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 III, § 2)
“Arrays” of k’s and r’s
APPENDIX TO CHAPTER III
Let
k be the ratio of deposits to money in circulation
M‘/
M which, on the average, the public prefers to keep;
k will then be derivable from the like ratios for the different persons and business firms in the community in the successive moments of the year, and we may, therefore, form an array on the analogy of previous arrays, of the form:—
PERSONS | PERIODS
|
AVERAGE | |
---|---|---|---|
1 | 2 | ||
1 | 1k1 | 2k1 | k1 |
2 | 1k2 | 2k2 | k2 |
— | — | — | — |
— | — | — | — |
Average | 1k | 2k | k |
Each letter outside the array is a weighted arithmetical average either of the row to its left or of the column above it.
k (in the lower right corner) also is both of these as well as the weighted arithmetical average of all the elements inside the lines (the weights being in all cases the amounts of money in circulation, which are the denominators of the ratios represented in the arrays). The same proportions hold true if “harmonic” be substituted for “arithmetic” (provided the weights be changed from the denominators to the numerators
of the ratios, viz. the deposits). These theorems can be easily proved analogously to those in § 7 of the Appendix to Chapter II, remembering that
k =
M‘/
M.
Similarly, we may let
r stand for the average ratio, for the year, of the reserves of all banks (
m) to their deposits (
M‘). This ratio (
r, or
m/
M‘) is resolvable into an array expressing the ratios for different banks at different moments, viz.:—
PERSONS | PERIODS
|
AVERAGE | |
---|---|---|---|
1 | 2 | ||
1 | 1r1 | 2r1 | r1 |
2 | 1r2 | 2r2 | r2 |
— | — | — | — |
— | — | — | — |
Average | 1r | 2r | r |
Here each element outside the lines is a weighted arithmetic (or harmonic) average of the terms in the row to its left or the column above it, while
r is both of these as well as a weighted arithmetic (or harmonic) average of all the terms inside, the weights being (for the arithmetic average) the deposits in each case or (for the harmonic average) the money in each case. The total currency of the community is
m +
M +
M‘, although only
M +
M‘ is actually in circulation.
§ 2 (TO CHAPTER III, § 4)
Algebraic Demonstration of Equation of Exchange Including Deposit Currency
The money expended for goods by individual 1 at moment 1 is
1e1 and his check expenditure is
1e‘
1. His total expenditure for goods by money and checks is, therefore,
1e1 +
1e‘
1 =
1p11q1 +
1p‘
11q‘
1 +….
By adding together all such equations for all persons in the community and all moments of the year, we obtain the equation
E‘ =
SpQ
which becomes
M‘
V‘ =
SpQ