Full text of Review (Federal Reserve Bank of St. Louis) : November 1976

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FEDERAL RESERVE BANK
OF ST. L O U IS
NOVEMBER 1976


Vol. 5 8 , No.


11

Derivation of the Monetary Base
ANATOL B. BALBACH AND ALBERT E. BURGER

. A l LTHOUGH the monetary base has been a key
concept in monetary analysis for two decades, its use
has been primarily restricted to the monetary systems
of industrial nations.1 Specifically, the base as con­
structed and measured in the United States has
tended to be applied with some modifications to other
economies. This article is an attempt to establish a
general definition of a monetary base applicable to
all relevant institutional structures and to provide
guidelines for the identification and measurement of
the base.
Given a set of institutional arrangements and pre­
dictable behavior on the part of market participants,
changes in the monetary base produce predictable
changes in the money stock. Under these conditions
the base can be used as a predictor of the money
stock and as a variable whose control implies the
control of changes in the quantity of money. Thus the
practical use of the base encompasses only those in­
stitutional structures where the money stock cannot
be predicted and controlled directly by monetary
authorities, but where the base can be measured and
affected.
Where it is the case that every unit of the money
stock can be directly created or destroyed by mone­
tary authorities, or that economic forces or policy
actions affect the base and the money stock by exactly
VFor further discussion of the concepts of monetary base and
high-powered money, see Karl Brunner and Allan H. Meltzer,
“An Alternative Approach to the Monetary Mechanism,” U. S.,
Congress, House of Representatives, Committee on Banking
and Currency, Subcommittee on Domestic Finance, 88th
Cong., 2nd sess., 17 August 1964, pp. 9-20; Milton Friedman
and Anna Jacobson Schwartz, A Monetary History o f the
United States 1867-1960 (Princeton: Princeton University
Press, 1963); Phillip Cagan, Determinants and E ffects o f
Changes in the Stock o f M oney 1875-1960 (New York: Na­
tional Bureau of Economic Research, 1965). Also see Leonall
C. Andersen and Jerry L. Jordan, “The Monetary Base — Ex­
planation and Analytical Use,” this Review (August 1968),
pp. 7-11.

Page 2


the same magnitudes, there is no reason to resort to
the use of the base concept. Alternatively, if the con­
straint on money creation consists solely of a single
money-creator’s decisions as to how much money to
create in order to have it acceptable as money to all
users, the base, while it exists in principle, is not
objectively measurable and cannot be used either as
a predictor or as a control variable. This leaves the
monetary base as a useful concept in monetary sys­
tems which are characterized by the existence of fiat
money, more than one money-creating institution, and
fractional reserve banking.

THE CONCEPT
In a system which exhibits these features, the money
stock in the hands of the public will potentially con­
sist of commodity money (such as gold and silver
coins), liabilities of monetary authorities (currency)
and liabilities of private institutions ( bank notes and/
or bank deposits). These assets of the nonbanking
public will be used as money only if transactions costs
associated with other assets are higher. In other words,
since the productivity of any asset used as money
lies in its ability to facilitate transactions, it must be
an instrument which minimizes the costs of conduct­
ing transactions. Apart from such features as divisibil­
ity, convenience and safety it must also reasonably
maintain its purchasing power vis-a-vis other assets.
Any asset that is convenient in every respect but
whose purchasing power fluctuates widely and unpredictably will impose high risks on its holders and,
in effect, high transaction costs.
The stability of purchasing power, as used here,
refers to its exchange value against the bundle of all
other available assets, goods, and services. One of the
main requisites Of this stability is a relatively stable
supply of this asset called money. If money is ere-

F E D E R A L R E S E R V E B A N K O F ST. L O U IS

ated without restraint or if its production fluctuates
widely, its purchasing power will fluctuate accord­
ingly, and the costs imposed on its holders will en­
courage them to use some other asset to facilitate
transactions. Thus, for any asset to function as money,
its users must be convinced that its supply is con­
strained either by some institution they trust or by
some set of other assets that are deemed to be rela­
tively fixed in quantity or adequately controlled by
market or institutional forces. The monetary base is
this set of assets that constrains the growth of the
money stock.
Commodity money is accepted because of the be­
lief that market forces are such as to assure a rela­
tively stable supply. Government liabilities — cur­
rency — are accepted so long as it is believed that
the monetary authorities will maintain a relatively
stable growth of these liabilities. But what induces
the nonbanking public to accept liabilities of private,
profit-making institutions such as banks? Obviously,
it is because something limits the growth of these
deposits and hence insures that there will remain a
fairly stable rate of exchange of these deposits for
other assets.
In a banking system where there exists more than
one bank and where the money stock is comprised
solely of bank liabilities ( deposits, currency, and coin
issued by the banks), the users of these liabilities
will frequently deposit liabilities of one bank at an­
other bank. If the banks were to use assets which
were each others’ liabilities as a basis for issuing new
money, there would be no effective constraint on the
expansion of money and, consequently, banks could
find that their liabilities cease to be accepted as money.
Knowing this, they will not accept each others’ lia­
bilities without being able to convert them into some
asset which is not dominated by actions of banks
themselves. The asset that will emerge will also have
the lowest transactions costs of all assets acceptable
for interbank transactions. This asset, whatever it is,
will then constitute part of the monetary base.
Each bank, knowing that its liabilities will be pre­
sented to it by other banks for conversion into this
acceptable asset, will have to hold a stock of this
asset as a reserve for conversion. In the absence of
legal constraints, the size of this cushion or reserve,
relative to the amount of monetary liabilities it
creates, will depend upon the probability with which
the bank’s monetary liabilities are deposited at other
banks. Thus, the total amount of this reserve asset
will constrain the amount of money that can be pro­
duced by the system.



NOVEMBER

1976

If the money stock includes commodity money or
currency issued by monetary authorities in addition
to private bank liabilities, then the banks will have
to be ready to convert their monetary liabilities into
forms acceptable not only to other banks but also to
the nonbanking public. Thus they will have to hold
a reserve of those assets that may be demanded by
both. The monetary base will then consist not only
of those assets that banks use to settle monetary lia­
bilities among themselves but also those assets that
are used to satisfy the conversion demands of the
public. This does not preclude the possibility that the
interbank settlement asset is the same as the one that
is used in settling with the public.
To sum up, in a system where the money stock
consists of commodity money, governmental liabili­
ties, and bank liabilities, the base will consist of com­
modity money, governmental monetary liabilities, and
whatever assets the banks use to settle interbank
debts. The assets that constrain the growth of money
stock (the monetary base) can therefore be identified
in any monetary system by ascertaining and summing
the following:
1. those assets which the consolidated banking sec­
tor uses to settle interbank debt;2 and
2. those items, aside from bank liabilities, which are
used as money.

MEASUREMENT AND CONTROL
Once the monetary base is identified and measured,
and the behavior of the banks and the public de­
scribed and estimated, changes in the base can be
used to predict changes in the money stock. What
remains is the task of finding what causes the base
to change and how to control these changes, since
control of the size of the base, given the behavior
of banks and the public, implies the control of the
money stock.
If the base were to consist solely of commodity
money or real assets, then one would have to analyze
the forces which affect the supply of these assets;
attempts at control of these forces would constitute
the exercise of monetary policy. For example, if gold
coin were the sole constituent of the base, then the
control of production and importation of gold coin
would allow for the control of the money stock. Under
-W e look at the assets of the consolidated banking sector in
order to eliminate correspondent balances which are used as
instruments of settlement among respondent banks. These
deposits are acceptable to respondent banks only because they
represent a claim on the reserves of correspondent banks.
Thus, the constraint is still exercised by the availability of
assets which are not dominated by actions of individual banks.
Page 3

F E D E R A L R E S E R V E B A N K O F ST. L O U IS

such circumstances, factors affecting the supply of
gold coin could be identified and measured in the
balance sheets of domestic gold producers and in the
balance of payments.
Suppose that the base consists of currency issued
by the government. If we were to assume that gov­
ernment maintains a complete balance sheet and that
its creation of currency depends upon changes in the
configuration of its assets and liabilities, then the
factors affecting the monetary base would be found
in and could be analyzed from the balance sheet of
the government. It is usually the case, however, that
governments cannot and do not maintain complete
balance sheets. Furthermore, the issuance of currency
may be based on arbitrary or political decisions that
cannot be quantified. Under such circumstances the
base or its currency component has to be taken as
given at any time and the control of the base rests
solely with governmental authorities who, in their
desire to have their liabilities acceptable as money,
will presumably limit currency growth.
When, in addition to the above-mentioned com­
ponents, the banking system uses central bank liabili­
ties as reserves necessaiy for conversion of their own
monetary liabilities, the factors affecting changes in
this component of the base are summarized in the
balance sheet of the central bank. Central banks do
maintain balance sheets and any changes in their
“reserve liabilities” reflect changes in their assets and/
or other liabilities. By definition, a balance sheet
implies that any subset of liabilities must equal the
algebraic sum of all assets and remaining liabilities
and capital in that balance sheet. Thus the central
bank component of the base can be alternatively
measured as the algebraic sum of all entries in the
central bank balance sheet other than its reserve
liabilities. This measure is frequendy referred to as
the “sources of the monetary base.” Since factors sup­
plying the central bank component of the base are
represented in the sources, the analysis, prediction,
and control of the monetary base must begin with the
identification and measurement of its sources.
At present, in virtually all modern monetary sys­
tems the base consists of either central bank liabilities,
government liabilities, or both. These items are the
ones used to settle interbank debt and some circulate
as money. Government liabilities must be taken as
given since decisions as to their supply are determined
by factors which cannot be quantified. In the case of
central bank liabilities, it is necessary to derive the
sources of the base component, which consist of the
algebraic sum of all other assets and liabilities in the

Page 4


NOVEMBER

1976

central bank balance sheet. These sources permit the
identification of causes of changes in the monetary
base and, consequently, of policy actions which con­
trol these changes.

