases used for all
the intervening time, but only for such periods as the items were actually
available.)
It is noticeable that the changes in business in 1910 as compared with
1909 are somewhat irregular the sales of stocks have declined ; exports
;
CHAPTER I
PRIMARY DEFINITIONS
1
In order to make clear the relation which the topic
treated ia this book bears to the general subject of
economics, some primary definitions are necessary.
In the first place, economics itself may be defined as
the science of wealth, and wealth may be defined as
material objects owned by human beings. Of wealth,
therefore, there are two essential attributes material- :
A transfer of wealth
is a change in its ownership.
fifty dollars.
2
Hitherto we have confined our discussion to some
of the consequences of the first prerequisite of wealth
that it must be
material. We turn now to the second
prerequisite, namely, that it must be owned. To own
wealth is simply to have the right to benefit by it;
that is, the right to enjoy its services or benefits. Thus,
the owner of a loaf of bread has the right to benefit by
it by eating it, by selUng it, or by otherwise disposing
8
Sec. 1] THE EQUATION OP EXCHANGE 9
DEPOSITS.
or of the National
banks.
FIDUCIABY SEVEN
Checks aside, we MONEY
may classify exchanges BILUONS.
PRIMARY ONE .
2
Overlooking the influence of deposit currency, or
checks, the price level may be said to depend on only
three sets of causes (1) the quantity of money in circu-
:
unvarnished truth.
The quantity theory will be made more clear by the
equation of exchange, which is now to be explained.
The equation of exchange is a statement, in math-
See Scott, "It has been a most fruitful source of false doctrines
3
The equation of exchange has now been expressed by
an arithmetical illustration. It may be also represented
visually, by a mechanical illustration. Such a repre-
sentation is embodied in Figure 2. This represents a
nr i J-'
Fio. 2.
Via.
relating to the whole community and the whole year), and the
corresponding elementary magnitudes relating to each individual
and each moment, see 4 of the Appendix to (this) Chapter II.
' See 6 of Appendix to (this) Chapter II.
Sec. 4] THE EQUATION OF EXCHANGE 27
if the Q's all vary in a given ratio, either the p's must
For the nature of the average here involved and for the aver-
ages involved in the other two following cases, see 7 of Appendix
to (this) Chapter II.
28 THE PURCHASING POWER OF MONEY [Chap. II
5
This completes our statement of the equation of
exchange, except for the element of check payments,
which is reserved for the next chapter. We have seen
that the equation of exchange has as its ultimate basis
the elementary equations of exchange pertaining to given
persons and given moments, in other words, the equa-
tions pertaining to individual transactions. Such ele-
mentary equations mean that the money paid in any
transaction is the equivalent of the goods bought at
the price of sale. From this secure and obvious premise
is derived the equation of exchange MV = 2pQ, each
element in which is a sum or an average of the like
elementary elements for different individuals and differ-
ent moments, thus comprising all the purchases in the
community during the year. Finally, from this equa- v
Sec. 5] THE EQUATION OP EXCHANGE 29
Gold $100,000 I
Due depositors . . $100,000
$100,000 $100,000
$100,000 $100,000
$100,000 $100,000
$150,000 $150,000
$200,000 $200,000
2
It cannot be too strongly emphasized that, in any
balance sheet, the value of the liabiUties rests on that
of the assets. The deposits of a bank are no excep-
tion. We naust not be misled by the fact that the
cash assets may be less than the deposits. When
the uninitiated first learn that the number of dol-
lars which note holders and depositors have the right
to draw out of a bank exceeds the number of dollars
in the bank, they are apt to jump to the conclusion
that there is nothing behind the notes or deposit habil-
ities. Yet behind all these obUgations there is always,
in the case of a solvent bank, full value if not actual
;
lAabilities
$250,000 $250,000
3
We have seen that the assets must be adequate to meet
the liabilities. We now wish to point out that the form
of the assets must be such as will insure meeting the lia-
bihties promptly. Since the business of a bank is to fur-
nish quickly available property (cash or credit) in place
of the "slower" property of its depositors, it fails of its
purpose when it is caught with insufficient cash. Yet
v/ it "makes money " partly by tying up its quick property,
i.e. lending it out where it is less accessible. Its prob-
Sec. 3] DEPOSIT CURRENCY 43
and so to
difficult when begins to ap-
forestall it
4
The study of banking operations, then, discloses two
species of currency: one, bank notes, belonging to
the category of money; and the other, deposits, be-
longing outside of that category, but constituting an
excellent substitute. Referring these to the larger
category of goods, we have a threefold classification
of goods first, money ;
: second, deposit currency, or
simply deposits ; and third, all other goods. And by
the use of these, there are six possible types of ex-
change :
(1) Money against money,
(2) Deposits against deposits,
(3) Goods against goods,
(4) Money against deposits,
(5) Money against goods,
(6) Deposits against goods.
For our purpose, only the last two types of exchange
are important, for these constitute the circulation of
currency. As regards the other four, the first and third
have been previously explained as "money changing"
and "barter" respectively. The second and fourth
' See Horace White, Money and Banking
48 THE PUECHASING POWER OF MONEY [Chap. Ill
Fio. 4.
5
With the extension of the equation of monetary
circulation to include deposit circulation, the influence
that there is not "any reason for limiting the amount of the deposit
currency, or the assimiption of an absolute scarcity of specie re-
serves." See Principles of Money, p. 127.
Sec. 5] DEPOSIT CUREBNCT 51
other.
It further follows that any change in M, the quantity
of money in circulation, requiring as it normally does
a proportional change in M', the volume of bank de-
posits subject to check, will result in an exactly pro-
portional change in the general level of prices except,
of course, so far as this effect be interfered with by
concomitant changes in the F's or the Q's. The
truth of this proposition is evident from the equation
MV + M'V = 2pQ ; for if, say, M and M' are
doubled, while V and V remain the same, the left
side of the equation is doubled and therefore the right
side must be doubled also. But if the Q's remain
Monetary Commission, Senate Document, 399, 61st Congress, 2d
Session, 1910, p. 188.
Sec. 6] DEPOSIT CURRENCY 53
6
The contents of this chapter may be formulated in
a few simple propositions :
(1) Banks supply two kinds of currency, viz. bank
notes
which are money and bank deposits (or
;
are rising at the rate of 3 per cent a year, and the nor-
mal rate of interest i.e. the rate which would exist were
prices stationary is 5 per cent, the actual rate, though
it ought (in order to make up for the rising prices) to
be 8.15 per cent, will not ordinarily reach that figure;
but it may reach, say, 6 per cent, and later, 7 per cent.
This inadequacy and tardiness of adjustment are fostered,
moreover, by law and custom, which arbitrarily tend to
keep down the rate of interest.
A similar inadequacy of adjustment is observed when
prices are falling. Suppose that, by the end of a year,
$97 will buy as much as $100 at the beginning. In that
case the lender, in order to get back a purchasing power
equivalent to his principal and 5 per cent interest,
should get, not $105, but only $97 + 5 per cent of $97
or $101.85. Thus the rate of interest in money should
in this case be 1.85 per cent, or less than 2 per cent,
instead of the original 5 per cent. In other words, the
3 per cent fall of prices should reduce the rate of interest
by approximately 3 per cent. But as a matter of fact,
such a perfect adjustment is seldom reached, and money
interest keeps far above 2 per cent for a considerable
time.'
2
We are now ready to study temporary or transitional
changes in the factors of our equation of exchange. Let
us begin, by assuming a slight initial disturbance, such
as would be produced, for instance, in the by an increase
quantity of gold. This, through the equation of ex-
change, will cause a rise in prices. As prices rise,
profits of business men, measured in money, will rise
also, even ifthe costs of business were to rise in the same
1 Rate of Interest, loc. cit.
Sec. 2] TRANSITION PERIODS 59
figure.
3
The expansion of deposit currency indicated in this
cumulative movement flhriormally increases the ratio of
M' to M. This is evident if the rise of prices begins in
a change in some element or elements in the equation
other than the quantity of money for if ilf remains ;
' For statistical proof, see Kerre des Essars, Journal de la SociStS
de Statistique de Paris, April, 1895, p. 143. The figures relate only
to velocity of bank deposits. No corresponding figures for velocity
of circulation of money exist. Pierre des Essars has shown that
in European banks V reaches a maximum in crisis years almost
without fail. The same I find true in this country as shown by
the ratio of clearings to deposits in New York, Boston, and Phila-
delphia.
64 THE PURCHASING POWER OP MONEY [Chap. IV
4
Evidently the expansion coming from this cycle of
causes cannot proceed forever. It must ultimately
spend itself. The check upon its continued operation
lies in the rate of interest. It was the tardiness of the
rise in interest that was responsible for the abnormal
condition. But the rise in interest, though belated, is
' This is the definition of a crisis given by Juglar and the his-
5
The contraction of loans and deposits is accompanied
by a decrease in velocities, and these conspire to pre-
vent a further rise of prices and tend toward a fall.
The crest of the wave is reached and a reaction sets in.
Since prices have stopped rising, the rate of interest,
which has risen to compensate the rise of prices, should
fall again. But just as at first it was slow to rise, so
now it is slow to faU. In fact, it tends for a time to
rise still further.
The mistakes compel
of the past of overborrowing
the unfortunate victims of these mistakes to borrow
stiU further to protect their solvency. It is this special
abnormality which marks the period as a "crisis."
Loans are wanted to continue old debts or to pay these
debts by creating new ones. They are not wanted
because of new investments but because of obUgations
connected with old (and ill-fated) investments. The
problem is how to get extricated from the meshes of
past coromitments. It is. the problem of liquidation.
Even when interest begins to fall, it falls slowly, and
failures continue to occur. Borrowers now find that
interest, though nominally low, is still hard to meet.
Especially do they find this true in the case of contracts
made just before prices ceased rising or just before they
began to fall. The rate of interest in these cases is
agreed upon before the change in conditions takes place.
68 THE PURCHASING POAVER OP MONEY [Chap. IV
and managed
is recklessly and wastef ully those working ;
6
In the present chapter we have analyzed the phe-
nomena characteristic of periods of transition. We
have found that one such "boom" period leads to a
reaction, and that the action and reaction complete a
cycle of "prosperity" and "depression."
It has been seen that rising prices tend towards a
' Marshall, Principles of Economics, 5th ed., London (Macmillan),
1907, Vol. I, p. 594.
Sec. 6] TRANSITION PERIODS 73
2
3 (a). Anything which facilitates intercourse tends
'X
to increase trade. Anything that interferes with inter-
course tends to decrease trade. First of all, there are
the mechanical facilities for transport. As Macaulay
said, with the exception of the alphabet and the printing
press, no set of inventions has tended to alter civilization
so much as those which abridge distance, such as
the railway, the steamship, the telephone, the tele- uU^^
graph, and that conveyer of information and advertise-
ments, the newspaper. These all tend, therefore, to "/TwT^g f
Hpinrfiasp pnV.ps
fahs
Having examined those causes 'outside the equation
which affect the volume of trade, our next task is to y
consider the outside causes that affect the velocities
of circulation of money and of deposits. For the most
part, the causes affecting one of these velocities affect
the other also. These causes may be classified as
follows :
/
This indirect effect on the price level must not be confused with
4
2 (a). The more frequently money or checks are
received and disbursed, the shorter is the average in-
terval between the receipt and the expenditure of money
84 THE PURCHASING POWER OP MONET [Chap. V
5
3 (a). The more densely populated a locality, the
v^
more rapid will be the velocity of circulation.^
There is definite evidence that this is true of bank
deposits. The following figures ^ give the velocities of
circulation of deposits in ten cities, arranged in order
of size:
Paris 116 lisbon 29
Berlin 161 Indianapolis 30
Brussels 123 New Haven 16
Madrid 14 Athens 4
Rome 43 Santa Barbara 1
G^'^Dk y = ^('\\ )
88 THE PURCHASING POWER OP MONET [Chap. V
6
Lastly, the chief specific outside influences on the
volume of deposits subject to check are:
(1) The system of banking and the habits of the
people in utilizing that system.
