The Purchasing Power of Money
By Irving Fisher
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 purchasing power of money–or its reciprocal, the level of prices–depends exclusively on five definite factors: (1) the volume of money in circulation; (2) its velocity of circulation; (3) the volume of bank deposits subject to check; (4) its velocity; and (5) the volume of trade. Each of these five magnitudes is extremely definite, and their relation to the purchasing power of money is definitely expressed by an “equation of exchange.” In my opinion, the branch of economics which treats of these five regulators of purchasing power ought to be recognized and ultimately will be recognized as an exact science, capable of precise formulation, demonstration, and statistical verification…. [From the Preface to the First Edition]
First Pub. Date
1911
Publisher
New York: The Macmillan Co.
Pub. Date
1922
Comments
Assisted by Harry G. Brown (Instructor in Political Economy in Yale U.) 2nd edition. Harry G. Brown, assistant.
Copyright
The text of this edition is in the public domain.
- Preface to the First Edition
- Preface to the Second Edition
- Suggestions to Readers
- Addendum
- Chapter 1
- Chapter 2
- Chapter 3
- Chapter 4
- Chapter 5
- Chapter 6
- Chapter 7
- Chapter 8
- Chapter 9
- Chapter 10
- Chapter 11
- Chapter 12
- Chapter 13
- Appendix to Chapter II
- Appendix to Chapter III
- Appendix to Chapter V
- Appendix to Chapter VI
- Appendix to Chapter VII
- Appendix to Chapter VIII
- Appendix to Chapter X
- Appendix to Chapter XII
§ 1 (TO CHAPTER VI, § 1)
Modification of Equation of Exchange required by International Trade
APPENDIX TO CHAPTER VI
We have already seen that there are two equations of exchange, one for purchases, and the other for sales. In a closed community, these two are necessarily identical, for every purchase by one member of the community is a sale by another member. But in a community with international trade they will be slightly different. The equation of exchange as developed in this book relates to the
expenditure of money for the purchase of goods, and not to the
receipt of money for the sale of goods. This equation of exchange at its last stage of elaboration was
M‘
V‘ +
E” –
E”’ =
SpQ
where the letters have the meanings previously given to them,
E” relating to the debts contracted in the given period in book accounts and promissory notes used in purchase of goods, and
E”’ relating to the extinguishment of such debts during the same period. Since
MV was developed from
E, and
M‘
V‘ from
E‘, this equation may be written as follows:—
E‘ +
E” –
E”’ =
Sp
bQ
b
where the letters
E on the money side of the equations are used to indicate that the money is
expended money and the subscripts
b on the goods side are used to indicate that the goods are goods
bought; likewise, if the letter
R is used to indicate
received money, and the subscript
s to indicate that the
goods are goods
sold, the following equation expresses the receipt of money, etc., in exchange for the sale of goods:—
R‘ +
R” –
R”’ =
Sp
sQ
s.
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 equation may be resolved into an equation in which are distinguished the home trade and the outside trade. Thus, for the first equation, relating to expenditures, the
E,E‘, etc., may be replaced by
H +
O,H‘ +
O‘, etc., where the
H‘s relate to the purchases at
home and the
O‘s to money spent
outward. On the other side of the equation the
Sp
bQ
b may be replaced by
Sp
hQ
h +
Sp
iQ
i 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”’) + (
O +
O‘ +
O” –
O”’) =
Sp
hQ
h +
Sp
iQ
i
which, for brevity, we may write
SH +
SO =
Sp
hQ
h +
Sp
iQ
i. Similarly, the second equation, relating to sales, may be written:—
SI =
Sp
hQ
h +
Sp
oQ
o.
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 last two equations, one relating to purchases and the other to sales, may be added together so as to give in a common 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 world. The combined equation will be:—
SH +
SO +
SI = 2
Sp
hQ
h +
Sp
iQ
i +
Sp
oQ
o.
Here the internal trade is counted twice, because every transaction occurs both as a sale and as a purchase. This expresses
the equation of exchange for the total trade (domestic and foreign) in which the country under consideration engages. If, instead of adding, we subtract one equation from the other, we obtain the following:—
SI =
Sp
iQ
i –
Sp
oQ
o.
which is the equation of the
balance of trade in its most general form, taking account, as it does, of credit as well as of money. The flow of money, as to or from a nation, depends upon this last equation.
The right-hand side of the penultimate equation, depends on three sets of prices,—the home prices (the
p
h‘s), the prices of goods which come into the country (the
p
i‘s), and the prices of goods which go out (the
p
o‘s).
If, for instance, the
p
h‘s are extremely high, the consequence will be a stimulus to goods coming in (
Q
i) and a discouragement to goods going out (
Q
o), thus tending to make the right side of the last equation large and, therefore, also increasing the left side. In other words, there will be a so-called unfavorable balance of trade and a tendency for media of payments to go out rather than to come in; that is, there will be an outflow of money (indicated by
O), or a transfer of bank credit to foreigners (
O‘), or a charging on the books of the foreigners (
O”), or a lessening of the liquidations of previous book accounts (
O”’); or else there will be opposite changes in
I,I‘,
I”,
I”’; or finally, a combination of both tendencies, while temporarily there will be fluctuations between these various magnitudes. In the long run and in the last analysis, the changes will relate largely to the actual export and import of money, that is, will concern the unprimed magnitudes
O and
I.
For a large country like the United States, the outside trade is so small, compared with the internal trade, as to be negligible. As we shall see in Chapter XII, the foreign trade of the United States is only a fraction of one per cent of the internal trade. And, because the export and import sides of the various magnitudes (
O‘s,
I‘s,
Q
o‘s and
Q
i‘s)
nearly cancel each other, the net balance remaining on either side of the equation of exchange seldom amounts to more than one eighth of one per cent of the internal trade of the United States.
Almost equally insignificant is the difference,
E” –
E”’, between debts annually contracted and liquidated, if we may judge from estimates of that indebtedness, such as Holmes’s. We are at any rate safe in saying that the corrections to our equation of exchange which have been discussed in this and the previous section are needless complications so far as the United States s concerned. We may therefore consider the equation
MV +
M‘
V‘ =
SpQ as practically a precise form of the equation.