EXAMPLES OF DERIVATION AND
USEFULNESS OF THE SOURCES OF
MONETARY RASE
Case I: Base Consists Solely of
Central Bank Liabilities
Suppose there exists a monetary system where the
money stock consists of the public’s deposits at banks
and currency issued by the central bank and held by
the public. Suppose that we observe further that the
asset of the consolidated banking sector which is used
to settle interbank debts consists of deposits at the
central bank. Conversion of monetary liabilities of
banks to the public is in the form of currency. This
implies that the monetary base consists of banks’ de­
posits at the central bank and currency issued by
the central bank, which is thus the sole producer of
the base. Since all changes in the base result in cor­
responding changes in all other entries of the central
bank balance sheet, the sources of the base can be
identified.
A hypothetical balance sheet of the central bank
is given below.
C e n tra l
A sse ts
G o ld ( G )

Bank
L ia b ilitie s

G o vern m ent Secu rities (B C )

Dem and D eposits of
B anks (D B )
Cu rre n cy held b y B an ks (C B )

Loans a n d Discounts (L D )

Cu rre n cy held b y Pub lic (C P )

O th e r A sse ts ( O A )

Dem and D eposits of
T re a su ry (D T )

Foreign A ssets (F A )

Dem and D eposits of Foreign
C e n tral B an ks (D F )
C u rre n cy held b y T re a su ry (C T )
O th e r L ia b ilitie s &
C a p ita l (O L )

The monetary base is comprised of demand deposits
of banks at the central bank (DB) and currency, is­
sued by the central bank, that is held by banks ( C B )
and by the public ( C P ). Thus the sources of the base,
as derived from the central bank’s balance sheet, are
the algebraic sum of all other balance sheet entries:
G + F A + B C + L D -fO A — OL—DT—D F—CT
Measures of these items are readily available from
central bank accounts and can be used to trace the

F E D E R A L R E S E R V E B A N K O F ST. L O U IS

NOVEMBER

impact of any transaction in the economy on the
monetary base.
The process is simple — one must merely ascertain
whether a transaction affects any of the items in the
sources of the base and sum the effects. Suppose
that the Treasury collects taxes and deposits the pro­
ceeds in its account at the central bank. The trans­
actions involved are:
C e n tral B ank
D B — 1 00

Banks
DB — 1 0 0

D P — 1 00

DT+100

The only entry that appears in the sources statement
of the base and is affected is demand deposits of the
Treasury (DT), which is a negative item and rises
by 100. Thus, the base declines by 100. It is immedi­
ately apparent what has happened with the base and
what has caused the change.
Another example could be a central bank pur­
chase of Government securities from banks ( B B ).
C e n tral Bank
B C + 10 0

DB + 1 00

Again, the only entry affected in the sources state­
ment is Government securities held by the central
bank, an item which affects the base positively. It
has risen by 100; thus the base has increased by 100.
Suppose this country engages in attempts to peg
the exchange rate. A deficit in its international bal­
ance of payments will cause the central bank to enter
the exchange market as a seller of foreign currencies
(its holdings of these currencies are represented by
the item foreign assets). A representative net trans­
action would be as follows:
Banks

C e n tral Bank
F A - 100

D B — 10 0

D B — 100

D P - 100

Foreign assets (FA) is the only item in the sources
statement that has been affected. Its decline of 100
implies the same change in the base.

Case II: Base Consists of Central Bank
and Government Liabilities
Another type of monetary system has a money
stock that is made up of the public’s deposits at pri­
vate banks, currency issued by the government or by
both the government and the central bank. If central
bank deposit liabilities function as an instrument of



interbank settlement and the public periodically con­
verts some of its deposits into currency, the mone­
tary base includes bank deposits at the central bank
and currency issued by the central bank and by the
Treasury.
In principle, this would mean that the sources
statement of the base would have to be derived from
the consolidation of Treasury and central bank bal­
ance sheets. But, as was discussed earlier, complete
Treasury balance sheets are universally unavailable.
In this case, the base and its sources must be modified
by simply adding Treasury currency in the hands of
banks and the public to both the base and the
sources of the base. The monetary base would then
become demand deposits of banks at the central bank
( DB ) plus central bank currency held by banks ( C B )
plus Treasury currency held by banks (TCB) plus
central bank currency held by the public (CP) plus
Treasury currency held by the public (TCP). And
the sources statement is:
G +FA +BC+LD +O A +TC B+TCP
—OL—DT—D F—CT

B anks
D B+100
B B — 10 0

1976

The analysis uses the new statement in exactly the
same way that previous transaction examples used
the preceding one. Suppose that the Treasury prints
and sells new currency to commercial banks and
deposits the receipts in the central bank.
Trea su ry
D T + 100

C entra

TCB+100

B ank

Banks

D B — 10 0

TCB + 1 0 0

D T+100

DB — 1 0 0

Treasury currency held by the banks increases and so
do Treasury deposits at the central bank. Since they
enter into the sources statement with opposite signs,
there is no change in the monetary base. Commercial
banks have simply changed the form of their reserves
without changing the total amount.
Another illustrative transaction is the sale of Treas­
ury currency to the central bank.
T rea su ry
DT+100

TCC+100

C e n tral Bank
O A + IO O

DT+100

Since Treasury currency at the central bank has not
been specifically included in the central bank balance
sheet, it must appear in other assets of the central
bank (OA), which rises by 100 together with de­
posits of the Treasury at the central bank (DT).
Since these items enter the sources statement with
opposite signs there is, again, no change in the mone­
tary base.
Page 5

F E D E R A L R E S E R V E B A N K O F ST. L O U IS

NOVEMBER

But if the Treasury prints new currency and buys
services from the public, the transaction is recorded
as follows:
Tre a su ry
Services + 1 0 0 ^ T C P + 1 0 0

C e n tral B an k
No Change

B an ks
No Change

No Change

I No Change

Public
T C P + IO O
S e rv ic e s— 1 0 0

While the central bank balance sheet is unaffected,
the sources statement indicates that the base rises by
100 because TCP has increased.
While the vast majority of relevant monetary sys­
tems are represented by the two cases discussed
above, there are occasionally some institutional or
market arrangements which require additional refine­
ments.
It may be that the consolidated banking system,
due perhaps to regulations imposed upon it, uses gov­
ernment securities as well as central bank deposits to
settle interbank liabilities. As is the case with Treas­
ury currency, there is no government balance sheet
which allows us to identify the sources of this base
component; therefore, holdings of government secu­
rities by banks and the public must be added to the
base and its sources as derived from the central bank
balance sheet. Similarly, if any other asset is used
for interbank clearing or as part of the money stock,
it must be accounted for in the sources of the mone­
tary base. The general rule for inclusion is as follows:
I. If the asset is the liability of an entity that main­
tains a balance sheet, the balance sheets of that entity
and the central bank are to be consolidated and the
sources of the base derived in a similar manner as
in Case I.
II. If the asset is a liability of an entity which does
not have a balance sheet, or is a real asset, then the
quantities of that asset that are held by commercial

1976

banks and the public must be added to the sources
and the monetary base which were constructed from
the central bank balance sheet.
Obviously, analysis and control are enhanced by
the ability to identify as many factors as possible
that may affect monetary base. Consequently, when
balance sheets are available, they should be used in
the derivation of base statements. The simple addi­
tion of other assets included in the base to the sources
statement assumes that these assets are predetermined
and not subject to control by the central bank.

SUMMARY
In most general terms the monetary base is that set
of assets held by the banks and the public which con­
strains the money stock. The items that constitute the
base in any country can be identified by determining
those assets which the consolidated banking sector
uses to settle interbank debt, and those items, aside
from bank liabilities, which are used as money. The
factors that cause the amount of base to change can
be determined by consolidating the balance sheets of
the producers of the base. In the case where the cen­
tral bank is the sole producer of base, this process
can proceed from the balance sheet of the central
bank. Any change in the base will appear as a change
in one or more other entries in the central bank’s
balance sheet. When there are other producers of base,
such as the Treasury, this article showed how the base
could be constructed to take this into account.
The sources statement of the base is most important
to the monetary authorities. This statement serves as
a scheme for analyzing how actions taken by the
monetary authorities, such as purchases or sales of
securities, or lending to banks, influences the base and,
hence, the money stock. It also permits them to ana­
lyze how other factors influence the base and, conse­
quently, permits them to identify the type of offsetting
actions that must be taken to counter these outside
influences.

APPENDIX
T h e purpose of this Appendix is to demonstrate how
the principles of monetary base construction can be ap­
plied to the U. S. monetary system and to show how a base
construct can be reconciled with data which is regularly
published in the Federal Reserve B ulletin.

Page 6


T h e U. S. monetary system is characterized by the
existence of three sets of m oney-creating institutions:
( 1 ) the U. S. Treasury which issues coin and which has
some Treasury notes and silver certificates outstanding,
( 2 ) the Federal Reserve System, which issues Federal

F E D E R A L R E S E R V E B A N K O F ST. L O U IS

NOVEMBER

Reserve notes and demand deposits, and ( 3 ) commercial
banks which issue demand deposits. Commercial banks,
which constitute the private money-creating sector, can
use as instruments of settlement currency (F ed eral R e­
serve notes and Treasury currency and coin) and demand
deposits at the Federal Reserve Ranks. Therefore, the base
consists of monetary assets of the consolidated domestic
private sector (currency and coin held by banks and the
public, and demand deposits of m em ber banks at Federal
Reserve R anks). These are the monetary liabilities of the
Government sector to the private domestic sector. Conse­
quently, the base and the sources of the base, as derived
from the Federal Reserve balance sheet, must be supple­
mented by the addition of Treasury currency and coin held
by commercial banks and the public.
It should also be noted that certain monetary relation­
ships betw een the central bank and the government are
unique to U. S. monetary institutions. For example, gold
is held by the Treasury, which issues gold certificates to
the Federal Reserve System, and coin is issued by the
Treasury while almost all of the currency is issued by
the Federal Reserve Banks. T hese unique features, how­
ever, present no difficulty in the development of base
statements and perhaps demonstrate even more force­
fully that such construction is applicable to all institu­
tional arrangements.
A simplified balance sheet for the Federal Reserve
System is given below:

Federal Reserve System
A ssets
G o ld Certificates ( G C )
S p e c ia l D ra w in g Rights (S D R )
C o in H eld b y the FR (T C C )
Loans an d D iscounts (L D )
G o vern m ent Secu rities H eld by
FR (B C )
O th e r A ssets ( O A )

L ia b ilitie s
FR N otes H eld b y :
Trea su ry (C T )
Co m m ercial Banks (C B )
Public (C P )
Dem and D epo sits:
Trea su ry (D T )
Com m ercial Banks (D B )
Foreign (D F )
O th e r L ia b ilitie s an d C a p ita l of
the FR ( O L )

The base, as defined and identified in the Federal R e­
serve’s balance sheet, consists of demand deposits of banks
at the Federal Reserve Banks ( D B ) , Federal Reserve
Notes held by banks and the public (C B + C P ) and
Treasury currency held by banks (T C B ) and the public
(T C P ):
(1 )