(2) The habit of charging.
1. It goes without sajdng that a banking system must
' Cf. Jevons, Money and the Mechanism
of Exchange, New York
(Appleton), 1896, p. 336; also Kinley, Money, New York (Mao-
millan), 1904, pp. 156 and 157.
Sec. 6] INDIRECT INFLUENCES 89
' Andrew, " Credit and the Value of Money." Reprint from Papert
and Proceedings of the Seventeenth Annual Meeting American Economic
Association, December, 1904, p. 10.
CHAPTER VI
1
We have now considered those influences outside the
equation of exchange which affect the volume of trade
(the Q's), the velocities of circulation of money and
deposits (V and V), and the amount of deposits (M').
We have reserved for separate treatment in this chapter
and the following the outside influences that affect the
quantity of money (M).
The chief of these may
be classified as follows :
1. Influences operating through the exportation and
importation of money.
2. Influences operating through the melting or mint-
i 1 ing of money.
\ I 3. Influences operating through the production and
'
consumption of money metals.
j
4. Influences of monetary and banking systems, to be
I
treated in the next chapter.
The first to be considered is the influence of foreign
trade. Hitherto we have confined our studies of price
levels to an isolated community, having no trade re-
lation with other communities. In the modern world,
however, no such community exists, and it is important
to observe that iatemational trade gives present-day
problems of money and of the price level an interna-
tional character. If all countries had their irredeem-
able paper money, and had no money acceptable
elsewhere, there could be no international adjustment
90
Sec. 1] INDIRECT INFLUENCES CONTINUED 91
3
The stock of bullion is not the ultimate outside
influence on the quantity of money. As the stock of
bullion and the stock of money influence each other,
so the total stock of both is influenced by production
and consumption. The production of gold consists of
the output of the mines, which constantly tends to add
to the existing stocks both of bulhon and coin. The
consumption of gold consists of the use of bullion in
the arts by being wrought up into jewelry, gilding, etc.,
and of losses by abrasion, shipwreck, etc. If we con-
sider the amount of gold coin and bullion as contained
in a reservoir, production would be the inflow from
the mines, and consumption the outflow to the arts
and by destruction and loss. To the inflow from the
mines should be added the reinflow from forms of art
into which gold had previously been wrought, but
which have grown obsolete. This is illustrated by
the business of producing gold buUion by burning
gold picture frames.
We shall consider first the inflow or production,
and afterward the outflow or consumption. The reg-
ulator of the inflow (which practically means the
production of gold from the mines) is its estimated
"marginal cost of production."
100 THE PURCHASING POWER OP MONEY [Chap. VI
4
In any complete picture of the forces determining
the purchasing power of money we need to keep prom-
inently in view three groups of factors (1) the
:
' The theory here presented, that the value of gold buUion
and the cost of production of gold affect prices by way of the
quantity of money, is the one which economists have generally
held. A different view is represented by LaugMin, who says, "the
quantity of money used as the actual media of exchange no more
determines price than the entries of deeds and conveyances in
the county records determine the prices of the land whose sale is
stated in the papers recorded," and that "price is an exchange
relation between goods and the standard money commodity, whether
that money commodity be used as a medium of exchange or not."
See The Principles of Money, New York (Soribner), 1903, pp. 317
and 318.
Sec. 4] INDIKBCT INPLTJENCES CONTINUED 105
Fig. 5.
1
Thus far we have considered the influences that de-
termine the purchasing power of money when the money
in circulation is all of one kind. The illustration given
in the previous chapter shows how the money mecha-
nism operates when a single metal is used. We have
now to consider the monetary systems in which more
than one kind of money is used.
One of the first difficulties in the early history of
money was that of keeping two (or more) metals in
circulation. One of the two would become cheaper than
the other, and the cheaper would drive out the dearer.
This tendency was observed by Nicolas Oresme,
afterwards Count Bishop of Lisieux, in a "report to
Charles V about 1366, and by Copernicus
of France,
about 1526 in a report or treatise written for Sigis-
mund King of Poland.^ Macleod in his Elements
I,
Fia. 6.
Fro. 7.
silver x above the mean line, mm, exceeds the total con-
tents of the money reservoir below this line; (2) when x
is less than said lower contents. In the first case, it
is evident that silver will sweep gold wholly out of
3
So much for the first case, where x is larger than the
contents of the money mm. In the
reservoir below
second case, x supposed to be smaller than the con-
is
is, there is not enough sUver to push all the gold out
4
BimetaUism is to-day a subject of historical interest
only. It is no longer practiced; but its former prev-
alence has left behind it in many countries, including
France and the United States, a monetary system
which is sometimes called the "limping" standard.
Such a system comes about when, in a system of
bimetalUsm, before either metal can wholly expel the
other, the mint is closed to the cheaper of them, but the
coinage that has been accomplished up to date is not
recalled. Suppose silver to be the metal thus excluded,
as in France and the United States. Any money
'Cf. Leonard Darwin, Bimetallism, London (Murray), 1897, 341
pp. ; Bertrand Nogaro, "L'exp6rience bimitalliste," Reviie d'Sconomie
politique, 1908.
128 THE PURCHASING POWER OF MONET [Chap. VII
Fio. 8.
5
We have now to illustrate, by historical examples, the
principles just explained. The first and most important
case is that of France. The ratio of 15J to 1 was
adopted by France in 1785 and continued by the law
of 1803. The history of France and the Latin Union
during the period from 1785, and especially from 1803,
to 1873 is instructive. It affords a practical illustration
of the theory that when conditions are favorable, gold
and sUver can be kept tied together for a considerable
period by means of bimetalhsm. During this period
the public was ordinarily unconscious of any disparity
of value, and only observed the changes from the rela-
tive predominance of gold to the relative predominance
of silver in the currency and vice versa. In the whole-
sale bullion market, it is true, there were slight varia-
> Cf. Charles A. Conant, " The Gold Exchange Standard," Eco-
39
M
T
>a
at
lU
Fig. 9.
7
The system now in use in France is employed
also
in many other countries which, like France, have been
forced to adopt it or else become silver-standard coun-
tries. After the rupture of the bimetallic tie, which
until 1873 linked all gold and silver countries together,
the commercial world broke into two parts, gold-stand-
ard countries and silver-standard countries; and many
desiring to join the ranks of the former, but in danger of
being thrust among the latter, saved themselves by
closing their mints to silver and thereby adopting the
limping standard. One was British
of these countries
India.
The case of India is interesting because it never was
a bimetallic country, and at the time of the adoption
of the present system, in which gold is the standard,
no gold was in circulation. The mints were closed to
silver in June, 1893, and the legal ratio put the rupee
Sec. 7] INFLUENCE OF MONETARY SYSTEMS 139
8
Among the nations which now have the limping
standard is the United States. In 1792, Congress
adopted complete bimetallism. Full legal-tender qual-
ity was given to both gold and silver coins ; both were
to be coined freely and without limit at the ratio of
15 ounces of silver to 1 of gold.
This soon came to be below the market ratio as
affected by conditions abroad and especially in France.
In consequence, gold tended to leave the country. It is
impossible to state with exactness how soon this move-
ment began, but Professor Laughlin sets it as early as
1810 and concludes that by 1818 httle gold was in cir-
culation.^ America, although nominally a bimetallic
country, became actually a silver country.
Influenced partly by the desire to bring gold back
into circulation, and partly also, perhaps, by the sup-
posed discoveries of gold in the South, Congress passed
acts in 1834 and 1837 establishing the ratio of " 16 to
Had not been for the law of 1873, the United States,
it
9
The system of the limping standard, now obtaining
in the United States, logically forms a connecting link
between complete bimetallism and those "composite"
systems by which any nmnber of different kinds of
money may be simultaneously kept in circulation. The
manner in which most modern civiUzed states have
solved the problem of concurrent circulation has been
to use gold as a standard, and to use silver, nickel, and
copper chiefly as subsidiary money, Umited in quantity,
with, in most cases, limited amounts of paper money,
the latter being usually redeemable. The possible
yariations of this composite system are unlimited.
In the United States at present we have a system
which is very complicated and objectionable in many
of its features especially (as we shall presently see)
Gold is the standard and is
in its lack of elasticity.
freely coined. A Umited number of silver dollars,
worth, moneywise, more than double their value bullion-
wise, are a heritage of former bimetalhc laws long
since rendered inoperative by the paper money of the
Civil War and expressly repealed in 1873. The two
attempts of 1878 and 1890 to return halfway to bi-
metalUsm by the piirchase of silver
attempts dis-
continued in 1893
have greatly swollen the volume
of coined silver. The attempt to force silver dollars
into circulation was not acceptable to the business
world, and Congress therefore issued instead the two
forms of paper mentioned. The chief form is the
"silver certificate." For each silver certificate a silver
144 THE PURCHASING POWER OP MONET [Chap. VII
1
The chief purpose of the foregomg chapters is
149
150 THE PURCHASING POWER OF MONEY [Chap. VIII
2
It is proposed in this chapter to inquire how far these
propositions are really causal propositions. We shall
study iQ detail the influence of each of the six magni-
tudes on each of the other five. This study will afford
answers to the objections which have often been raised
to the quantity theory of money.
To set forth all the facts and possibilities as to causa-
tionwe need to study the effects of varying, one at a
time, the various magnitudes in the equation of ex-
change. We shall in each case distinguish between the
effects during transition periods and the ultimate or
normal effects after the transition periods are finished.
For simplicity we shall in each case consider the normal
or ultimate effects first and afterward the abnormal or
transitional effects.
Since almost all of the possible effects of changes in
the elements of the equation of exchange have been
already set forth in previous chapters, our task in this
chapter is chiefly one of review and rearrangetiient.
Our first question therefore is: given (say) a doubling
of the quantity of money in circulation (M), what are
the normal or ultimate effects on the other magnitudes
in the equation of exchange, viz. : M', V, V, the p's
and the Q's ?
We have seen, in Chapter III, that normally the effect
of doubling money in circiilation (M) is to double
rests :
(1) The equation of exchange, MV + M'V = 2pQ.
(2) An M normally causes a proportional
increase of
increase M'. of
An increase of M does not normially
(3) V, V, affect
or the Q's.
If these three premises be granted, the conclusion
must be granted. If any of the premises be denied, the
objector must show wherein the fallacy lies. Premise
(1) has been justified in Chapter II and Chapter III,
and mathematically demonstrated in the Appendices to
Chapters II and Til. Premise (2) has been shown to
be true in Chapter III and premise (3) in the present
chapter.
So much pains has been taken to establish these prem-
ises and to emphasize the results of the reasoning based
on them because it seems nothing less than a scandal
in Economic Science that there shoiild be any ground
for dispute on so fundamental a proposition.
The quantity theory as thus stated does not claim
that while money is increased in quantity, other causes
may not M', V, V, and the Q's, and thus aggra-
affect
vate or neutrahze the effect of M
on the p's. But these
are not the effects of M
on the p's. So far as by M
itself is concerned, its effect on the p's is strictly propor-
tional.
The importance and reaUty of this proposition are not
diminished in the least by the fact that these other
causes do not historically remain quiescent and allow
the effect on the p's of an increase in M
to be seen alone.
The effects of M
are blended with the effects of changes
in the other factors in the equation of exchange just as
Sec. 3] QUANTITY THEORY 159
4
^^ As to deposits {M'), this magnitude is always depend-
ent on M. Deposits are payable on demand in money.