DB + CB + CP + TCB + TCP

T h e sources statem ent consists of the algebraic sum of all
the remaining assets and liabilities in the Federal R e­
serve balance sheet plus monetary liabilities of the
Treasury held by banks and the public (T C R + T C P ).
Therefore, the sources of the base consist of the following
balance sheet entries:
(2 )

LD + BC + OA + GC + SDR + TCC - CT
- DT - D F - OL + TCB + TCP

D ata for derivation of sources of the base is published
monthly in the Federal Reserve B u lletin in a table entided “M em ber Bank Reserves, Reserve Bank Credit,
and R elated Item s.” This T ab le is divided into two parts:



1976

Factors supplying reserve funds:
Reserve Bank Credit Outstanding (R R C )
Gold Stock (G )
Special D raw ing Rights (S D R )
Treasury Currency Outstanding (T C O ), and
Factors absorbing reserve funds:
Currency in Circulation (C C )
Treasury Cash Holdings (T K )
Deposits, other than M em ber Bank
Reserves with F R (d )
O ther Federal Reserve Liabilities
and Capital (O L )
M em ber Bank Reserves with F R Banks (D B )
Currency and Coin held by
M em ber Banks (C M B )
In terms of this statement, the base consists of member
bank deposits at Federal Reserve banks (D B ) plus cur­
rency and coin in circulation issued by the Federal R e­
serve Banks (C B + C P ) and issued by the Treasury
(T C B + T C P ). Thus, in terms of our balance sheet nota­
tion, it consists of D B + C B + CP + T C B + T C P which
is identical to statem ent ( 1 ) from the balance sheet of
the Federal Reserve.
For the sources statem ent we have to define the pub­
lished entities in terms of balance sheet notation.
R B C = L D + B C + OA (w here Federal Reserve float1
is included in O A )
G
= Gold
S D R = Special Drawing Rights
T C O = T C B + T C P + T C C + T C T (w here T C T re­
fers to Treasury currency held by the Treasury)
TK
= (G - G C ) + T C T + C T
d
= DT + DF
OL
= O ther Liabilities
T he sources statement, w hich is derivable from factors
supplying and absorbing reserve funds, is:
(3 )

RBC + G + SDR + TCO - TK - d - OL.

W hen balance sheet notation is substituted for published
notation, and addition and subtraction are completed,
statement ( 3 ) becomes,
(4 )

LD + BC + OA + GC + SDR + TCC - CT
- D T - D F - OL + TCB + TCP

This statem ent is an identical statement to ( 2 ) which
implies that the data published in the form of factors
supplying and absorbing reserve funds is consistent with
the sources statem ent as derived from the Federal Reserve
balance sheet.
As an example of this procedure the following numer­
ical example is presented. T h e balance sheet for the
Federal Reserve System is for Septem ber 2 9 , 1976, as
reported on page A 10 of the O ctober 1 9 7 6 Federal
Reserve B ulletin.
’ Federal Reserve float is computed from the balance sheets and
is cash items in process of collection minus deferred avail­
ability cash items. See Federal Reserve Bank of New York,
Glossary: W eekly F ed eral R eserve Statements, “Factors Affect­
ing Bank Reserves” (October 1975), pp. 17-18.
Page 7

F E D E R A L R E S E R V E B A N K O F ST. L O U IS

NOVEMBER

C onsolidated Statement of Condition of
All Federal Reserve Banks
(m illio n s o f d o lla rs )
A ssets
G o ld C ertificates

Lia b ilitie s
$ 1 1 ,5 9 8

FR N otes

$ 7 9 ,8 0 2

Dem and D epo sits:

SDR

700

C a sh H eld b y FR

365

Tre a su ry

1 2 ,2 1 2

324

M em ber B an k
Reserves

2 9 ,8 0 7

Loans a n d Discounts
G o vern m ent Secu rities
H eld b y FR

9 9 ,2 2 4

O th e r A ssets

1 9 ,6 9 4

Foreign

$ 1 3 1 ,9 0 5

O th e r L ia b ilitie s 2
an d C a p ita l

245
9 ,8 3 9
$ 1 3 1 ,9 0 5

In the notation used in this appendix, the base con­
sists of demand deposits of commercial banks held at
Federal Reserve Banks (D B ) which equal $ 2 9 ,8 0 7 plus
currency held by com mercial banks and the public
(C P + C B + T C P + T C B ) . This currency consists of F R
notes ($ 7 9 ,8 0 2 ) plus Treasury currency outstanding
($ 1 0 ,7 5 7 ) which comes from the Treasury accounts, less
the currency and coin held by Treasury ( $ 4 2 5 ) , called
“Treasury cash,” less Federal Reserve holdings of coin,
called “cash held by F R ” ( $ 3 6 5 ) .3 T h e total currency
component of the base consists of $ 8 9 ,7 6 9 million. T here­
fore, the base amounts to $ 2 9 ,8 0 7 plus $ 8 9 ,7 6 9 and equals
$119,576.
T h e sources of the base consist of Treasury currency
and coin held by com mercial banks and the public, and
all the items in the Federal Reserve’s balance sheet except
the two entries demand deposits o f commercial banks
( member|bank reserves) and Federal Reserve notes. In
other words, if one consolidates all the entries in the F ed ­
eral Reserve balance sheet for the week of Septem ber 29,
2Includes $920 million of other deposits.
3FR notes held by F R banks are excluded from the entry. “FR
notes” in the consolidated balance sheet.


Page 8


1976

1976, excluding Federal Reserve notes ($ 7 9 ,8 0 2 ) and de­
mand deposits of m em ber banks ($ 2 9 ,8 0 7 ), the total
amount is $ 1 0 9 ,6 0 9 million. As was shown previously the
amount of Treasury currency and coin held by commercial
banks and the public was $ 9 ,9 6 7 million for the same
date.4 Hence, the total base is $ 1 0 9 ,6 0 9 plus $ 9 ,9 6 7 equals
$ 1 1 9 ,5 7 6 million.
Using th e notation presented in this appendix, the
sources of the base m ay also be constructed from the
entries that appear in the table “M em ber Bank Reserves,
Federal Reserve Bank Credit, and Related Item s” that
appears on pages A2 - A3 of the O ctober 1 9 7 6 Federal
Reserve B u lletin . F or Septem ber 2 9 , 1976, th e data are as
follows:
Reserve Bank Credit (R B C ) ______$ 1 1 3 ,9 7 2 million
Gold (G ) _________________________
1 1,598
700
S D R ______________________________
Treasury Currency
Outstanding (T C O ) ____________
10,757
Treasury Cash (T K ) ______________
425
D em and Deposits of
Treasury (D T ) __________________
1 2 ,2 1 2
Foreign Dem and Deposits ( D F ) __
245
O ther Liabilities5 (O L ) ___________
4 ,5 6 9
Using the previous formula for the sources of the base
given in equation ( 3 ) :
RBC + G + SDRs + TCO - TK - D T - D F — OL
we find that the summation of the sources stated in this
manner, and applying the appropriate sign, equals
$ 1 1 9 ,5 7 6 which is exactly equal to the base as derived
from the Federal Reserve’s balance sheet with the addi­
tion of Treasury currency held by com mercial banks and
the public.
^Treasury currency and coin held by banks and the public is
the sum of silver certificates, United States notes and total
coin. These amounts are available for the end of the month
in Table MS-1, “Currency and Coin in Circulation,” U. S.
Department of the Treasury, Treasury Bulletin.
5Includes $920 million of other deposits.

The Welfare Cost of Inflation
JOHN A. TATOM

O n e of the most controversial and least understood
concepts of economic theory is that of the “welfare
cost” associated with fully anticipated inflation. Other
costs or burdens of inflation receive considerable
attention in the press, but the burdens usually dis­
cussed are those associated with unanticipated infla­
tion. Moreover, most of the costs of inflation which
are widely recognized and discussed involve transfers
of income and wealth from one group to another. For
society as a whole, the value of these losses, or costs
to some, tend to be offset by the value of gains, or
benefits, accruing to others. In contrast, little or no
attention is focused on the net loss of valuable serv­
ices which society bears due to inflation, or what
economists call the welfare cost of inflation.
It is widely agreed that most of the costs of inflation
can be eliminated by the creation of an environment
where the inflation rate is stable or reasonably con­
stant and the rate is correctly anticipated by parties
to financial contracts. Indeed, it has been suggested
that not only can the costs of inflation be eliminated,
but some benefits of inflation may be preserved or
enhanced by promoting a stable anticipated positive
rate. This argument has been put forward by many
analysts, especially by a group of economic develop­
ment economists of the “structural” school.1 More re­
'The leading proponent of this school is generally regarded to
be Raul Prebisch. A discussion of the inflation theory of this
school may be found in Dudley Seers, “A Theory of Infla­
tion and Growth in Under-developed Economies Based on the
Experience of Latin America,” Oxford Econom ic Papers
(June 1962), pp. 173-95; or Julio H. G. Olivera, “On
Structural Inflation and Latin-American ‘Structuralism’,”
Oxford Econom ic Papers (November 1964), pp. 321-32.



cently, such an argument has been developed by
monetary economists in this country. The implication
of such arguments is that a stabilization policy which
ensures that existing inflation is fully and correctly
anticipated is, at worst, a satisfactory substitute for a
policy to eliminate inflation and at best, superior to
the elimination of inflation.
An orthodox analysis of inflation suggests that there
is a trade-off involved in anticipated inflation. Ac­
cording to this analysis, there is a revenue resulting
from inflation which accrues to a government which
controls the production of fiat money. This revenue
provides greater purchasing power to the government,
allowing it to increase government expenditures, or to
reduce alternative sources of purchasing power, that
is, other taxes. Moreover, when the rate of inflation is
correctly anticipated, the capricious effects of infla­
tion on the distribution of income and wealth do not
occur.
But there is an “excess burden” of inflation, even if
it is correctly anticipated. That is, a given rate of
anticipated inflation will cost members of society more
than the revenue which accrues to the government.
The excess is called the excess burden, or “welfare
cost” of inflation. Both the revenue and the welfare
cost of inflation are positively related to the level of
the rate of inflation. Therefore, the “best” rate of in­
flation must be chosen with reference to the revenuecost trade-off of inflation and the revenue potential
and associated costs of alternative revenue sources.
The case supporting a stable perfectly anticipated
positive rate of inflation is strengthened by arguments
Page 9

F E D E R A L R E S E R V E B A N K O F ST. L O U IS

which assert that the welfare cost of inflation is very
small. In some of these arguments, the size of the
welfare cost of inflation is absolutely dismissed. A
notable example is the Presidential Address of Pro­
fessor James Tobin to the American Economics Asso­
ciation in December 1971. Discussing the relationship
between unemployment and inflation, he said of the
cost of inflation:
According to econom ic theory, the ultimate social
cost of anticipated inflation is the wasteful use of
resources to economize holdings of currency and
other noninterest-bearing means of payment. I sus­
p ect th at intelligent laymen would be utterly as­
tounded if they realized that th is is the great evil
economists are talking about. They have imagined a
much more devastating cataclysm, with Vesuvius
vengefully punishing the sinners below. Extra trips
betw een savings banks and commercial banks? W hat
an anti-clim ax!2

Other important examples may be found in the litera­
ture on public finance. One of the best treatments of
the welfare cost of taxation is that of Richard A. and
Peggy B. Musgrave in their book, Public Finance in
Theory and Practice. However, their work contains
no discussion of the welfare cost of anticipated infla­
tion. Moreover, they do emphasize the revenue from
inflation.3
This article is intended to serve two purposes. The
first purpose is to explain the welfare cost of antici­
pated inflation. It is shown that this cost is not negli­
gible. Thus, it is not a matter of indifference whether
a government follows a policy of pursuing a very
high or a very low rate of fully anticipated inflation.
The second purpose is to show that, on the grounds
of efficient taxation alone, the optimal rate of antici­
pated inflation and its revenue potential are not large.
On rather generous assumptions favoring inflationary
finance, it is demonstrated that tax efficiency does
not justify a positive rate of inflation.
The concern here is the cost associated with a con­
stant and correctly anticipated inflation rate. The
costs of unanticipated inflation which impact on par­
ties to transactions in credit or resource markets, fixed
income recipients, and taxpayers in general are ig-

NOVEMBER

1976

nored.4 These costs are substantial; indeed, they
dwarf the cost addressed here. Nonetheless, it is
theoretically conceivable that these costs may be
avoided in an inflationary environment if inflation is
correctly anticipated.

INFLATION AND THE COST OF MONEY
The seminal article on the welfare cost of inflation
is Martin J. Bailey’s 1956 article “The Welfare Cost of
Inflationary Finance.”5 He examined the cost of per­
fectly anticipated inflation to holders of real money
balances in a stationary economy and illustrated those
costs using data from several famous hyperinflations
in various countries. Bailey also identified the revenue
from inflationary money creation which accrues to a
government which produces fiat money. This revenue
is a transfer from money owners to all households
through the government. Therefore, he argued that
the social cost or excess burden of an inflation tax is
the total cost to money owners less the transfer to
government. Bailey’s analysis is almost identical to
the analysis of the welfare cost of an excise tax.6
A considerable literature has developed following
Bailey’s cost analysis. The focus of this literature has
been on the implications of analyses such as Bailey’s
for an “optimum” rate of money growth and inflation.
The primary extensions of Bailey’s work have been
accounting for growth of real output and for some
technical considerations such as measurement, differ­
ent expectation formation processes and the stability
of an inflationary economy. Here we are interested in
an exposition of the analysis of the cost of inflation
and so a rigorous treatment of the development of the
'The costs of unanticipated inflation are treated in most intro­
ductory textbooks. An excellent and brief discussion may also
be found in J. Huston McCulloch, Money and Inflation: A
Monetarist A pproach (New York: Academic Press, 1975). See
also Hans H. Helbling and ]ames E. Turley, “A Primer on
Inflation: Its Conception, Its Costs, Its Consequences,” this
Review ( January 1975), pp. 2-8; Albert E. Burger, “The
Effects of Inflation (1960-68),” this R eview (November 1969),
pp. 25-36; Michael R. Darby “The Financial and Tax Effects
of Monetary Policy on- Interest Rates,” E conom ic Inquiry
(June 1975), pp. 271-73; and Jai-Hoon Yang, “The Case For
and Against Indexation: An Attempt at Perspective,” this
Review (October 1974), pp. 2-11.
5Martin J. Bailey, “The Welfare Cost of Inflationary Finance,”
The Journal o f Political Econom y (April 1956), pp. 93-110.

2James Tobin, “Inflation and Unemployment,” The American
Econom ic Review (March 1972), p. 15.
:iRichard A. Musgrave and Peggy B. Musgrave, Public Finance
in Theory and Practice ( New York: McGraw-Hill Book
Company, 1973), p. 526 in footnote 11, they dismiss the
notion of a welfare cost of inflation by arguing that, as
presented by some theorists recently, it is “a rather quaint
basis on which to assess the case against inflation.”

Page 10
http://fraser.stlouisfed.org/

Federal Reserve Bank of St. Louis

‘‘See the screen insert, “The Welfare Cost of An Excise Tax.”
The methodology and theory underlying the concept of a
welfare cost and its measurement here and in the discussion
of the excise tax follow Arnold C. Harberger, “Three Basic
Postulates for Applied Welfare Economics: An Interpretive
Essay,” The Journal o f Econom ic Literature (September
1971), pp. 785-97; and John C. Hause, “The Theory of
Welfare Cost Measurement,” Journal o f Political Economy
(December 1975), pp. 1145-82.

F E D E R A L R E S E R V E B A N K O F ST. L O U IS

NOVEMBER

literature is not pursued. Instead an attempt is made
to present a “state of the arts” analysis drawing gener­
ously upon this literature.
Suppose that the economy is initially in equilibrium
and there is no inflation. The purchasing power of the
stock of money is exactly that which households de­
mand. This situation is represented in Figure I. The
demand for real money balances, a nominal stock of
money deflated by the price level, is represented by
D. The demand for real money balances is deter­
mined by the level of real income, real wealth, and
the cost of holding real or financial assets.7 In Figure
I, the demand for real money balances is shown to be
inversely related to the level of market interest rates
represented by “the” interest rate, i. Other factors
affecting the demand for money are held constant
along D. The supply of real money balances is the
dollar value of the existing stock of money (M ) de­
flated by the general level of prices of goods and
services, the equilibrium price level (Po). The exist­
ing stock of money is assumed to have been produced
by a central bank acting as an agent of the govern­
ment. No interest is paid on money in this analysis.
The quantity of money can be changed through
central bank purchases and sales of financial assets, in
particular, by buying and selling government bonds.
It is assumed below that each government bond has
a principal amount equal to one dollar and pays the
nominal rate of interest i. Given the initial levels of
the other determinants of the demand for money, the
equilibrium level of the rate of interest is i<>. Since
there is no expected inflation initially, this rate of
interest will be the same as the real rate of return ( r )
on capital, or real assets.
The price level depends on all factors determining
the demand and supply of goods and services. In a
stationary economy the price level depends primarily
on the quantity of money.8 With unchanged prefer­
ences of all spending units, the general level of prices
will be steady, if the quantity of money is constant.
The actual rate of inflation will be the rate necessary
to insure that real balances and the level of other
real variables are equal to their equilibrium levels.
If the nominal stock of money grows at rate p in­
stead of zero, money holders will attempt to spend the
7An excellent discussion of the demand for money may be
found in Milton Friedman, “The Quantity Theory of Money
— A Restatement,” in Studies in the Quantity Theory of
Money (Chicago: The University of Chicago Press, 1956),
pp. 3-21.
8A stationary economy is characterized by an absence of
growth of resources or aggregate real income.



F ig u r e

1976

I

The Dem and for and Supply of
Real M oney Balances
In te re s t

(M/P)

excess cash on goods and other assets in order to
maintain the purchasing power of their initial money
balances. Because of the increased demand for goods
and assets, all dollar prices begin rising. The price
level will rise at rate p to eliminate a continuing ex­
cess supply of cash and excess demand for goods and
other assets. After adjustment to the increase in the
rate of monetary expansion from zero to p, the actual
and anticipated rate of inflation, it, will equal p.
Inflation is a tax on real money balances because it
raises the cost of holding a constant dollar of purchas­
ing power. Since the nominal rate of interest rises to
compensate lenders for the erosion of wealth which
inflation would otherwise cause, the cost of holding a
real dollar rises. An alternative way of viewing this
cost is that owners of money must increase their hold­
ings of dollars at the same rate as inflation in order to
maintain the purchasing power of their cash balances.
For each dollar held, the anticipated rate of inflation
represents a cost of maintaining the purchasing power
of the dollar, in addition to the real return which
could have been earned on real assets.
The effects of a positive rate of monetary expansion
and actual and expected inflation at rate it can be
seen in Figure II. The initial equilibrium, in the
Page 11

F E D E R A L R E S E R V E B A N K O F ST. L O U I S

F ig u r e II

The Demand for and Supply of
Real Money Balances with Inflation at Rate I T
In te re st
R ate

NOVEMBER

1976

For each unit of real balances given up by money
owners, the value of the foregone services is measured
by the corresponding interest rate along the demand
curve.
The revenue from the tax on real money balances
accrues to the government through the central bank.
The revenue is reflected in the higher interest pay­
ments on the growing amount of bonds held by the
central bank. This revenue is the area A in Figure II.
The revenue per period to the central bank is
equivalently the real value of the continuous increase
in its nominal money output (p “jjr)- Since the rate
of monetary expansion ( ^ ^

= p ) equals the rate

of inflation ( i t), the revenue per period ( i

m]

mQ

R e a l M oney
B a la n c e s
______________________________________________________________ (M/P)

absence of inflation, is indicated at point 1. The an­
ticipation of inflation at rate tt will raise the cost of
holding real balances to (r0 + it), given the real rate
of interest. Households will reduce their demand for
real money balances to mi, substituting other goods
and assets for the relatively more expensive services
of money. Given the other determinants of the de­
mand for money, equilibrium is restored at point 2.
The growth in the nominal money supply will be
matched by the rate of inflation so as to maintain the
purchasing power of money balances at the level
indicated by m^
The total cost of perfectly anticipated inflation to
owners of money is indicated in Figure II by the area
(A -f- B -|- C ). Area A is the increased cost of holding
mx units of real money balances. Money holders pay
a cost of h per period per dollar of real cash balances,
instead of io. This additional cost is a maintenance
cost. It measures the real value of goods and services
foregone to add nominal money balances at rate n.
The total maintenance cost is this cost per unit of real
money balances, it , times the level of real money bal­
ances, mj.
The second component of the total cost, the area
B
C, is the real value of the services of money
which is given up by money owners due to inflation.
The demand price, i, at each level of real balances
indicates the value of a unit of real balances per period.