They require bank reserves of money, and there must
be some relation between the amount of money in cir-
culation {M), the amount of reserves (/"), and the
amount of deposits {M'). Normally we have seen that
the three remain in given ratios to each other. But
what a normal ratio at one state of industry and civi-
is
7
We have now studied the effects of variations in
each of the factors in the equation of exchange (save
one) on the other factors. We have found that in
each case except in the case of trade (the Q's) the
ultimate effect was on prices (the p's). The only
group of factors which we have not yet studied as cause
are the prices (p's) themselves. Hitherto they have
been regarded solely as effects of the other factors.
But the objectors to the quantity theory have main-
tained that prices should be regarded as causes rather
than as effects. Our next problem, therefore, is to ex-
amine and criticize this proposition.
So far as I can discover, excejit to a limited extent
during transition periods, or during a -parsing season (e.g.
the fall), there is no truth whatever in the idea that the
price level is an independent cause of changes in any of
the other magnitudes M, M', V, V, or the Q's. To
170 THE PITECHASING POWER OF MONEY [Chap. VIII
an effect
of the world's money, deposits, velocities,
and trade.
We have seen that high prices in any place do not
cause an increase of the money supply there; for money
flows away from such a place. In the same way high
prices at any time do not cause an increase of njoney
at that time; for money, so to speak, flows away from
that time. Thus if the price level is high in January as
compared with the" rest of the year, bank notes will not
tend to be issued in large quantities then. On the con-
trary, people will seek to avoid paying money at the
high prices and wait till prices are lower. When that
time comes they may need more currency; bank notes
and deposits may then expand to meet the excessive
demands for loans which may ensue. Thus currency
expands when prices are low and contracts when prices
are high, and such expansion and contraction tend to
lower the high prices and raise the low prices, thus work-
ing toward mutual equality. We see then that, so far from
its being true that high prices cause increased supply of
affecting the rise andJaJljjf_a_Eajrticialar price with re-
~
"
spect to tEatleveL
9
~"
cially where the contracts are for a long time ; these in-
clude bonds, mortgage notes, use of real estate by leases.
2. Contract prices of properties and services, where
'Time' Money and Lower Bond Prices," in The Gold Supply and
Prosperity, editedby Byron W. Holt, New York (The Moody
Corporation) 1907, p. 163 and after.
Sec. 1] DISPEBSION OF PRICES 189
2
The fact that wages, salaries, the price of gold in non-
monetary forms, etc., and especially the prices of bonded
seciu-ities,cannot change in proportion to monetary
fluctuations, means, then, that the prices of other things,
such as commodities in general and stocks, must change
much more than in proportion. This supersensitiveness
to the influence of the volume of currency (or its velocity
of circulation or the volume of business) applies in a
maximum degree to stocks. Were a railroad to double
in money value, the result would be, since the monej'
value of the bonds could not increase appreciably, that
the money value of the stock would more than double.
Stocks are shares in physical wealth the value of which,
in money, can fluctuate. Since the money price of
bonds is relatively inflexible, that of stocks will fluctuate
1125,000,000
3
Corresponding to changes in an individual price there
will be changes in the quantity of the given commodity
which is exchanged at that price. In other words, as
each p changes, the Q connected with it wiU change also ;
this, because usually any influence affecting the price
4
In this chapter we have seen that prices do not, and
in fact cannot, move in perfect imison. The reasons
Sec. 4] DISPERSION OF PRICED 197
1
In the previous chapter the necessity for an index
number (P) was shown and a particular form of index
number was suggested. This form of index number
had been shown in Chapter II and its appendix to meet
certain conditions (of proportionaUty of price level to
quantity of money, etc.) required by the equation of
exchange, MV+M'V'=PT. In the present chapter,
this index nimaber will be compared with others and
the general purposes of index numbers discussed, in-
cluding purposes having Uttle direct concern with the
equation of exchange.
Index numbers may be compared in respect to (1)
form, under which term are included methods of weight-
ing and of determining the "base" prices; (2) the
selection of elements to be included. In this section
we shall consider the question of form.
The number of possible forms of index numbers is
infinite. They differ enormously in complexity, in ease
of calculation, and in conformity to various other tests.
A few of the simplestmay here be mentioned. Their
discussion will be brief and will in many cases be dog-
matic. Full proofs and discussions are contained in
the mathematical appendix.^
If in 1900 the average price per pound of sugar was
6 cents, and in 1910 it was 8 cents, the ratio of the price
' See Appendix to (this) Chapter X, 1-8, where 44 types of
index numbers are compared.
198
Sec. 1] THE BEST INDEX NUMBERS 199
Advancement of Science for 1887, pp. 247-301 ditto for 1888, pp.
;
181-209 ditto for 1889, pp. 133-164. Nitti, La misura delle varia-
;
sioni di valore della moneta, Turin, 624 pp. also the Appendix to
;
(this) Chapter X.
200 THE PUKCHASING POWEB OF MONEY IChap. X
lens can be constructed which will focus in one point
all the rays of Ught reaching it from a given point.
But, although in the science of optics we learn that a
perfect lens is theoretically impossible, nevertheless, for
all practical purposes lenses may be constructed so
nearly perfect that worth while to study and
it is well
construct them. So, also, while it seems theoretically
impossible to devise an index number, P, which shall
satisfy all of the tests we should Uke to impose,^ it is,
nevertheless, possible to construct index niunbers which
satisfy these tests so well for practical purposes that we
may profitably devote serious attention to the study
and construction of index numbers.
The index number mentioned in Chapter IX may be
constructed by the following process: Suppose that the
year 1910 is the period to be considered in our equation
of exchange + MV M'V
= ^pQ = PT. We select
another year (say 1900) and call it the " base " year.
This means that the prices of 1910 are to be expressed
as a percentage of the prices of the equation of exchange
for 1910.
Next we obtain an expression for trade (or 7^.
As shown in the appendix to this chapter, every form
of index number, P, for prices implies a correlative
form of index for trade, T, and vice versa. It is con-
venient to select T first. We observe that trade (or T)
is not the value of transactions measured at the actual
3
Perhaps the most important purpose of index num-
bers is to serve as a basis of loan contracts.^ It is
4
To cut these Gordian knots, perhaps the best and
most practical scheme is that which has been used in
the explanation of the P in our equation of exchange,
an index number ia which every article and service
218 THE PtTECHASING POWER OF MONEY [Chap. X
is weighted according to the value of it exchanged at
base prices in the year whose level of prices it is desired
to find.^ By this means, goods bought for immediate
consumption are included in the weighting, as are also
all durable capital goods exchanged during the period
ble.^ We
should content ourselves with securing the
naaximum attainable improvement in the standard of
deferred payments, without attempting to secure an
ideal distribution of " the benefits of progress."
It will also simplify our problem if we remember that
om" ideal not primarily constancy of 'the dollar but
is
5
We are brought back again, therefore, to the conclusion
that on the whole the best index number for the purpose
of a standard of deferred payments in business is the
same index number which we found the best to indicate
the changes in prices of all business done ; in other
words, it is the P on the right side of the equation of
exchange.^
It is, of course, utterly impossible to secure data for
all exchanges,nor would this be advisable. Only
articleswhich are standardized, and only those the use
of which remains through many years, are available
and important enough to include. These specifica-
tions exclude real estate, and to some extent wages,
retail prices, and securities, thus leaving practically
nothing but wholesale prices of commodities to be in-
cluded in the list of goods, the prices of which are to be
2
The stock of money metals at any time in any country
is evidently the difference between the total product and
the sum of the consumption and the net export. Jacob'
has estimated roughly the stock in Europe at various
dates. The following table compares the estimated me-
talhc stocks in Europe with the estimated price levels:
Date
238 THE PURCHASING POWER OP MONEY [Chap. XI
the Royal Statistical Society. For many years Sauerbeck has pub-
lished yearly his index number in the March issue of this journal.
Sec. 3] STATISTICAL VERIFICATION 239
4
We may, therefore, summarize the course of price
movements during the nineteenth century by the f ol-
lowing probable statements:
1. Between 1789 and 1809 prices rose rapidly, the
but that it did not increase so fast as trade therefore prices fell.
;
slightly
probably about 10 per cent up to 1890-1893
and more up to 1896. This is because the stocks of
specie in silver countries were less than half those in gold
countries ^ (including those with the " limping stand-
ard " from left-over silver) ; so that had there been a
transfer of a given amount of silver from the silver
Orient to the gold Occident, this would have affected
Oriental prices about twice as much as Occidental.
The transition of India from the silver to the gold
side has left about nine tenths of the specie (gold and
^
Enolish
Sec. 5] STATISTICAL VERIFICATION 247
6
The outlook for the future is apparently toward a
continued rise of prices due to a continued increase in
the gold supply. To-day almost as much gold is pro-
duced every year as was produced in the whole of the
16th century.
The most careful review of present gold-mining con-
ditions shows that we may expect a continuance of gold
inflation for a generation or more. "For at least
thirty years we may coxmt on an output of gold higher
than, or at least comparable to, that of the last few
years." ^ This gold will come from the United States,
Alaska, Mexico, the Transvaal, and other parts of
Africa and Australia, and later from Colombia, Bohvia,
Chili, the Ural Province, Siberia, and Korea. It must
be remembered that it is the stock of gold and not the
annual production which influences the price level;
and that the stock will probably continue to increase
for many years after the production has begun to
decline, as long, in fact, as production keeps above
consumption.
A lake continues to rise long after the freshet which
feeds it has reached its maximum. So the stock of
gold will continue to increase long after the annual
production of gold has stopped increasing. Whether
or not prices will continue to rise depends on whether
the increase in gold and the circulating media based
on gold continues to exceed the growth of trade. It is
the relation of gold to trade that chiefly affects prices.
Even if the stock of gold should increase for many years,
prices may not rise ; for trade may increase still faster.
7
We have briefly summarized the history of price
movements since the discovery ofAmerica and shown
their relation to the stock of the precious metals. But,
as we have emphasized in previous chapters, the pre-
cious metals do not include all forms of circulating
media. Paper money and bank deposits have come
during the nineteenth century to occupy very important
places in cm-rency systems.
We not attempt any complete review of the
shall
effects of paper money on prices. The best that can
be done is to mention briefly the most striking cases of
paper money inflation and contraction. These are all
cases of irredeemable paper money. When paper
money is redeemable, its possible increase is restricted
by that fact and, what is more important, the effects of
the increase are dissipated over so large an area as to
have little perceptible effect on prices. This dissipa-
tion takes place through the export of specie from the
country in which the paper issues occur. Though
the paper cannot be itself exported, it can displace
gold or silver, which amounts to the same thing so far
as spreading out the effect on prices is concerned.
But when the paper is irredeemable, after specie has
been expelled from circulation (whether by export,
melting, or hoarding in anticipation of disaster) there
is no such spreading-out effect. The effects on prices
are then entirely local and therefore greatly magnified.^
* See Ricardo, Essay on the "High Price of Bullion," Works,
2d ed., London (Murray), 1852, p. 278.
Sec. 7] STATISTICAL VERIFICATION 251
8
One of the early paper-money schemes was that of
John Law, who established a bank of issue in France
in 1716. Two years later (December 4, 1718), the bank
was taken over by the Crown. Soon shrewd traders
were acquiring specie for notes and exporting the
specie secretly, although exportation of specie was illegal.
May 27, 1720, only four years after its establishment,
the bank stopped payment of specie. By November of
the very same year the paper had fallen to one tenth of
its par value, and after this it became utterly worthless.
The case of the assignats of the French Revolution is
classic.^ It was in December, 1789, that the first issue,
four hundred miUion francs, was ordered, based osten-
sibly on the landed property of the nation. The notes
were issued in April, 1790, and bore 3 per cent interest.