Page 12


) is

equal to the level of real money balances times the
M
rate of inflation (-p- p = mx u). The added revenue of
the central bank accrues to all households through the
government so the area A is not a net cost. Instead, it
is a transfer from money holders to all households.
Therefore, the net cost to all households is the area
(B + C ).
Area (B -(- C) is the excess of the costs to money
holders over the benefits of inflation at rate it. It is the
excess burden or welfare cost of inflation. Bailey and
others have illustrated this cost. During periods of in­
flation (especially hyperinflation), payments proce­
dures and habits change to avoid the capital losses
which inflation imposes upon cash holding.9
However, it should be noted that the efforts to
economize on money balances cited as illustrations of
the excess burden of inflation are not necessary to the
analysis which identifies area ( B - f C) as the welfare
cost. The identification of area ( B -)-C) as the wel­
fare cost implicitly assumes that the adjustment to
perfectly anticipated inflation requires no use of re­
sources. The adjustment has no direct cost, in the
sense that scarce resources are diverted from the pro­
duction of other real goods and services in order to
economize on money holdings. Changes in the pay­

‘•'See Bailey, “The Welfare Cost,” pp. 96-102. More detailed
descriptions of the changes in the payments process during
rampant and expected inflation have been written by Frank
D. Graham, Exchange, Prices, And Production In Hyper­
inflation: Germany, 1920-1923 (New York: Russell & Russell,
1930); and Constantino Bresciani-Turroni, The Econom ics of
Inflation (London: G. Allen & Unwin, Ltd., 1937).

F E D E R A L R E S E R V E B A N K O F ST. L O U IS

NOVEMBER

ments process and habits are costless in Bailey’s
analysis.
The area ( B + C ) is a measure of the lost value of
the services of real money balances per period to all
households. If the attempt to economize on real
money balances due to inflation uses resources, the
output of final goods and services available to house­
holds will be reduced and there will be additional
deadweight losses to society. These additional adjust­
ments are associated with the recession or depression
which many believe must accompany continuous in­
flation, even a prolonged steady rate inflation, and
which have been observed with prolonged periods of
hyperinflation.10

A Measure of the W elfare Cost of Inflation
The size of the welfare cost of inflation, area
( B + C ) is the area of a triangle ( C ) and a rectangle
( B ). The area of the triangle is one-half the base, the
reduction in real balances, times the height, the actual
and expected rate of inflation. The area of B is the
same base times the height, the real rate of interest.
Using the concept of elasticity, a general measure of
the welfare cost may be written as:
(1 )

W. C. = e * ( ~ 7^) i t (n/2 + r)

10

where e° is the elasticity of demand for real money
balances with respect to the nominal interest rate,
given the real rate of interest ro .11 The welfare cost
of inflation is directly proportional to the elasticity of
demand and the level of real money balances which
would prevail in the absence of inflation or deflation.
The welfare cost of inflation is inversely related to the
real rate of return on capital in an economy. The
welfare cost increases at an increasing rate with the
inflation rate.
A rough estimate of the size of the welfare cost of
inflation can be made using existing empirical re­
search on the demand for money. Most estimates of
the interest rate elasticity of demand for money (de­
fined positively) indicate that it is about .15. That is,
10Since this article concerns the cost of a sustained and cor­
rectly anticipated “pure” inflation, such arguments are out­
side the scope of the analysis here and will be ignored.
n The elasticity may be written symbolically as ( —

)

so that e* ( -y -) is the reduction in real money balances per
unit increase in the expected rate of inflation. The total
reduction in real balances is this amount times the level of
the expected rate of inflation.



1976

a one percent rise in the interest rate (for example,
from 5 percent to 5.05 percent) will result in a .15
percent reduction in the demand for money.12
The level of real money balances (measured in
current prices) which would exist in the absence of
inflation, and the level of the real rate of return to
capital are more difficult to determine. A level of 5
percent for the real rate of return is, if anything, a
high estimate. An alternative estimate which is illus­
trative is a 2 percent real rate.13 The U. S. money
supply is about $300 billion. Most observers believe
that the rate of inflation to be expected, in the near
term, is about 5 percent.
Other things being equal, the percentage increase
in the nominal rate of interest due to a 5 percent ex­
pected rate of inflation as compared to no inflation is
100 percent if the real rate is 5 percent, and 250 per­
cent if the real rate is 2 percent. For a real rate of 5
percent, one could expect mo to be 15 percent
(.15 x 100 percent) higher than the present level, or
about $345 billion. Alternatively, a 2 percent real rate
implies a level of real balances 37.5 percent larger
than at present, or $412.5 billion.
These estimates imply a range of the welfare cost of
inflation in equation (1 ) of $(52 it + 517 u2) billion
to $(62 it + 1547 it2) billion. For an expected rate of
inflation of 10 percent per year, the welfare cost
would be $10 to $22 billion per year measured in
current dollars. Alternatively, a 5 percent rate of
anticipated inflation involves a welfare cost of $4 bil­
lion to $7 billion per year. These estimates give a
rough measure of the order of magnitude of the wel­
fare cost of inflation.
Welfare costs of various parts of the U. S. tax sys­
tem have been estimated. To provide some compari­
sons, a few of the early estimates are cited here.
While the state of the art in some areas is crude, these
estimates provide useful approximations of the order
'-See the survey of a literature by David E. W. Laidler,
The Demand fo r Money: Theories and Evidence ( Scranton,
Pennsylvania: International Textbook Company, 1969),
Chapter 8. To the extent that .15 is too low, the welfare cost
estimates given below understate the welfare cost of infla­
tion. Milton Friedman has suggested that the .15 estimate
may be too low. See Milton Friedman, The Optimum
Quantity o f Money and Other Essays (Chicago: Aldine
Publishing Company, 1969), p. 143.
l:iMilton Friedman, “Government Revenue from Inflation,”
Journal o f Political Econom y (July/August 1971), p. 852
and p. 854, has suggested that a real rate of interest about
equal to the rate of growth of real per capita income has
“some basis in experience and theory.” This rate of growth
for the United States is about 2 percent.
Page 13

F E D E R A L R E S E R V E B A N K O F ST. L O U IS

NOVEMBER

1976

F E D E R A L R E S E R V E B A N K O F ST. L O U IS

NOVEMBER

1976

THE WELFARE COSTpF AN EXCISE TAX

T h e analysis of the welfare cost of a tax is part of
the overall theory of the effect of taxation. Most an­
alysts of the cost of inflation argue by analogy that
inflation is a tax on the purchasing power of money or
real cash balances. To understand inflation as a tax it
is necessary to review the analysis of the effect of
taxation of another good, such as an excise tax on
tobacco, alcohol, or long-distance phone calls.
In the accom panying Figure, the demand (D ) for a
product X is shown. The demand for X depends upon
the price of the product. O f course, the demand de­
pends on other characteristics of the econom ic en­
vironment of all potential purchasers of product X.
T h e most important of these other determinants are
the prices of closely related goods such as complement
or substitute goods, the preferences of households, the
real income of households, and its distribution. These
other factors are assumed to be fixed in the Figure.
Suppose that product X, in the absence of a tax, can
b e produced and sold at a current cost of $ l/ u n it of
X , given technology and the value of resources neces­
sary to produce a unit of X. This is indicated by the
supply curve in the Figure labeled S. In the absence
of a tax, competition among producers insures that the
market price will be $ l/ u n it and the amount pur­
chased and sold will be the amount households de­
mand, for example, 1 million units in the Figure.
Now suppose the government levies a tax on product
X of $ 1/unit or 100 percent. The cost of producing and
selling the product will rise to include the cost of the
tax. The market price will rise to $2/unit of X. House­
holds will not continue to buy as much of the product.
Instead, they will substitute, buying other goods which
have not changed in price. In the Figure, the demand
for X falls to .8 million units per period of time.
The burden, or cost, of the tax to households is com­
posed of three parts. First, households pay more for
the units they continue to buy. Second, households
forego the benefits of consuming the units which they
no longer purchase each period (2 0 0 ,0 0 0 ) . T h e demand
price at a given quantity indicates the value of a
unit of X to households. Therefore, consumers lose a
value of X indicated by the area under the demand
curve from .8 million units to 1 million units. Finally,
households gain the benefits of more of other products
as resources move from the production of X to the pro­


Page 14


The Eifect ot an Excise Tax
on the Price and Output of Product X
P rice Per U nit
of P ro d u ct X

p e r Tim e P e rio d

duction of these other goods. T h e supply price in­
dicated by curve S measures the cost of resources
needed to produce a unit of X. T h at cost is the maxi­
mum value of these resources in producing other goods
for households. Therefore, the value of the additional
other goods which households obtain is the area under
S from 1 million units of X to .8 million units of X .1
T h e cost of the tax to households, in this example,
is $ 9 0 0 ,0 0 0 . T h e first component, the additional cost of
the units households continue to purchase, is $ 8 0 0 ,0 0 0 .
This is the area of rectangle A in the Figure. T h e sec­
ond part of the cost, the value of X which households
lose is $ 3 0 0 ,0 0 0 . This is the area of the rectangle B
($ 2 0 0 ,0 0 0 ) and the triangle C ($ 1 0 0 ,0 0 0 ). T h e third
part of the cost, the gain in the value of alternative
products is the area of the rectangle B ( - $ 2 0 0 ,0 0 0 ) .
1In the case of fiat money the third aspect here is absent. No
resources are free to move into the production of other
goods.