According to the original plan, all of the assignats received
Cf the mention of this influence on
. depreciation in the Bullion
Report, III.
" For the following facts, see Andrew
D. White, Paper Money
Inflation in France, Economic Tracts, No. VII, No. 3 of Series, 1882.
Sec. 8] STATISTICAL VERIFICATION 253
10
Austrian experience with paper money is instructive.*
Like so many of the European banks, that of Austria
was used by the government as an instrumentaUty for
obtaining loans. This was done by allowing the bank
to issue large sums in notes. The wars with Napoleon
demanded supplies, and during these wars the issue was
largely increased. In 1796 the note issue was 47,000,000
gulden; in 1800 it was 200,000,000; in 1806, it was
449,000,000. The notes were much below par. In
1810 the bank notes fell successively to ^, ^ and about
^of par. In 1811 a proclamation openly valued them
at one fifth of their nominal value and decreed their
exchange at this rate for redemption notes, called the
' See W. G. Sumner, History of American Currency, New York
(Holt), 1874, Chapter III.
256 THE PTTBCHASING POAVBR OP MONET [Chap. XI
11
Many of the American colonies had experience with
paper money. In fact, one of the grievances against
England was the parliamentary prohibition of paper
money issues In practically all cases ^ there was over-
!
' lUd.
12
The were so disastrous that, in the Constitu-
effects
tion of the United States, a provision was incorporated
prohibiting any state from issuing "bills of credit."
But, during the Civil War, the temptation again came
to resort to this easy way of seeming means of pay-
ment and the federal government itself issued United
;
13
It is necessary to remember that the confidence with
which we have to deal is not primarily confidence in
redemption, but confidence in the paper money, its
purchasing power. This confidence may rest on ex-
pectation of redemption or on other conditions, particu-
larly the expectation of further inflation or contraction.
The explanation of the value of the greenbacks appears
to me to be in brief as follows :
The Redemption Act of 1875 announced the intention
of oiu"government to redeem the greenbacks on and af-
ter January 1, 1879. Each greenback being thus kept
equal to the discounted value of a full dollar due Jan-
uary 1, 1879, they rose steadily toward par as that date
approached. Some of them were withdrawn from cir-
culation to be held for the rise. The value of a green-
back dollar could not be much less than this discounted
value of the gold dollar promised in 1879; otherwise
speculators might withdraw the greenbacks wholly.
This would pay them well provided they were certain
that the government's promise would be fulfilled. On
the other hand, the value of greenbacks could not, with
paper money redundant for trade, be greater than said
discounted value, because in that case speculators
would return it all to the circulation, the prospective
rise being "too small to repay the interest" lost in
carrying it. Thus speculation acted as a regulator of
the quantity of money.
15
expansion did not begin at the same time in all the prin-
cipal commercial countries, the beginning of it in one
country would be quickly communicated to others.
For the same reason the arrest of rising prices and the
beginning of falling prices would occur at about the
same time in most of the principal countries. As a
matter of fact this is what we find to be the case. Juglar
has made out a table showing the crises in England,
France, and the United States from 1800 to 1882.i
With the addition of the dates of later crises the table
is as follows :
Fbance
268 THE PURCHASING POWER OP MONET [Chap. XI
back to 114 the next year, and that the deposits rose
from 84 miUions to 103, faUing back to 91 that from ;
17
Not only do money and deposit currency (M and M')
rise regularly to a maximum at the time of a crisis, but
their velocity of circulation, so far as statistics indicate,
goes through the same cycle. Pierre des Essars has
demonstrated this beyond peradventure, so far as
velocity of circulation of deposits is concerned.^
For the United States we have scarcely any statistics
of velocity of circulation of deposits, but those for two
New Haven banks and for an IndianapoUs bank, which
I have secured for the last few years, show a maximimi
in the crisis year 1907.
After a crisis, a decrease occurs in M, M', V, and V.
Bank reserves are iacreased, and this causes a decrease
in M.
Since, then,' currencyand velocity both increase
before a crisis, reach a maximum
at the crisis, and fall
after the crisis, it is small wonder that prices follow the
same course. That they do is the real meaning of a
crisis. In fact, as we have seen, Juglar defines a crisis
as an arrest of a rise of prices. The index numbers of
prices show the rise, maximum, and slump for almost
every crisis year for which price statistics exist.'
'Juglar, op. cit, tables following p. 291.
'"La Vitesse de la circulation," Journal de la Sociiti de Statistique
de Paris, April, 1895, p. 148. From 1810 to 1892 in France, taking
the thirteen crisis years and the twelve years of "liquidation," Des
Essars finds that, without exception, the velocity of circulation of
deposits at the bank of France is a maximum in the crisis years
and a minimum in the years of liquidation.
The detailed figures will be seen in the Appendix to the next
chapter (Chapter XII).
Sec. 17] STATISTICAL VERIFICATION 271
No
attempt has been made in this chapter to review
all [thephenomena or even all the typical phenomena
of crises. We are not here concerned with crises
except in relation to currency. Our concern is with
the magnitudes entering the etjuation of exchange, es-
18
This chapter has been devoted to an historical study
of changes in the quantity of currency and of the effects
of these changes on prices. We have seen that, on the
whole, increases in the amount of money have tended
to raise prices from century to century during the last
thousand years, and especially since the discovery of
America. The changes in the last century, or more
exactly, from 1789 to 1909, have been considered in
somewhat more detail, covering five periods of alter-
nately rising and falling prices. We have seen evidence
to connect these price movements with changes in the
quantity of money and in the volume of business. The
periods 1789-1809, 1849-1873, and 1896-1909 were
periods of rising prices and large increases of the money
supply. In the period 1809-1849 prices fell presiunably
because of a falling off in gold and silver production and
a continuing increase of business while between 1873
;
prices.
Finally, our study of deposit circulation and crises
has afforded further illustration. Preceding a typical
crisis, there is, in general, a tendency for deposits to
1
The last chapter was devoted to a brief sketch of price
movements and their causes, in so far as the scanty data
available make even a tentative interpretation possible.
From this telescopic view of the past we turn to a micro-
scopic view of the present. We shall confine it to a
study of the events of the last three decades in the
United States. In the study of the last chapter we
found the facts of history to be in accord with the a
priori principles already set forth in the equation of
exchange. But these facts of history were too general
and vague to constitute a quantitative fulfillment of the
equation of exchange. We shall find, however, much
fuller data in the last few decades. We shall see that
the equation of exchange, which has already been
proved a priori, may also be verified by actual statistics
within at least the limit of error to which the statis-
tics are liable.
Agood beginning of such a study is afforded by the
pioneer work of Professor Kemmerer, already often re-
ferred to. He has estimated ^ roughly the chief magni-
tudes of the equation of exchange and found that these
conform in a general way to the conditions which the
equation of exchange imposes. For each year, begin-
* Money and Credit Instruments in their Relation to General Prices,
New York (Holt), 1909, Book II.
276
Sec. 1] STATISTICS OF EECBNT TEABS 277
Fig. 12.
2
I shall now attempt to makeas precise statistical
estimates of the magnitudes in the equation of exchange
for the years 1896-1909 as the data available will allow.
This period 1896-1909 is selected chiefly because
its two end years afford the only known data making
possible an estimate of velocity of circulation of money
and of bank deposits.
The magnitudes will be considered in the order
M, M', V, V, T, P. For each the figures to be used
are new.
M. The following table gives the estimated amount of
money in circulation in the United States. By this
we mean the total amount of money (coin and paper)
outside of the federal treasury and outside the banks
of deposit and discount (national, state, private and
trust companies). The excluded be-
treasury stock is
1896 . , .
Sec. 2] STATISTICS OP RECENT TEARS 281
3
Having found M and M', the circulating media, we
next proceed to ascertain V and V, their velocity of cir-
culation. We shall find it convenient to consider the
latter first.
The velocity of circulation of bank deposits is found
by dividing respectively the total check circulation
(M'V) by the bank deposits {M'). The divisor, M',
has already been found. As to the dividend, M'V, this
is practically the total checks drawn in a year, for we
(1)
Sec. 5] STATISTICS OF RECENT YEARS 291
the coefficient, not for the raw figures, but for their
successive year-to-year ratios. In other words, we
tabulate and compare the ratios of each year's P to the
show a
ratios should rise or fall together, the curves would
close parallehsm or agreement in their successive changes
of direction. As a matter of fact, the results of this
method show a coefficient of correlation of 57 per cent
(or .57 .10, where .10 is the probable error). This
figure, 57 per cent, is a moderately high coefficient of
correlation.^ We may conclude, therefore, that the
"quantity theory" is statistically verified to a high
degree of correlation.*
be emphasized that the coefficients of correla-
It is to
tion as just given compare the price level with what it
should be according to the statistics of the five magni-
tudes on which, by the so-called quantity theory, it is
dependent. The correlation would be less if instead of
these five magnitudes only one were taken. Thus the
coefficient of correlation for 1896-1909 as between
money, M, and prices, P, by the year-to-year-ratio
' For instance, no one would deny that the length and breadth
of nuts are highly correlated. The coefficient of their correlation is
57 per cent. The height of a man and the breadth of his face are
correlated to the extent of 35 per cent.
2 Incidentally we may here compare the relative degree of corre-
Ifany one has ever really imagined that the price level
depends solely on the quantity of money, he should
certainly be corrected. But the really important
matter is that students of economics should appreciate
7
To those who have faith in the a priori proof of
the equation of exchange the real significance of the
remarkable agreement in our statistical results should
be understood as a confirmation, not of the equation
by the figmres, but of the figures by the equation.
There are discrepancies in our inductive verification;
but these are aU well within the limit of errors of meas-
urement. The discrepancies prove that sUght errors
exist among the figures; otherwise, they would conform
exactly to the relation prescribed by the equation of
exchange.
Our next task is to examine the discrepancies and lo-
cate, so far as possible, the errors involved. The degree
of total mutual discrepancy between the independently
calculated magnitudes is best expressed by the degree
of inequality between the calculated values of + MV
M'V and PT, which should be equal. That is, PT
divided by MV + M'V should always be unity. Ac-
tual division gives the figures in the column headed
" original" in the following table. The other column
will be explained presently.
Sec. 7] STATISTICS OF RECENT TEARS 299
^9$ JS7 la^a 1SSS jgoo igoi i902 1903 1994 >eoi laps. I9Q7 t90& (SOS
'
Fig. 14.
than 3 per cent for P; and less than 4 per cent for T. We
conclude then that the figures fit each other better than
might be expected from their known lack of precision.
The corrections which we have assigned to the va-
rious factors are so insignificant that it would be haz-
ardous to attempt to explain them specifically. The
errors which they presumably represent might be due
to numerous sources, such as the varying ingredient in
the New York clearing house transactions of bank trans-
fers as distinct from ordinary check transactions; or
such as errors or defects in the statistics of trade in grain,
etc. ; or such as an over or underestimate of the devia-
tion from normal of the particular days in 1896 and 1909
on which the statistics of deposits made in banks were
gathered; or such as over or underestimates of the un-
reported deposits, or over or underestimates of the gold
in the United States, or over or underestimates of wages
and of other numerous minor though often conjectural
elements in our calculations.
The sources of error just mentioned were named
in the order of their probable importance. It is, per-
haps, significant that the greatest discrepancies are in
304 THE PURCHASING POWER OF MONEY [Chap. XII
8
After making the above named mutual adjustments
among the six magnitudes in the equation of exchange,
we reach the following figures, constituting our final
table of values for M, M', V, V, P, and T; they are the
figures plotted in the dotted curves above given:
Finally Adjusted Values of Elements of Equation of
Exchange
Sec. 8] STATISTICS OP KECENT YEARS 305
tion (V) has increased only 10 per cent that the de- ;
9
There has been much discussion as to the most im-
portant causes which have increased prices during re-
cent years. It is, therefore, interesting to compare the
four proximate causes which, as we have seen, have alone
tended to increase prices in the period 1896-1909. Per-
haps the simplest and best method is to compare the
actual rise of prices with what it would have been if
any one cause of that rise had been absent. That is,
we test the importance of any price-raising factor by
answering the question. What difference does it make
to prices whether that factor is present or absent?
We shall find that the growth of money is by far the most
important cause. The growth of deposits is less impor-
tant than appears at first glance. The growth of deposits
would have to be regarded as the most important cause
if deposits could be'considered as independent of money.
308 THE PURCHASING POWER OP MONEY [Chap. XII
since 1896,
(3) If the velocity of circulation of money (7) had
not grown at all since 1896,
(4) If the velocity of circulation of deposits (F') had
not grown at all since 1896,
(5) If the volume of trade {T) had not grown at all
since 1896,
assuming in each case that all the other four factors
had grown in exactly the way they did grow. We have
taken the actual price level in 1909 as 100 per cent and
shall continue to do so, expressing on this basis what
the price level would have been under each of the five
hypotheses above named. We reach the following
results :
'
* The calculations needed are obvious and simple. They consist
of substituting, for aU the factors but one in the right side of the
mv+m(^\ V
equation P = "L =
^ - tlie statistics already
obtained for 1909, and for that one factor remaining, the figure for
1896. This one factor remaining is, for the first hypothesis, M;
for the second, M'/M for the third, V ; the fourth,
; ; and the V
fifth r.
310 THE PURCHASING POWER OF MONET [Chap. XII
10
But the full effect of the increase in the quantity of
money is really greater even than these figures indicate
for we have not included the effect of the overflow of
money abroad, caused by the great increase in Ameri-
can bank deposits. Evidently this overflow must be
taken into account; for the other three price-raising
factors, by crowding out money and usurping its place,
have given themselves an exaggerated appearance of
importance. In other words, there has been a greater
increase in money than appears from the United States
figures by the amount which has overflowed into foreign
lands. The United States is only a small part of the
world's market, and its price level is largely determined
by the world's price level. Whatever raises prices in
one country tends to raise prices in all countries, and in
the last analysis the only correct way to measure the
relative importance of price-raising causes is to consider
the world as a whole. If the statistics we have worked
out for the United States were typical of the world,
the resulting estimate of the relative importance of the
four price-raising causes would be true of the world.
312 THE PimCHASING POWER OP MONET [Chap. XII
11
Throughout this book we have aimed at explaining
the general purchasing power of money, not its purchas-
ing power over any particular goods or class of goods.
The problem of the rise in " the cost of living " is partly
a general problem of the purchasing power of money,
and partly a special problem of the prices of food, cloth-
ing and other costs of "living." With the special
problem we have here nothing to do. But it so hap-
pens that the special changes in the cost of hving are
very small as compared with the general change ta
316 THE PUKCHASING POWEE OP MONET [Chap. XII
(1)
318 THE PtTECHASING POWER OF MONEY [Chap. XII
1
We have seen that the purchasing power of money
(or its reciprocal, the level of prices) depends exclu-
sively on five factors, viz. the quantity of money in cir-
:
2
But while there is much to be hoped for from a greater
foreknowledge of price changes, a lessening of the price
changes themselves would be still more desirable. Va-
rious preventives of price changes have been proposed.
We shall first consider those which are more particularly
appUcable to secular price changes, and afterward con-
sider those more particularly apphcable to the price
changes involved in credit cycles. The secular price
changes are, as we have seen, chiefly due to changes in
money and in trade. There has been for centuries, and
promises to be for centimes to come, a race between
money and trade. On the results of that race depends to
some extent the man. The com-
fate of every business
mercial world has become more and more committed to
the gold standard through a series of historical events
having little if any connection with the fitness of that or
ripe.
One suggestion has been to readopt bimetallism. This
has already been discussed in Chapter VII. We were
then concerned, however, chiefly with the "mechanics
' Man and the Earth, New York (DufBeld), 1906, p. 62.
Sec. 2] is THE PEICE LEVEL CONTROLLABLE ? 325
A
more important objection remains to be noted.
Since bimetallism, as usually proposed, would greatly
overvalue one of the two metals, the first great effect
of its adoption might be not to steady prices but to
disrupt them and upset the relation of debtor and
creditor. While the great overvaluation of one metal
isnot a necessary feature of bimetallism, it has always
been the feature which has made it politically popular.
Thus, the bimetalhsm advocated in the United States
during the last twenty or thirty years has been a bimet-
allism which would grossly overvalue silver. It pro-
posed that 16 ounces of silver should circulate as the
equivalent of an oimce of gold, when during much of
this time it really required 30 or 35 ounces of silver to
be equivalent to one of gold. Such an overvaluation
of silver would mean that silver would be imported
from Mexico, India, China, and other silver countries,
as well as mined ia larger quantities and coined in the
United States, thus depreciating the currency both
greatly and suddenly. The proposal was well satirized
by a cartoon in the "free silver" campaign of 1896
representing the United States as a ship sailing over
Niagara Falls in order to reach smooth sailing below
the falls,
if only it survive the shock of the fall!
3
Recognizing the force of the arguments against bi-
metallism (and polymetaUism), Professor MarshaU has
suggested as a substitute a system which has been called
symmetaUism. Under this scheme
symmetaUism
two (or more) metals would be joined together physicaUy
in the same coin or in "linked bars." Evidently any
ratio could be used, and neither metal coxild push the
other out of circulation. The value of the composite
coin would be the sum of the values of its two constit-
uents, and the fluctuations in its value would be the
mean of the fluctuations of its constituents.^
Many other schemes for combining metals have been
suggested. Among them are the "joint-metalhsms" of
Stokes and Hertzka, which are kinds of bimetaUism at
a variable instead of at a fixed ratio. Another, advo-
cated by Walras,^ the gold standard with a "sUver
is
of Currency, etc., 14, 15, 21-28 and " A Gold Standard for the
;
4
The next plan to be considered is that advocated by
Professor Marshall and the Committee of the British
Association.^ It is, in essence, the revival of the tabu-
lar standard proposed and discussed by Lowe,* Scrope,'
Jevons,* and others; a standard which is relatively in-
dependent of special legislation. This involves the
passing of a law merely permissive
first by which
contracts could be expressed in terms of an index num-
ber. Such a law would not be necessary, but it might
serve to draw attention to the index method. The
' See Report of the British Association for the Advancement of
Science, 1890, p. 488, containing a draft of a proposed Act of Par-
liament for this purpose.
^ Present State of England in regard to Agricidture, Trade, and
Finance. London, 1622.
' Principles of Political Economy, London, 1833, p. 406.
* Investigations in Currency and Finance, London (Macmillan),
1884, p. 122 ; also Money and the Mechanism of Exchange, London,
(Kegan, Paul), 1893, Ch. XXV.
Sec. 4] is THE PRICE LEVEL CONTKOLLABLE ? 333
Cf. Francis Walker, Money, T<iew York (Holt), 1891, pp. 157-163.
2 See Joseph French Johnson, Money and Currency, Boston
(Ginn), 1906, p. 175.
334 THE PURCHASING POWER OF MONEY [Chap. XIII
also the Scotch fiars prices have existed for more than
two centuries for similar piirposes, establishing the price
of grain on the basis of which rents contracted in grain
should be paid in money.^
As has been already indicated, government action
looking to this result need not necessarily be taken. i
' See L. V. Mises, " The foreign exchange policy of the Austro-
Hungarian Bank," Economic Journal, June, 1909, p. 201.
Sec. 5] is THE PRICE LEVEL CONTROLLABLE ? 345
' A recent
popular pamphlet by A. C. Lake, Currency Reform the
Paramount Memphis (28 N. Front St.), Tenn., proposes to
Issue,
stop the free coinage of gold. As I write, other evidences of the
spread beyond academic circles of the idea that gold is an unstable
standard come to hand. The rapid rise in the cost of living has of
course thrust the subject on the attention of the magazine and news-
paper press. Mr. Edison, in a recent interview, predicts the further
downfall of gold, through the discovery, sure to be made sooner
or later,
of cheap methods of extracting immense quantities of gold
from some Southern clays. He asks the pertinent question " Is it
:
Tj-
2
The mean is a modification of the
weighted arithmetical
simple arithmetical mean. Suppose it is desired to find the
mean height of two groups of trees, one tall, the other short.
' For discussion of certain statistical averages, see Dr. Franz
Zizek, Die Staiistischen Mittelwerte, Leipzig (Duncker & Humblot),
1908, in which (p. 2) will be found further references.
349
350 THE PURCHASING POWER OF MONEY [Append. II
o o
which is evidently equal to A ; thus the test is satisfied.
Again, be the geometrical mean of a, b, and c so
let G ;
of a, b, and c is H= :j
z = This also conforms, because
- + I+-
a b c
H=
1 + 1+1
3
For a weighted arithmetical average A^ of a, b, c, the
. + P^w + yAw
^- Aa, a+p+y _
{a + a' + Ka?)fb+-^
^-=^ ^rZ. . This may be employed to obtain a
c +' V6c
352 THE PTJKCHASING POWER OF MONEY [Append, II
ix + x' + Koi?)(x+^^
it with the similar form 3^= That x as
X 'VX^ +
determined by this equation will conform to oiu: definition of
an average is evident, since substituting x for a, b, and c,
the equation becomes a truism, showing that the proposed
new average of the identical terms x is x.
A special case of the definition, requiring particular men-
tion, is that in which two or more means (not necessarily of
the same kind) are related to one another. In order that
A should be a mean of ai, Oa, as, when we know that B is
a mean of 6i, 62, h, it is only necessary to have a deter-
mining formula such that if ai = 02 = 03 and at the same
time &i = &2 = &3 (each of which by hypothesis must be
equal to B), then A shall also be equal to each of the magni-
tudes Many examples of pairs of means like
ai, (h, os, etc.
A and B
be given in Chapter
will (on the construction of X
index numbers). The following is a simple example
:
261, 361, "-in the first line representing the amounts expended
by him moments during the year. Likewise,
at successive
E2 is sum expended by the second person during the
the
year, and ^s is the sum expended by the third. lE at the foot
of the first column is the amount expended by all persons in
Sec. 4] APPENDIX TO CHAPTER II 359
Feesonb
360 THE PtTRCHASING POWER OP MONET (Append. II
Or, again, M
is a simple average of the row to its left, iM,
^ = iWi+iiWi + 3mi+"-
mi _ ,
,
etc.,
n
and the equations iM imi + iw^ + iwia + . It is, of course
easy also to express M directly in terms of imi, etc., within
1M + 2M+ -
1M + 2M+ -
^ iM jM
"" M + 2M-\--
iM + 2M+ -
1M + 2M+ - ^'''
_ \ imi/
^ Simii7i
Simi
E
That is, ^ is a weighted average of the net velocities of cir-
^ In 4 of this Appendix.
364 THE PURCHASING POWER OF MONET [Append. II
From this equation and others like it, for every person in
the community and for every moment in the year, simply
by adding them together, we obtain, for the left side of the
equation, the sum of the e's which we call E and for the ;
right side the sum of all the pq's. We have already seen in
the text how the left side, E, may be converted (by multiply-
ing and dividing by M) into MV, and we have also just seen
( 3 of this Appendix) how the sum of all the terms relating to
each particular commodity represented on the right side may
be converted (by similar simple algebraic operations) into one
term of the form pQ so that the whole sum becomes SpQ.
The final result is, therefore, MV = SpQ. This reasoning
constitutes, therefore, a demonstration of the truth of this
formula, based on the simple elementary truth that in every
exchange the money expended equals the quantity bought
multiplied by the price of sale.