T h e second and third part of the cost can be com­
bined to obtain the net cost to households of the shift
in the allocation of resources. This cost is $ 1 0 0 ,0 0 0 in
the example, the area of triangle C. It measures the
cost to households of the distortion of their consump­
tion patterns resulting from the tax. Society can pro­
duce 1 million units of X and less of other goods or
.8 million units of X and more of other goods. In the
absence of the tax, consumers would prefer the output
mix with 1 million units of X to that with .8 million
units. The value of the prefered mix over its alterna­
tive is the $10 0 ,0 0 0 measured by triangle C. The total
cost to purchasers of X may be stated as the sum of
areas A and C. It includes the value of product which
households must forego to pay the tax (A ) and the net
value of the product X which households forego due to
the tax.
The proceeds or revenue from the tax is the tax/unit
times the number of units which households continue
to buy. In the example, this is the area of rectangle A.
The proceeds of the tax are not truly a cost to house­
holds. In fact, the proceeds will be spent on goods or
transferred back to households. T h e tax revenue does
not affect the capacity of the economy to produce
goods and services. T h e value of the foregone product
for households, measured by rectangle A, is the value of
the product which government either purchases for all
households or permits households to continue to pur­
chase through a transfer of the tax revenue back to
them. Rectangle A is not a cost to society. It is merely
a financial transfer within the economy. Area C, the
triangle, is the only remaining cost of the excise tax.
T h e analysis of the cost and benefits of a tax may
be summarized as follows. T h e tax imposes costs on
household purchases of the taxed good. The cost is
measured by areas such as ( A + C ) . T h e government
receives proceeds of the tax equal to an area such as A.
This benefit of the tax accrues to all or some members
of society. The cost of the tax exceeds the benefit of
the tax by an area such as C. T h e excess is called an
“excess burden” or the “welfare cost” of the tax on X.
It measures the net loss to all households due to the
distortion of resource allocation caused by the inter­
ference in the market for product X. In the example,
the welfare cost is $ 1 0 0 ,0 0 0 per period.
A general measure of the welfare cost of an excise
tax may be developed from the concept of the price

elasticity of demand. This elasticity is a measure of
the responsiveness of the quantity of a product which
households demand, to changes in the price of the
product. It may be defined as:

' ^' e

percentage change in quantity of X demanded
percentage change in the price of X

The elasticity measures the percentage reduction in
the quantity which households demand for each one
percent rise in the price of product X.
T h e size of the welfare cost, approximately the area
of a triangle such as C, is one-half the product of the
size of the reduction in demand and the size of the
increase in price. The size of the reduction in demand
is related to the rise in price through the elasticity of
demand. The welfare cost of a tax can be written as:
(2 )

W. C. = % e (P„Xo) t2

where t is the percentage rate of the tax, the tax/unit
divided by the original price.2 In the example, the
elasticity of demand is .2, the total expenditure on
the good (P 0X 0) is one million dollars per year, and
the tax is 100% . Thus, the welfare cost is $ 1 0 0 ,0 0 0 per
period.
In equation ( 2 ) , the welfare cost of a tax is shown
to be an increasing function of the elasticity of de­
mand. T h e welfare cost of a tax increases with the
square of the tax level, and is proportional to the size
of the original tax base.
Equation (2 ) is not the most general measure of
the welfare cost of a tax. There are other considera­
tions, such as the level of existing taxes on other goods
and services and the technical or market conditions
determining supply, which affect the measurement of
welfare cost. However, the treatm ent of this simple
case is sufficiently general for the discussion of money
and inflation.
-Similar equations may be found in Arnold C. Harberger,
“Taxation, Resource Allocation, and Welfare,” Taxation and
W elfare (Boston: Little, Brown and Company, 1974), p.
34; and Richard A. Musgrave and Peggy B. Musgrave,
Public Finance in Theory and Practice (New York: Mc­
Graw-Hill Book Company, 1973), p. 456.

Page 15

F E D E R A L . R E S E R V E B A N K O F ST. L O U IS

of magnitude of the costs. The major tax in the
United States is the personal income tax. It distorts
the choice between labor and leisure, encouraging
longer vacations, greater absenteeism, early retire­
ment and other means of reduced effort. The welfare
cost of this tax has been estimated for 1961 to be one
billion dollars per year. If the welfare cost per dollar
of revenue were the same in 1975 as in 1961, the wel­
fare cost in 1975 would be about $3 billion. Account­
ing for the substantial increases in the marginal tax
rate since 1961 would dramatically raise this esti­
mate.14 Musgrave and Musgrave have placed the
order of magnitude of the welfare cost of selective
sales and excise taxes at $3 to $4 billion per year
for 1970 and that of the corporate income tax at
about $1 billion per year.15 The welfare cost of five
percent anticipated inflation exceeds the welfare cost
of the corporate income tax and it may be as large as
that of the personal income tax.

Qualifications of the Estimated Cost
There are two problems with the cost measures
which must be pointed out. First, they rely on an
estimate of the elasticity of demand for money with
respect to the anticipated inflation rate which may be
a serious underestimate of that elasticity.16 Second,
the measure in equation (1) is for an economy with
zero growth of real output, not for a growing economy
such as the United States.
The relevant elasticity of demand for money is the
elasticity of demand with respect to the anticipated
rate of inflation. This elasticity will only be related to
the interest rate elasticity if, during the period when
the interest elasticity is estimated, movements of the
interest rate reflect only changes in inflation expec­
tations and not changes in the real rate of return on
capital. There is a substantial volume of literature
which argues that the demand for money is not very
sensitive to changes in real rates of return on capital,
while it is sensitive to changes in the anticipated rate
of inflation. A given change in market interest rates
which reflects a change in inflation expectations
14See Arnold C. Harberger, “Taxation, Resource Allocation,
and Welfare,” Taxation and W elfare (Boston: Little, Brown
and Company, 1974), p. 47.
15See Musgrave and Musgrave, Public Finance, pp. 458-59.
18Robert Barro implicitly uses an estimate of this elasticity of
one half. Accordingly, his estimate implies a welfare cost of
inflation more than three times the size given here. See
Robert J. Barro, “Inflationary Finance and the Welfare Cost
of Inflation,” Journal o f Political Econom y (September/
October 1972), pp. 978-1001.

Page 16
http://fraser.stlouisfed.org/

Federal Reserve Bank of St. Louis

NOVEMBER

1976

should have a sizeable impact on the demand for
money vis-a-vis the demand for real and other finan­
cial assets. On the other hand, a given change in the
market rate due to fluctuations in the real rate of
return on capital will affect household consumptionsaving choices with little impact on the composition
of desired asset portfolios, in particular, the demand
for money. To the extent that observed interest rate
changes have been due to changes in the real rate,
the estimate of the interest elasticity understates the
elasticity of demand for real money balances with
respect to the expected rate of inflation.17 Conse­
quently, the true welfare cost measure would be
higher than these estimates.
The second problem with the analysis above is that
it ignores the effect of economic growth on the wel­
fare cost of inflation. It has been suggested that the
welfare cost of inflation is smaller in a growing
society.18 If this suggestion is correct, the estimate of
the annual cost of perfectly anticipated inflation is
too large.
To assess the effect of growth on the welfare cost,
consider Figure III. Growth increases the demand for
real money balances from D to D'. The process of
growth is continuous but it is sufficient to look at the
discrete shift from one period to the next. For the
same rate of anticipated inflation, it, the percentage
increase in the quantity demanded of real balances is
equal to the “income elasticity of demand” times the
rate of growth of income. Since the demand for
money at each point along D increases by the same
percentage, the demand at points 1 and 2 grows by
that percentage, in one period of time, to points 1'
and 2'. The demand for real money balances at the
smaller level, 2, grows by a smaller absolute amount
than at the higher level 1. The base of the triangle C'
and of rectangle B' is larger than in C and B by the
percentage growth in demand. For the same rate of
17A classic discussion of the propositions concerning the de­
mand for money may be found in Friedman, “The Quantity
Theory,” or “Interest Rates and the Demand for Money.”
Both may be found in Friedman, The Optimum Quantity
as Chapter 2 and Chapter 7, respectively. An example of a
more rigorous derivation for an inventory theoretic demand
model may be found in Edi Kami, “The Value of Time and
the Demand for Money,” Journal o f Money, Credit and
Banking (February 1974), pp. 45-64. Considerable confu­
sion continues to exist over the difference between these
two elasticities. For an example, see Edmund S. Phelps,
“Inflation in the Theory of Public Finance,” T he Swedish
Journal o f Econom ics (March 1973), pp. 67-82, especially
p. 76 and p. 82.
18See Charles D. Cathcart, “Monetary Dynamics, Growth,
and the Efficiency of Inflationary Finance,” Journal of
Money, Credit and Banking (May 1974), p. 189.

F E D E R A L R E S E R V E B A N K O F ST. L O U IS

F ig u re III

Interest

Growth of Income and the
Welfare Cost of Inflation at Rate IT

Rate

il-r0+1T

'

0 - r0

anticipated inflation, the annual welfare cost in­
creases through time in a growing economy. It grows
at the rate of growth of the demand for money.19
Therefore, the estimates of the annual welfare cost of
anticipated inflation are again, understated, contrary
to the position mentioned above.

WEALTH EFFECTS, THE REVENUE
FROM INFLATION, AND THE
EFFICIENT RATE OF INFLATION
The analysis of the welfare cost of perfectly an­
ticipated inflation in the last section is based upon an
assumption of long-run adjustment to the anticipation.
The analysis compares two equilibrium situations such
as points 1 and 2 in Figure II. It ignores the adjust­
ment process by which real money balances are re­
duced and any short-run cost which may be associ­
ated with the transition. This assumption appears to
be critical in light of the theoretical results arising
from the recent rediscovery of wealth effects on
economic behavior. The anticipation of inflation will
not leave “other things equal” along the demand for
1!,The analysis here, following the empirical literature, assumes
that the interest rate and anticipated inflation rate elasticities
of demand for money are unaffected by the level of other
determinants of demand such as the level of income.
It may be noted in Figure III that at the given rate of
inflation, n, the supply of real money balances, mi, grows at
the rate of growth of demand. Therefore, the equivalent of
area A in Figure II also grows at this rate.