M (g)'.o+(^)pw-+-
PO+P-0-+...
Mo PoQ + p'oQ'+- PoQ + p'oQ"+-
The last expression is evidently a weighted arithmetical
PQ + P'Q'+-
which is a weighted harmonic average of -^, -V' ^tc, in
p Po
which the weights are pQ, p'Q', etc., that is, the values, not
in the base year, but the other year.
If Mand the Q's remain invariable, while V changes from
V to Vi, evidently the ratio will be expressed by pre-
formulae.
Again the same formulae apply if M
and V remain invari-
able while the Q's all vary in a given ratio, or if the Q's all
Similarly, we may let r stand for the average ratio, for the
year, of the reserves of all banks (/i) to their deposits (Af')-
since, by definition,
E and V E'
F = tt
M ^rrr,'
M'
2b
APPENDIX TO CHAPTER V
1 (to Chapter V, 5)
goods are goods sold, the following equation expresses the re-
ceipt of money, etc., in exchange for the sale of goods:
R + B' + R"-R"' = %p,Q,.
If there is no external trade, the several magnitudes in these
two equations will evidently be identical on each side. If
external trade exists, each equationmay be resolved into an
equation in which are distinguished the home trade and the
outside trade. Thus, for the first equation, relating to ex-
penditures, the E, E', etc., may be replaced hjH-\-0,H' + 0',
etc., where the H's relate to the purchases at hmne and the
O's to money spent outward. On the other side of the equa-
tion the SpsQft may be replaced by SpsQs -|- Sp^Qi where the
subscripts h relate to the goods purchased at home and the
subscripts i to those coming inward. The equation will then
become:
{H + H' + H" - H"') + {0 + 0' + 0" - 0"')
= ^PhQk + MQt
which, for brevity, we may write ^H + SO = ^phQn + ^PiQt.
Similarly, the second equation, relating to sales, may be
written:
Sr + S/ = SpftQ*-|-SpoQo.
That is, the net sum of the receipts at home (of money, bank
credit, and book credit) plus the sum of payments for goods
coming inward, is equal to the sum of the value of the goods
sold at home plus the value of those sent out of the country.
The two equations, one relating to purchases and the
last
other to sales, may be added together so as to give in a com-
mon equation the total trade in which the given community
is concerned, that is, the total sales and purchases within
itself and the sales and purchases with respect to the outside
SO - 57 = SpiQt - SjJoQo
Here we see that the richer men averaged about three times
as great an expenditure as the poorer, but carried only 50
per cent more cash on hand. In consequence, the velocity
of the richer was 93 as against 43 for the poorer, or more than
double. The progressive relation between expenditure and
rate of turnover may be seen by arranging the 113 cases into
five groups according to expenditure.
' The mathematical necessity of this result can be seen from the
rp _ SpiQi _ SpiQi
n po
V \,
^
^
(formula 7 of the table), then Ti has the correlative form
-Wsi.^....
*Po p'o
=
Pi^Ti SpiQi,
it follows that p _ SpiQi
'
Ti
P - SpiQi ^ SpiQi
'
Ti SpoQi
(Formula 11 of the table.)
Sec. 1] APPENDIX TO CHAPTER X 387
ties [i.e.
\
an average of ^ -j^r '^T
Qo Qo Qo
"'\^^'^
y
-^i' being
-2i3i,
therefore jg the "aggregate price," that is, the value
said to define either one of the two averages (Pi and Qi) in
terms of the other. One or the other must be defined irre-
spective of the equation.
Thus there are three ways of resolving SpiQi, as follows :
^-'*
We wish now to prove that if either Pi or Qi is first de-
termined in any way conformably to the definition of an
average, leaving the other to be determined by the above
equation, then the latter also necessarily conforms to the
definition of an average. We have to prove that if ^i is
QI Q>
taken as an average of ^, ^'"' tlien the correlative ex-
n po
arithmetical average -S
n Qa
^
then we discover in its correlate
SpiQi
"
anew formula for Pi, viz. . In this way any given
n Qo
formula for Pi leads to another formula for Pi which may be
called its antithesis. This second formula for Pi is identical
in form with the formula for Qi correlative to the first for-
mula for Pi, differing merely in the fact that the pi's and Qi's
are interchanged.
The four forms and their relations are best seen by placing
them in a square, as in the following example :
52.1 SpiQi
Pi ^ antithetical to Pi = ^!#
n l^Qi
n Qo
correlative to correlative to
ft = ^ n Po
antithetical to ft ^^
Sec. 2] APPENDIX TO CHAPTER X 391
ure for the base year being the actual exchanges SpoQo in
that year. Likewise ft and Ti differ merely as percentage
and dollar measurements, the base figure being 100 per cent
and SpoQo dollars respectively.
392 THE PURCHASING POWER OP MONET [Append. X
1889, pp. 50-54, where allowance is made for changes in the price
level. Index numbers of the Economist, of Sauerbeck, and of
Soetbeer are cited. Professor J. S. Nicholson has advocated such
a capital-standard in the Journal of the Royal Statistical Association,
March, 1887, pp. 152 ff. This method is discussed by Bdgeworth,
Report of the British Association, 1887, p. 276.
Sec. 3] APPENDIX TO CHAPTER X 393
n
This formula was used by Dutot in 1738,^ and has been
used recently by Bradstreet,^ who applied it practically.
Although it is a ratio of average prices, it may also be
thrown into the form of a weighted arithmetical average of
the jmce ratios, 'Si, Hi 2^, etc., as the following transfor-
Po Po V
mation shows:
1 See Walsh, Measurement of General Exchange Value, New York
<MaomiUaii), 1901, pp. 534, 553.
Bradstreet's Journal from 1895.
394 THE PURCHASING POWER OF MONET [Append. X
Po + p'o + p"o+
The formula in this last form is evidently the weighted arith-
metical average of the ratios in parenthesis, the weights be-
ing the prices po, p'o, p"o, - of the year 0. A change in
the units of quantity for the various goods would change
these prices; thus a change from ounces to pounds would
multiply the number expressing price by sixteen. Such a
change in any price, such as po, would entirely change the
relative importance of the "weights," po, p'o, etc. Conse-
quently this system of weighting is, as Walsh says, quite
accidental or haphazard.^
The same formula is also a harmonic average, as the follow-
ing transformations show:
5pi pi+ p'i+
Spo po + p'o-l-
_ Pi + p'i +
-+<:) +:
^+^-#j +
pi + p'l
The last expression is evidently the reciprocal of a weighted
arithmetical average of the price ratios in parenthesis. But
year 1.
unity, for dividing the price, po, in the original units by the
factor Po, we obtain unity.
Hereafter, however, we shall treat all index numbers as
averages of price ratios.
It is interesting to note that the antithesis of Dutot's or
Bradstreet's formula (No. 2), found by dividiag the frac-
tion i^^ by the correlative formula for Qi, viz., -^, turns
396 THE PURCHASING POWER OP MONEY [Append. X
out to be that advocated by Drobisch,^ and earlier by Sir
Rawson-Rawson.''
Formula (3)' is evidently the familiar simple arithmetical
average,
IW or PlVo:*Z_Po^
n
barkeit derselben auf die Berechnung des Steigens und Sinkens des
Geldwerthes " (Berichte uber die Verhandlungen der Koniglich sacks-
ischen Gesellschaft der Wissenschaften zu Leipsig; Mathematisch-
physische Classe, Band XXIII, 1871, pp. 25-48). Also " Ueber die
Berechnung der Veranderungen der Waarenpreise und des Geld-
werthes" (Jahrhucher fur National-oehonomie und Statistih, 1871,
Band XVI, pp. 143-156) ; and " Ueber einige Einwiirfe gegen die in
diesen Jahrbliehern veroffentliohte neue Methode, die Verander-
ungen der Waarenpreise und des Geldwerthes zu bereehnen"
{ibid., 1871, Band XVI, pp. 416-427). See also Walsh, op. cU.,
pp. 97-99, where the method is explained.
* See Edgeworth, Report of the British Association for the Ad-
^>
Po p
, ) ^i
p
etc., but the weights are different in the two
cases.
(11) has the interesting property that its antithesis (12) is
of the same form except that the subscripts for Q are now
in place of 1. Similar reasoning shows that this formula (12)
is also both an arithmetical and an harmonic average, weighted
Report on Wholesale
' Prices, Senate Report 1394, 2d Session,
52d Congress, 1893.
400 THE PURCHASING POWER OP MONEY [Append. X
It will be seen that all of the 44 formulae selected for the
table are based on a few simple principles of averaging.
Most are arithmetic, harmonic, or geometric averages or
their combinations.Needless to say, numerous other and
more complicated forms might be constructed.
2d
402 THE PtJECHASING POWEK OF MONEY [Append. X
ismeasured by the ton, it should remain twice, when coal is
that the corresponding relation is also true for the T's, viz.
that
Ti,o .
(2)
(3)
(4)
p
Divide (1) by (2) and (3) by (4). The quotients are
ri,o-/^SpiQiYP2,o\
^2,0 K^MKPuJ'
cance of tests 2, 4, 6.
Test 2 tells us that if all the trade ratios agree, their index
should agree with them; that is,
if
0.1 = 0^ = 011= ...=fc,
Q, Q'2 0".
[obtained by substituting kQi for Qi, kQ'2 for Qi, etc., and kTi
The last form is derived from the next to the last by multi-
plying both numerator and denominator by k and then sub-
stituting Qi for kQi, Q'l for kQ'2, etc.
SpoQi
Therefore test 1 is fulfilled for the particular case when
one of the years is the base year.
But, as we have noted, it does not follow that the test is
fulfilled in general. For "the general case" of any two
years the test may be thus stated: If the price of each good
for the year 1 is fc times the price of the same good for the
year 2, then the index number for the year 1 (in terms of
the year 0) should also be k times the index number for the
year 2 (in terms of the year 0). That this may be true, '
ei = 2j = ^= ... =]e^
Pi p'i p"i
i.e. if pi = hpi, p'l = kp'i, p"\ kp"i etc.,
p
then must ^=
Pi
^
side, -2?^ J
of the supposed equality would be unaffected, but
'^"'''
t-f.-Pr
-"
then should
T
7ir~^- '
Evidently & = ?# =
which was to have been proved. Therefore test 2 is com-
^ = *'
If, in the formula for Pi, namely J^^^ some but not
,
all
SpoWi
of the prices, as pi, or one of the quantities, as Qi, should
become zero, it is clear that the above expression would still
be determinate, and He between zero and infinity. It will
merely happen that some of the numerous terms in the
niunerator will vanish, but all the other terms will remain.
P
Since the same reasoning applies to Pa, it follows that -^
analogous to the third, and states that the trade index num-
ber must not be rendered indeterminate, zero, or infinity
simply because some price or prices should become zero.
The formula for Ti is always -^^- Since, as neither the
Pi
numerator nor the denominator of this fraction becomes
zero, infinity, or indeterminate by the vanishing' of some but
not all of the p's or Q's, the quotient must Ukewise be non-
zero, finite, and determinate. Thus, test 4 is completely
fulfilled.'
2i2i =
then ;fc.l
P<H\
SpiQi-piOi _j,^. _
SpoQi PoQi
that is,
-o /r\/^
~ ^' wbich was to have been proved.
Sgi '1
That is, if
P^ = k,
SpoQz
and if also ^ = k,
Pi
^V\Q'1
then -a /"n/^ will ^ot in general be equal to k.
Sp'oQ'i2
p'oQ'2 Sp'oQ'2"
Sec. 6] APPENDIX TO CHAPTER X 415
it follows that
P0Q2
SpoQz
That IS,
VoQT '
should be equal to ^^
SpoQo
That this is not necessarily true is evident, since there is
no necessary relation between the Qo's and the Qi's. If the
equation should accidentally hold true for a particular set of
Qo's and Qi's, the change, even in the smallest degree, of a
single letter, say Qo or Qi, would evidently disturb the rela-
tion. Therefore the test not fulfilled even for the par-
is
Pi _ SpoQi
SpoQa
numbers
p
-^ will be unaffected. Hence the test is completely
fulfilled.'
Pi = ,
2'po
fails to conform.
pi_2pi
po 2po
Consequently, the index number is dependent upon the un!t~of
measurement. Such an index nimiber is entirely arbitrary, and by
sufflcient manipulation of the units of measurement could be made
to favor any particular commodity. The larger the unit of any
particular commodity employed, the higher the price for it which
enters into the formiila, and the more that commodity tends to
affect the result.
Bradstreet uses 96 commodities in common use, aU of which are
measured by the pound. The result is that silver, for instance,
dominates over iron, entering at several doUars a pound instead of
a few cents. If radium, which recently cost $8,000,000 an ounce, were
included, it would absolutely dominate the group, and we would
reach the absurd result that since radium has fallen to hundreds of
thousands instead of millions of doUars an ounce, the general price
level must have fallen several fold in spite of the general impression
of rising prices ! An index number of this kind is fitly called by
Walsh one of accidental or haphazard weighting.
2x1
418 THE PURCHASING POWER OF MONEY [Append. X
= PiT (2)
<^)^ (3)
Qi's.
As noted, these are the basic theorems for which the equa-
tion of exchange stands. "We would naturally like to remove
the restriction as to the Qi's changing uniformly. We should
consider an index number perfect (so far as needed in the
equation of exchange) if we could assert of it the same
theorem of proportion as above, without the restriction as to
the Qi's changing uniformly, so that we might substitute an
average change in the Q's in place of a uniform change. No
such index is found in the table, and no such index seems
possible. Practically this conclusion does not greatly mat-
ter, for we are interested in prices far more than in quantities,
the latter being chiefly important as supplying weights for
the price indexes. As we have already noted, Edgeworth
has shown that considerable variation in weighting is of
comparatively little practical importance.
The chief use of index numbers is to compare successive
years, not years remotely distant from each other. We are
Sec. 7] APPENDIX TO CHAPTEK X 423
' That this test is the most difficult one to meet is shown by the
fact that the total " score '' as given in the last column opposite test
7 is the lowest in that column, being only 12 out of a possible 44;
the next most difficult test to meet is test 5 (or 6) opposite which
,
*
" Modes of constructing Index Numbers," Quarterly Journal oj
Economics, August, 1907, pp. 613-631.
424 THE PUBCHASING POWER OP MONET [Append. X
culty of non-unifonn changes in the Q's, for any inequahties
for successive years are relatively small.
Such successive index numbers, each on the basis of 100
per cent for the previous year, will, if multipUed together,
give a chain of index numbers showing the fluctuations from
year to year, like any ordinary series, but much more suitable
for comparison of neighboring years.
Let us now reexamine the comparative merits of index
niunbers on the supposition that they are to be used only for
successive years, that is, for comparison between each year
pp. 99-101.
Edgeworth, Report, etc., 1887, p. 291, and "On the Choice of
9. Summary
The conclusions of this Appendix may be briefly stated as
follows :
1. Any sum
of products of two factors each, such as SpQ,
may be converted into any one of three forms (1) PT, in :
average of the ratios of the Q's to some base Qo's, and A is the
' Gold, Prices, and Wages under the Greenback Standard, Publica-
tions of the University of California. Mitchell's use of deciles,
however, is of small value, as he employs a common base, 1860, so
that his figures for each subsequent year give the dispersion of that
year relatively to 1860. There is practically no use in knowing the
dispersion of prices in 1909 or 1910 as compared with 1860, and this
knowledge throws no light on whether prices change uniformly or
disperse widely from 1909 to 1910. What is needed is a knowledge
of price dispersion from year to year, and this can readily be in-
dicated by drawing three radiating lines from 1909 to 1910, the
central one to show the movement of the median, and the other two
to show the movements of the two neighboring quartiles.
Sec. 9] APPENDIX TO CHAPTER X 429
Method of Calculating M
The estimates for M, or money in circulation in the United
States, are based on the reports of Comptroller of the Cur-
rency. The calculations are shown in the following table :
Monet in the United States, etc. (in Billions op Dollars)
(1)
Sec. 2] APPENDIX TO CHAPTER XII 433
Column (2) gives the money in the United States in the middle
of each calendar year according to the official estimates of the
director of the mint. In 1907 these official estimates were
corrected by subtracting an estimated error of $135,000,000
from the gold beheved to be in the United States, this cor-
rection being made in view of the investigations of Maurice
L. Muhleman. The mint corrections were made, however,
only for the ends of calendar years.* In order to make the
corrections apply to the middle of a given calendar year, the
corrected figures for gold in the United States at the begin-
ning and end of it were averaged. The average thus obtained
was assumed to be the corrected figure for gold at the middle
of the year. This corrected figure was then compared with the
official figure for gold for the middle of the year and the differ-
ence assumed to be the correction for that date. This correc-
tion was then deducted from the figures for money in the
United States given in colimm (2) above. We thus obtain the
figures in colxman (3). Mr. Muhleman has made independent
corrections for the middles of the years 1896-1900 inclusive.
These are slightly smaller than those calculated from the mint
figures as given above, the differences being in successive
years, .05, .03, .00, .03, .05. Columns (4) and (5) of our table
give the money in the federal treasury and the money re-
ported in banks as stated in the annual reports of the Comp-
troller of the Currency. Column (6) gives the estimated per-
centage not reported. This estimate is found by assuming
that the unreported reserves bear the same ratio to there-
ported reserves as unreported deposits bear to reported de-
posits, the latter ratios being calculated from the table given
in the next section ( 3) of this Appendix.
This estimated percentage being calculated and the correc-
tion found by it being added to the money in reporting banks,
(column 5), we get the total estimated money in banks,
(coliman 7) Column (8) is then found by subtracting from the
.
the third report of national banks for each year and are taken
from the Comptroller's Reports. The figures for 1896-
1899, on the other hand, are estimates. These estimates are
based on the fact that the deposits of savings banks and trust
companies in national banks are (whenever comparison is
possible, viz. 1900-1908) found to be approximately equal to
the deposits of state banks in national banks. As the state
bank figures are available for 1896-1899, they are taken in
lieu of the missing trust and savings figures. Any error from
this procedure could scarcely affect the final column more
than 1 or 2 per cent.
I
s I ii
SO
a f=2 JL"B
TlAB mU * ft s
I +S I*!
ell's
sas K
IS si
Q Ma
SoSs
ausg WH mEQ
deposits unreported.
The figures for nonreporting banks for 1900 and 1902-1909
436 THE PURCHASING POWER OP MONET [Append. XII
from drawing against it again. Such a person say Smith
regards the $100 as transferred to drawee say Jones his
and no more Smith's than money would be which he had
paid out. But it takes time before the bank on which Smith
draws knows of this transfer of Smith's deposits to Jones.
In the meantime the bank books still include this $100 among
Smith's deposits. The total figure for deposits is not dis-
turbed by the inclusion of the $100 in Smith's account pro-
vided it is not included in Jones's account also. But when
Jones deposits the check in his bank, this (Jones's) bank adds
$100 to Jones's account before Smith's bank can deduct it from
Smith's account. That is, the $100 is temporarily coimted as
both Smith's and Jones's. If both sides of this transfer were
recorded at the same time, there would be no double counting.
But until the check reaches Smith's bank the only record of
the deduction which should be made from Smith's accoimt is
in the "exchanges for clearing house" which, accordingly, we
must deduct in our statistics.
These figures, however, have to be estimated. Only for
April 28, 1909, are they given for all banks, the figures being
those of the special Report of the Monetary Commission al-
ready referred to. Of this amount, four fifths are of national
banks and as national banks report annually their exchanges
;
Report from Banks of the United States, April 28, 1909, p. 261 ; also
Report of Comptroller of the Currency, 1909, p. 835. The figures are
exclusive of Hawaii, Porto Rico, and the Philippines, although the
sum thus excluded is scarcely appreciable.
Sec. 3] APPENDIX TO CHAPTER XII 439
sponding ratio for 1896 as 85 per cent for 1899 as 89 per cent
;
shghtly more complete than what I had already used from the
Comptroller's Report (viz. 4.95), doubtless because, for this
particular inquiry, a larger number of banks were included
than had originally been used in the Comptroller's tables.
Mr. Andrew gives the checkable deposits as 2.59 billions.
This figure is subject to two corrections: one to account for
unreporting banks, and one to account for exchanges for clear-
ing house. We have estimated the deposits of nonreporting
banks at .40 ; and, since Mr. Andrew has discovered in such
banks .02 more total deposits (4.97) than the Comptroller
reported, we must assume that there are .02 less unreported
deposits in his figures than in the Comptroller's. This would
make the estimated unreported deposits for Andrew's figures
.38 instead of .40 which we assumed for the Comptroller's.
The part of this ascribable to the deposits subject to check
For 1899, Andrew's figures for total net deposits are 4.38 and
for checkable deposits 4.09. His figures for total deposits
(7.07) are .30 completer than those of the Comptroller em-
ployed in the first colmnn of the above table, and thus reduce
the estimate for nonreporting banks appHcable to Andrew's
X .61
were larger still,i because it was then that occurred the bulk of
the heavy July 1 deposits of checks. If the $228,000,000 clear-
ings on July 1, 1896, were representative for each day of
1896, we could, simply by multiplying by the mmiber of
settling days of 1896, 305 days, find the total clearings of the
coimtry. But the result of this multiplication is 67.1 bil-
lions, whereas the actual clearings of the country for 1896
were only 51.2 biUions. This is conclusive evidence that the
clearinigs on July 1, and presumably still more those of July 2,
exceeded the daily average and need to be reduced at least ip
cially as .60 and .76 are so very safe or extreme limits. Fig-^
give the daily average for the entire country, on the assump-
tion that only New York City was abnormal on the day se-
lected. The compared with the actual deposits
result (1092),
on the day selected (1025), shows the correction factor
on the
assumption that only New York was abnormal. This factor
is 1.07. This furnishes a lower hmit for the correction factor
we are seeking.
check transactions and clearings, viz. .90 for New York and
4.4 for "outside," would indicate that the pubKshed figures
for clearings should be weighted in the ratio of 4.4 to .9 or
about 5 to 1. That is, on the basis of 1909 figures, five times
the outside clearings plus once the New York clearings should
be a good barometer of check transactions.
Of 1896, unfortunately, we lack the figures for New York
City deposits. We have, however, figures for the deposits
in New York state in both 1896 and 1909 and a study of
;
it in banks (Cj). These three types are not the only ones, but
they are so much more important than any others that they
merit our imdivided attention before a completer study is
undertaken. Figure 18 has been constructed for the purpose
of exhibiting them uncomplicated by other details.
It will be noted that not all of the flows described are ex-
amples of the circulation of money. As already indicated,
money may be said to circulate only when it passes in ex-
change for goods. Its entrance into and exit from banks is a
flow, but not a circulation against goods. In the diagram
the horizontal arrows represent such mere banking operations,
not true circulation. On the other hand, the arrows along the
sides of the triangle represent actual circulation. The dia-
gram shows four such arrows, representing the four chief
types of circulation: Oe payments of money from "Other
454 THE PURCHASING POWER OP MONEY [Append. XII
F= Oc + Co + Nc + C + 0 + No + c + o + n. (1)
Qi
a
Fio. 19.
which is, therefore, the algebraic expression for the first ap-
proximation.