NOVEMBER

1976

money curve in Figure II. In the short-run the analy­
sis of the welfare cost of inflation must either account
for shifts in the demand curve or for other changes
which are necessary to keep the demand curve in its
original position. The latter method is pursued here.
A policy of implementing a permanent rate of inflation
is described below which obviates the shift in the
demand curve. This policy also clarifies the effect of
inflation on the government’s budget.
Given a level of nominal money balances, a change
in anticipations to a higher rate of expected inflation
will reduce real money balances through a one-time
change in the general level of prices. The price level
must be sufficiently higher to eliminate the excess
supply of real money balances. This is illustrated
in Figure IV, Panel A. The reduction in real money
balances demanded, from point 1 to point 2 will
create an excess supply of real money balances, given
the initial price level, Po. The corresponding excess
demand for other real goods and services will result
in a one-time surge in prices to Pj. This rise in the
level of prices eliminates the excess supply of real
cash balances at point 2.
The analysis of the previous section has two implicit
assumptions. The first is a technical point. The wel­
fare cost analyzed there is not the cost associated with
moving along a price path such as P„AP in Figure V.
Instead, the level of prices will surge upward when
the rate of money growth rises from zero to p = 710.
Thus, the price path associated with the nominal
money supply path M in Figure V will be P0ABP',
where time to is the point when the rate of money
growth rises.
The second implicit assumption is more serious. The
analysis above ignores wealth effects. In particular,
the surge in prices to level P, will reduce the real
value of net monetary assets in household portfolios.
The analysis assumes that this short-run reduction in
real wealth has no effect on the demand for real cash
balances and other goods and services.
The initial reduction in real wealth due to a price
surge will cause households to attempt to restore their
lost wealth. Thus, households reduce their spending
on goods and services and their desired holdings of
real cash balances. Since part of the excess demand
for goods and services is eliminated due to the wealth
reduction, the price surge will be smaller when
wealth effects are included. Also, the increased sav­
ing rate of households to restore wealth will reduce
the real rate of return on physical capital. Thus, the
Page 17

F E D E R A L R E S E R V E B A N K O F ST. L O U IS

F ig u r e IV

Anticipated Inflation (IT ),
W ealth Effects, and the Price Level

NOVEMBER

1976

inflation tto, but at interest rate i2 instead of ij. The
real rate of interest is lower, ri- The earlier analysis is
complicated by short-run changes in two of its param­
eters: the decline in the real rate of interest, and the
smaller level of real wealth.

i;r + T T

(Mo/P])

(M0/PC>)
PANEL A

i ; r+ T T

The cost of moving along a price path such as
PoAP in Figure V, allowing for the short-run effects of
the reduction in desired real balances, may be found
in a policy context which removes these analytical
complications. The reduction in desired cash balances
can be facilitated by a one-time accommodating mone­
tary policy, rather than the one-time surge in the price
level. An open market sale of bonds in exchange for
the excess cash balances, (m0 — m j) in Panel B, will
leave wealth unaffected.20 The real money supply
falls to mi via a decline in the nominal money supply
rather than a higher price level. Wealth, the price
level, and the real rate of interest will be unchanged.
Since these are the major determinants of the demand
for money, other than the expected rate of inflation,
there will be no shift in the demand for money. The
increase in the rate of monetary growth requires an
open market sale of bonds initially to, in effect, “soak
up” the excess real cash balances which it initially
causes.21 Furthermore, to avoid a wealth effect in the
future from the rising price level, net financial wealth,
the money stock plus the value of debt held by the
public, must grow at the same rate as prices.
The revenue from inflationary finance may also be
more clearly seen in such a conceptual framework.
The open market sale of government bonds by the
central bank increases the real value of government
debt held by the public. From the government’s
viewpoint, the revenue effect of the inflation includes
the additional revenue of the central bank (n m j)
less the real interest payment on the increase in public
debt. Since the increase in the public debt equals
the permanent desired reduction in real money bal­
ances due to the inflation expectation, the revenue
of inflation in Figure II is the area A less area B
[r„ (m„ — mj)].

(M 0 / P ,)

( M0 /P 0 )
PANEL B

nominal rate will not increase by the rate of antici­
pated inflation.
The ultimate effects on the analysis are shown in
Figure IV, Panel B. The demand for real money bal­
ances will shift to the left due to the smaller level of
wealth ( W x) with price level P2. Also the nominal
interest rate will be higher and reflect the rate of

Page 18


20The relevant real wealth variable includes real money bal­
ances, the real value of government debt, and the real value
of capital.
- lrThe effects of inflationary expectations on the price level
and real rate of interest have also been noted by Cathcart,
“Monetary Dynamics,” and Leonardo Auemheimer, “The
Honest Government’s Guide to the Revenue from the Crea­
tion of Money,” Journal o f Political Economy (May/June
1974), pp. 598-606. Auemheimer also pointed out the
importance of the initial open market sales prior to a higher
rate of monetary expansion to avoid the one-time price
surge.

F E D E R A L R E S E R V E B A N K O F ST. L O U IS

F ig u r e V

The Money and Price Path:
From Price Stability to Money Growth
and Expected Inflation at R a t e lT g

N o m in a l
M o n e y S u p p ly (M)
P rice Le v e l (P)
(L o g a rit h m ic S c a le )

NOVEMBER

1976

current dollars, or, with a 5 percent rate of expected
inflation, $15 billion. The area B in Figure II depends
upon the size of the reduction in real money balances
due to a 5 percent rate of inflation and upon the level
of the real rate of return on assets, the nominal in­
terest rate in the absence of inflation. Employing the
earlier estimate of an elasticity of demand of .15, and
either of the two estimates of the real rate of interest
(2 percent or 5 percent), the area of rectangle B is
$2.25 billion. The area (A —B) for a 5 percent rate
of inflation is $12.75 billion, in current dollars.22
The measure of revenue as the area A less area B
is subject to an additional important qualification. Not
all of the money stock is provided through the mone­
tary authority. In fact the stock of money supplied
by the monetary authority, the monetary base, is less
than forty percent of the stock of money. The rela­
tionship between the monetary base and the money
supply is remarkably stable, so the government’s
share of the total stock of money may be defined
as ( sm) where s is the ratio of the monetary base to
the money supply.

The subtraction of area B from the revenue of in­
flation also affects the earlier analysis of the cost of
inflation. Area B remains part of the real value of
lost money services per period. In addition, it repre­
sents the increase in the real value of interest pay­
ments per period due to the larger public held debt.
Therefore, the gross burden or total cost is (A + C).
The analysis in the previous section is little affected
by dropping the long-run perspective. Both the reve­
nue and the total burden of inflation are reduced by
the size of area B. The revenue (A) is reduced to
account for the increased interest payments required
on the larger public debt. The total burden (A -f- B
-j- C ) is reduced because of the receipt by households
of larger annual interest payments on the public debt
represented by area B. Hence, the excess burden or
welfare cost remains the same, area (B -f C) in Fig­
ure II.

The Revenue From Inflationary Finance
The size of the revenue from inflation depends on
the elasticity of demand for real money balances with
respect to the expected rate of inflation. The area A
in Figure II is the rate of inflation times the level of
real money balances, about $300 billion measured in



The base for government revenue from money
creation is not the total money supply, but only the
monetary base. Therefore, the revenue area (A —B)
above must be multiplied by s to present an accurate
estimate of the government revenue from inflationary
finance.23 With an estimate of s of 40 percent, the
government revenue from a 5 percent rate of inflation
is approximately $5.1 billion (.4 x $12.75 billion).
In contrast, the Federal revenues in 1975 from the
corporate income tax and personal income tax were
$42.6 billion and $125.7 billion, respectively. A rate
of inflation of 5 percent appears to be a very costly
method to raise a modest amount of Federal reve­
nue. The welfare cost per dollar of revenue raised
from a monetary policy which yields a 5 percent
actual and expected rate of inflation, using the cost
and revenue figures above, is 80 to 120 cents per
dollar of government income. The welfare costs per
dollar of revenue from the personal income tax and
'-'-In a growing economy, the annual revenue from money
creation is larger since even price stability requires that the
supply of nominal money grow at the rate of growth of
demand for real money balances. This larger revenue grows
at the rate of growth of money demand and the welfare
cost. See footnote 19 above.
'-■''■The remainder of the revenue ( A -B) accrues, through the
banking system, to bank owners and, through competition,
to their depositors. The welfare cost analysis above is not
affected by relaxing the assumption that all money is sup­
plied by the monetary authority. The cost of holding bank
money rises in the same manner as it does for currency.
Page 19

F E D E R A L R E S E R V E B A N K O F ST. L O U I S

the corporate income tax in 1975 were on the order
of three cents per dollar of revenue.

Efficient Taxation and the Optimum Rate
of Inflation
The relevant measure of cost for an efficient tax
system is the marginal cost per dollar of additional
revenue, not the average cost.24 An efficient tax
system raises a given total revenue from various
taxes with a minimum total cost. Therefore, for each
tax, the cost per dollar of revenue must be equated
at the margin. It is difficult to reach definitive con­
clusions concerning the optimum rate of monetary
expansion and inflation without knowledge of the
marginal cost of alternative revenue sources. Unfor­
tunately, this cost for all alternative taxes has not
been estimated. Nevertheless, an upper bound on
the size of such marginal costs has been placed at
10 cents per dollar of government receipt and this
may be used here.25
The marginal welfare cost of inflationary finance
may be written as:
(2)

e"

1

C= ( T ^ ) ( 7 >

-(i

Additional revenue is obtained from a higher rate
of inflation only when the interest elasticity is less
than one; if the interest elasticity rises with the rate
of inflation, maximum revenue from inflation occurs
when e° is equal to one. According to Equation (2),
as e° approaches one, the marginal welfare cost ap­
proaches infinity. Also, Equation (2 ) indicates that
the marginal cost is greater, the greater is the rate
of inflation or interest elasticity of demand for money,
and the smaller is the government’s share of the
money supply. Therefore, the estimates of an interest
elasticity of .15 and share, s, of 40 percent, yield
downward-biased estimates of the marginal welfare
cost of government revenue from money expansion.
a4This point has been emphasized by Alvin C. Marty, “A
Note on the Welfare Cost of Money Creation,” Journal of
Monetary Econom ics (January 1976), pp. 121-24; and in
Edward Tower, “More on the Welfare Cost of Inflationary
Finance,” Journal o f Money, Credit and Banking (Novem­
ber 1971), pp. 850-60; Cathcart, “Monetary Dynamics;”
Phelps, “Inflation;” Barro, “Inflationary Finance.”
- 5See Tower, “More on the Welfare Cost,” p. 856. The esti­
mate of 10 percent is also consistent with the work of
Edgar K. Browning, “The Marginal Cost of Public Funds,”
Journal o f Political Econom y (April 1976), p. 295. He
estimates the marginal cost for the individual income tax,
including administration and compliance costs, to be 9 per­
cent in 1974.
26The derivation of this equation is found in the Appendix
as equation (8 ) , where e° above is the interest rate elas­
ticity of demand for real money balances, given the real
rate of interest.

Page 20


NOVEMBER

1976

The marginal welfare cost in equation (2 ) is con­
stant and equals 44 percent, given the estimates
above. This level is well above the maximum estimate
of the marginal welfare cost of alternative revenues
above. Therefore, efficiency of the tax system does
not warrant inflation or inflationary finance. Addi­
tional revenue, within the relevant range for the
United States may be more cheaply obtained through
other sources of revenue, not through inflation.27

CONCLUSION
In recent years, some economists have argued that
there are benefits to inflation and, if the rate is stable
and can be fully anticipated, there is little or no cost
to society. The cost of perfectly anticipated inflation
is its welfare cost. It results from the loss in welfare
due to the substitution away from real money bal­
ances. While this cost may be small in relation to the
costs of redistributions of income and wealth when
inflation is unanticipated, it is comparable to the wel­
fare costs of other major components of the U. S. tax
system at levels of inflation as low as 5 percent.
Moreover, the size of the welfare cost of inflation
increases rapidly with the size of the rate of inflation
itself. The welfare cost of inflation is independent of
resource costs incurred to economize on cash bal­
ances; indeed, the analysis assumes these costs to be
zero. To the extent that valuable resources are used
to economize on cash holdings, the cost of perfectly
anticipated inflation is even greater.
One of the primary benefits of inflation is the
revenue it produces for the government. It has been
suggested by some analysts that efficient taxation
requires taxing cash balances through inflation. In­
deed, since the demand for money is relatively
insensitive to changes in the cost of holding money,
high rates of inflation, appear to some to be justified
on tax efficiency grounds. It has been shown here
that tax efficiency can not justify a positive rate of
inflation, even employing strong assumptions favoring
the inflationist case.
The “tax efficiency argument” forces the question
of the optimal rate of inflation into the domain of
public finance. The answer depends upon the mar­
27A marginal welfare cost which is constant and above the
marginal cost of alternative revenue actually suggests an
efficient policy of deflation with revenue losses for money
creation being replaced by additional revenue from alterna­
tive taxes. However, it may be expected that the interest
elasticity of demand for money is an increasing function of
the rate of inflation. Therefore, the marginal welfare cost of
revenue from money creation will fall to the 10 percent level
at a small rate of deflation.

F E D E R A L R E S E R V E B A N K O F ST. L O U IS

NOVEMBER

ginal costs of alternative revenue sources. While fur­
ther research on the nature of other taxes is thereby
required, the examination here supports some strong
conclusions. Even if the marginal cost of alternative
sources of revenue is much larger than the level sug­
gested here as an upper bound, tax efficiency offers
no support for inflationary public policy.
The efficiency of the tax system and the revenue
potential of inflation appear to be insignificant argu­
ments in the debate over the “optimum” rate of infla­
tion. Such arguments have considerable theoretical

1976

appeal but, upon close examination, are of little prac­
tical importance. A positive rate of inflation is not
supported by these arguments. Furthermore, the ad­
ditional revenue obtained from a rate of inflation as
high as 5 percent is small relative to the revenue
obtained through money creation with price stability
or relative to the revenue from alternative taxes. The
practical importance of the “tax efficiency argu­
ment” is also limited by existing inefficiencies in the
present tax system as well as the apparent difficulties
of maintaining a steady and fully anticipated rate of
inflation.

APPENDIX
The Efficient Taxation of Money

A general derivation of the welfare cost, revenue, and
marginal cost of inflationary finance may be found which
is independent of the functional form of the demand for
real money balances. T h e revenue from money produc­
tion is:
(1) R = s i m
where s is the ratio of the monetary base to money and
is assumed to b e constant. T h e effect on revenue of a
change in the rate of inflation is:
,n, dR
i <tm , i
(2)—— = s m (1 + ----- — ). 1
an
in fln

T h e marginal cost of inflationary finance, c, is:
(5) c =

d
dW
W, dR
,^
dn dn

dW
dR

- ict>'
(m + icp') s

T h e elasticity of demand for money with respect to the
nominal rate of interest, given th e real rate of interest,
and with respect to the expected rate of inflation are
defined as:
(6) E i = —

(7) E

n

dm

i

3m

3i

in

an

=—

an in

m

= —<
TJ>' —
m and

J L

m,

L et the demand for real money balances be written
as a function of the expected rate of inflation, 0 ( n ) . The
welfare cost of inflation is:

Then the marginal cost, c, may be written alternatively
as:

(3) W =/ q <?) (x) d x - i <(>(n) + r 0 (o)

(8) c =

The effect of an increase in the expected rate of inflation

(4)

dW
= -ic f.
dn

lit is assumed here, as in the text, that the real rate of return
is unaffected by the expectation of inflation or that a one
percentage point rise in the expected rate of inflation adds
one percentage point to the nominal interest rate.



iEn
s(n -i En)

Ei
s (l-E i)

In the usual analysis of the welfare cost of inflation a
special functional form is employed in which the elasti­
city of demand for money with respect to the expected
rate of inflation is an increasing function of the expected
rate of inflation. In particular, it is written as:

(9) E n =bn
where b is a constant. F o r this case, the earlier equations
becom e:
Page 21

NOVEMBER

F E D E R A L R E S E R V E B A N K O F ST. L O U IS

zero to 4 8
for b = 10.
tax system
maximizing

(2' ) - ^ — = s m ( l - i b )
dn

,A
dW
(4 n) ——

1 m l
=b

Since the elasticity of demand for money increases with
the rate of inflation, the demand will becom e elastic with
respect to either the rate of inflation or the nominal inter­
est rate at a sufficiently high rate of inflation. Therefore,
there is a rate of inflation which maximizes revenue, a
higher rate of inflation yields lower revenue from money
production. This maximum rate of inflation (itm u ) may
be found by letting 4 ^ equal zero in equation ( 2 ') .

dn

( 1 0 ) Tlmax —

t------fO

b

T h e marginal cost in
inflation.

( 5 ')

is infinite at this rate of

T h e size of the revenue maximizing rate of inflation
depends upon the value of b and the real rate of interest,
ro. The precise level of b for the United States is un­
known, although some evidence exists on the appropriate
number. A level of 2 is probably far too low and may serve
as a lower bound. Estim ates ranging up to 7 8 have been
made for the U. S. Some illustrative values which have
been cited are: 2, 10, and 2 0 years.2 Together with the
alternative real rates of interest in the text, the revenue
maximizing annual rate of inflation is found to vary from
-See Milton Friedman, “Government Revenue from Inflation,”
Journal o f Political Econom y (July/August 1971), pp. 851-53.


Page 22


1976

percent with the mid-range, 5 to 8 percent,
T h e rate of inflation warranted by an efficient
will be substantially less than the revenue
rate.

T h e marginal welfare cost of revenue from money
creation is larger, according to equation ( 5 ') , the larger
is b, the real rate of interest, or the expected rate of infla­
tion. T h e marginal cost, c, is zero when the nominal
interest rate is zero, that is, when the expected rate of
d eflation equals the real rate of return on capital. The
marginal welfare cost of revenue with price stability may
b e found from equation ( 5 ') by letting the nominal rate
equal the real rate of interest.
Using the levels of b above and the two levels of the
real rate of interest, 5 percent or 2 percent, the marginal
welfare cost ranges from 10 percent to infinity, for
TT = 0. In the smallest case (1 0 p ercen t), th e level of b is
2 years, and r is 2 percent, i.e. the interest rate elasticity
of demand (rb ) is only .04, much less than the elasticity
generally observed. Moreover, this minimum level of the
marginal welfare cost with price stability is equal to the
maximum estimate of the alternative marginal cost cited
in the text. Therefore, under the most extrem e assump­
tions used here to support inflationary finance, efficient
taxation warrants price stability. E ven if the alternative
marginal cost is doubled to 2 0 percent, the warranted
rate of inflation with these assumptions is only about
1.5 percent. For more reasonable assumptions concerning
b and r, efficient taxation would warrant deflation.
T h e “tax efficiency” argument may not b e used to
justify high rates of inflation. In fact, this argument sug­
gests that the warranted rate is negative, but less in
magnitude than the real rate of interest.

F E D E R A L R E S E R V E B A N K O F ST. L O U IS

NOVEMBER

1976

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T IT LE OF ARTICLE

Elements of Money Stock Determination
Monetary and Fiscal Influences on Economic Activity —
The Historical Evidence
The Effects of Inflation (1960-68)
Interest Rates and Price Level Changes, 1952-69
The New, New Economics and Monetary Policy
Some Issues in Monetary Economics
Monetary and Fiscal Influences on Economic Activity: The Foreign Experience
The Administration of Regulation Q
Money Supply and Time Deposits, 1914-69
A Monetarist Model for Economic Stabilization
Neutralization of the Money Stock, and Comment
Federal Open Market Committee Decisions in 1969 —
Year of Monetary Restraint
Metropolitan Area Growth: A Test of Export Base Concepts
Selecting a Monetary Indicator— Evidence from the United States and
Other Developed Countries
The "Crowding Out" of Private Expenditures by Fiscal Policy Actions
Aggregate Price Changes and Price Expectations
The Revised Money Stock: Explanation and Illustrations
Expectations, Money and the Stock Market
Population, The Labor Force, and Potential Output: Implications for
the St. Louis Model
Observations on Stabilization Management
The Implementation Problem of Monetary Policy
Controlling Money in an Open Economy: The German Case
The Year 1970: A “ Modest” Beginning for Monetary Aggregates
Central Banks and the Money Supply
A Monetarist View of Demand Management: The United States Experience
High Employment Without Inflation: On the Attainment of Admirable Goals
Money Stock Control and Its Implications for Monetary Policy
German Banks as Financial Department Stores
Two Critiques of Monetarism
Projecting With the St. Louis Model: A Progress Report
Monetary Expansion and Federal Open Market Committee
Operating Strategy in 1971
Measurement of the Domestic Money Stock
An Appropriate International Currency — Gold, Dollars, or SD Rs
FOMC Policy Actions in 1972
The State of the Monetarist Debate
Commentary: Lawrence R. Klein and Karl Brunner
The Russian Wheat Deal — Hindsight vs. Foresight
A Comparative Static Analysis of Some Monetarist Propositions
Balance-of-Payments Deficits: Measurement and Interpretation
Real Money Balances: A Misleading Indicator of Monetary Actions
The Federal Open Market Committee in 1973
A Primer on the Consumer Price Index
Channels of Monetary Influence: A Survey
A Primer on Inflation: Its Conception, Its Costs, Its Consequences
The FOMC in 1974: Monetary Policy During Economic Uncertainty
A Monetary View of the Balance of Payments
A Monetary Model of Nominal Income Determination
Observed Income Velocity of Money: A Misunderstood Issue in Monetary Policy




ISSU E
October 1969
November 1969
November 1969
December 1969
January 1970
January 1970
February 1970
February 1970
March 1970
April 1970
May 1970
June 1970
July 1970
September 1970
October 1970
November 1970
January 1971
January 1971
February 1971
December 1970
March 1971
April 1971
May 1971
August 1971
September 1971
September 1971
October 1971
November 1971
January 1972
February 1972
March 1972
May 1972
August 1972
March 1973
September 1973
October 1973
December 1973
November 1973
February 1974
April 1974
July 1974
November 1974
January 1975
April 1975
April 1975
June 1975
August 1975

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