To obtain the difference, F F', between the exact and the
approximate formula, we subtract (2) from (1), canceling Nc
and No and placing the negative terms first. We thus obtain
for a remainder (r) the following :
r=F-F'= -Ct-0i-N,+0c+ Co+C+0+c+o+n. (3)
That the value oi F F' is small may be seen clearly by
transforming (3) We shall transform it by means of another
.
tents of any reservoir must equal the net decrease in its con-
tents during the same time, or (algebraically expressed) that
the net outflow (positive or negative) plus the net increase
in contents (negative or positive) must be zero. We may
apply this principle to any reservoir or store of money, but
shall here find it most helpful to apply it to the reservoir of
money contained among the "Commercial depositors" and
" Nondepositors" taken together as one group. Let us desig-
nate the combination of these two as the "CN group." The
total outflow indicated in the diagram from this "CN group"
is evidently C^ + Co + Nt + No, and the total inflow Be +
Oc + B + On. Hence, the net outflow, so far as the diagram
shows us, is :
C, + Co + N, + No - Bo-Oo-B- 0.
This, plus the net outflow not shown in the diagram, is the
true net outflow. Since the diagram was constructed to show
only flows against goods (monetary circulation), and flows to
or from banks, we have still to take account of money flow-
ing in the community in exchange for something else than
goods, and that flowing without any exchange at all, as well
as any net outflow outside of the commimity.
We
have thus to take account of three imdiagramed flows.
458 THE PURCHASING POWER OF MONEY [Append. XII
C, + C + Nt + No-Bc-Oc-Bn-0 + a + g + e.
We now place this new equation (4) under the old equation (3),
giving the value of r = F F' in the following manner :
+ e) + i-Bn (1)'
per cent, or 1.9 per cent higher. The excess would have been
still greaterboth the figures were for receipts instead of one
if
viz. .68 in 1896 and 1.17 in 1909, with the results given in
column
the following table:
(1) of
466 THE PTJECHASING POWER OF MONEY [Append. XII
Increase Estimate
1890 1900 Per 1909
Cent
Agricultural pursuits . 8,565,926 10,381,765 21.2 12,362,605
Domestic and personal
service .... 4,220,812 5,580,657 32.2 7,377,628
Total 19,740,233
Trade and transporta-
tion 1,977,491 2,617,479 35.2 4,275,913
ManufactuTu^ and
mechanism . . . 4,251,613 5,208,406 6,935,113
Total 11,211,026
which are not known with exactness, but all of which are
known to be small. The term "small" is always relative,
and in this case a term is small for 1896 which is small com-
pared to 16 billions. For instance, 160 millions is a mere
trifle, being only 1 per cent of 16 billions, while 16 millions is
wages. From
this and other clews, we may safely set half a
billion as an upper limit for the fourth term in 1896. Pro-
fessor Kinley places .8 billion as the upper limit in 1909.
The fifth term (c + o + n) is the circulation within each
of the three groups. Obviously only in trifling cases does
money between one "Commercial depositor" and
circulate
another, between two "Other depositors," or between two
"Nondepositors." Half a billion is put as an extreme upper
limit for the total for 1896 and .8 by Professor Kinley for 1909.
This would mean that about one dollar out of every thirty-five
expended is passed on to other persons who are within the class
to which the expender belongs. In fact, the universal testi-
mony of such few representatives of c, o, and w as I have been
able to interrogate personally is that the true ratio is less than
this.
per cent. A
still simpler makeshift is to add the deposits
be but half the truth, the measurable part would still con-
stitute the great bulk of the total. The measurable part
would therefore still be a safe practical index, or barometer
of changes in the volume of circulation. Any excess of varia-
tion in the conjectural part, as copapared with the measurable
part, would, when spread over the whole, produce a disturb-
ance only one fourth as great. It is reasonable to suppose
that the conjectural and measurable parts will ordinarily vary
together. If the measurable part varies 10 per cent, it is natu-
ral to suppose that the conjectural part, and therefore also the
total of both, will vary likewise. But suppose this assump-
tion erroneous and that, while the measurable part varies 10
per cent, the conjectural part really varies 14 per cent or 6 per
cent. The difference between these and 10 per cent, i.e. A
per cent, representing a supposed excess or deficiency of vari-
ation of the conjectural part, would produce a difference of
only 1 That is, the total, instead of
per cent in the total !
OC050t~l>.HOC0(Nt>03rH00ai
(N(NC<l(N(MCOC0CQC<3COeO'*MCO
^1^1 Si THCOiHCOOi-HWOCDt^TlHOOOUJ
Q005000(N'-lirO(N-*>OCO-*in
,S-'3 a cooococooiioinotoi-iio-*'*
my. a S i>i>ooaiaiOi-H(N(MTt<ioioic
00 s^><
ds-s
fc .SB I CO CO i> o 00 OS o o rH (N CO * in
o
a l^OStHOOWOOOSOt^TfrHINN
tI>050SOO'-lC0(N-^t0t^i0
O *3
o
8 +
<iss COOai(NiH(3>0>Ol005C3(Min(M
OOOOi-HrHC^KNCON-^lOCOTtHlO
S S+
K- oo
o
mteocooocoo5'-it-cO'*owm
IOt-'-Ht~C<5CD00tO00CO00O5O3rH
t3
3l >H.-l>-l?gi-li-I.HC(l(NrHi-ie<l
b00<-HtNTHrtO>^l>05
S.1S. t^00050000000i-l>-lT-l(M
osM'-ii-Hi-iiftOJOsioosNt'ogco
00O'-l'-Hi-HC<Ji-IC0<N^>C0Tt<lO
cowxcJOi-HNeciiiocot^oooi
OiOiOSOiOOOOOOOOOO
00000000O>O5O5O5O5O5O!O5O5Oi
480 THE PURCHASING POWER OF MONET [Append. XII
ASTICLES
482 THE PURCHASING POWER OF MONEY [Append. XII
Abtioles
Sec. 9] APPENDIX TO CHAPTER XII 483
and cotton, 5 each and for pig iron and wool, 1 each.
;
The data for 1896-1899 are far inferior to those for 1900-
1909 taken from the Monthly Summary, and this for three
reasons (1) because they are so few in number
: (2) be- ;
cause except the grains are for flscal years and the hypo-
all
indices.
The combined by weighting the internal
direct indices are
commerce, twenty, the exports and imports, three, and sales
of stocks, one. These weights are, of course, merely matters
of opinion, but, as is well known, wide differences in systems
of
Method of Calculating P
The numbers of prices is taken
table in the text for index
from the last column on page 103.
of the table
Column (2) gives the index numbers of the United States
Labor Bureau (No. 81, March, 1909, p. 204).
I am under obfigations to the Commissioner of Labor, Mr.
Neill, for his courtesy in supplying me with the figure for 1909
in advance of publication.
Column (3) is taken from the Bulletin of the Bureau oj
Labor, July, 1908, p. 7.
May, 1910. These figures are doubtless the best yet avail-
able in this difficult subject.
(0
Ybab
488 THE PURCHASING POWER OF MONEY [Append. XII
coo
1696 1807 1858 1899 1900 1901 1902 1503 1904 19W 1904 1907 IADS 1909
Fig. 20,
490 THE PURCHASING POWER OF MONEY [Append. XII
per cent, and consequently the "safe maximum" for cash as 20 per
cent, we shall obtain in the above table 14 per cent, instead of the
figure 16i, which would make the last two columns agree absolutely.
INDEX
Barter, the exchange of goods against
goods, 13.
Aldrich Report on Wholesale Prices, Base, selection of a, in constructing
cited, 259, 260, 399. index numbers, 203.
Aldrich-Vreeland bill of 1908, 146 n. Benefits of wealth, meaning of, 6
American colonies, paper money in future benefits are those referred
the, 256-258. to, 6.
Arrays, use of, in calculating BiUs of exchange, comparative ad-
quantities, prices, and averages, justability of prices of, 186.
355-362, 367-368. Bimetallism, mechanical operation
Arts, influence on quantity of money of, 115 ff. ; two requisites of com-
of consumption of gold in the, 103. plete free
: and unlimited coinage
Assets of bank, must be adequate to of both metals at a fixed ratio,
meet liabilities, 38-39 form must
; and the unlimited legal tender of
be such as to meet liabilities each metal at that ratio, 117
promptly, 42-47. illustrations of workings of, by
Assignats, experience of French Rev- the case of France and the Latin
olutionists with, 252-253. Monetary Union, 132-135; the
Atkinson, F. J., on "Silver Prices in claim that prices would be
India," 243. steadied by, 324^325; shown to
Aupetit, Albert, cited, 157, 234, 237, be an indifferent remedy for vari-
240. ations in price level, 325-326;
Australia, rise of prices due to gold possibility of the system breaking
discoveries in (1851-1852), 241- down, 326 possible disruption of
;
before, during, and after crises, Brown, Harry G., cited, 37 n., 65,
velocity of circulation of, to have money side and the goods side,
increased 50 per cent in fourteen 16-17 the magnitude called ;
496 INDEX
currency on, 33 ff. application ; by, 25 n.2, 115, 174, 190, 210, 211,
of, to bank deposits or circulating 244, 384.
credit, 48-49 disturbance of,
; Fleetwood, Bishop William, work by,
during periods of transition, 55 cited, 208 n.
ff. implies no causal sequence,
; Flow or stream of goods, distinction
149-150; statistical verification between stock or fund of goods
of, 276-318; construction of and, 7 three classes of economic
;
Fairohild, F. R., article by, cited, 193. in prices predicted, due to in-
Falkner, Roland P., index numbers crease in production of, 248-249
of, 229. increasing output of, 249 statis- ;
Gold mining, chief cause of increase cations, 205-206 use of, to serve ;
money will drive out dear money, periences of various countries with,
112 ff. comparison of stocks of,
; 252 ff. John Law's scheme, 252 ;
statement of check and cash trans- Pareto, work by, cited, 70.
actions, 317-318, 491-492; sub- Pars, readjustment of gold, under
stitutes for, unlike other sub- author's proposed plan for reg-
stitutes, 376-377. See also Quan- ulating price level, 341-342,
tity of money. 344r-345.
Money changing, the exchange of Pearson, Karl, the "correlation co-
money against money, 13. efficient" of, 294.
Money famines, causes of, 67-69. Persons, Professor, cited, 278-279,
Morawetz, Victor, cited, 45. 294.
Mortgage notes, prices of, among Person-turnover concept of velocity,
least adjustable, 186-187. 353, 362-363.
Muhleman, Maurice L., calculations Peru, adoption of gold standard by
of, 245, 433-434. (1897), 243.
500 INDEX
328^329 by inconvertible paper
; conditions of production and
money, 329 by a varying seign-
; consumption, individual habits,
iorage charge, 330-331 by ; foreign trade, melting and mining,
convertible paper currency, re- etc., 74 ff. influence of monetary
;
194 ; effect on, of changes in rate ing through the production and
of interest, 193 ; impossibility of consumption of money metals,
a uniform change in, 194-195; 99-104; influence of monetary
changes in quantities of commodi- systems, 112 ff. doubling of, ;
to its own increase, 151-159 the 193 small part taken by, in total
; ;
beings, 1-2 ; possibility of measur- Wicksell, Knut, article by, cited, 59,
ing, in physical units, 2-3 ; trans- 60.
fer, exchange, price and value of, Workmen, relative adjustability of
defined, 3-4 ownership of, or
; price of services of, 186-187.
property, 4; meaning of "bene-
fits of wealth," 6.
Weighted averages, 199-203, 349-
352. Yale University, statistics of rapidity
Wells, David
A., referred to, 176. of individual turnover at, 167,
White, Andrew D., Paper Money 379-382.
Inflation in France by, cited, Z
252.
White, Horace, Money and Banking Zizek, Franz, work by, cited, 349.
by, cited, 47. Zuckerkandl, cited, 14 n.
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