Fisher’s Quantity Theory of Money: Equation,

Example, Assumptions and Criticisms.

In this article we will discuss about:- 1. Fisher‟s Equation of Exchange 2. Assumptions of Fisher‟s Quantity
Theory 3. Conclusions 4. Criticisms 5. Merits 6. Implications 7. Examples.

Fisher’s Equation of Exchange:

The transactions version of the quantity theory of money was provided by the American economist Irving
Fisher in his book- The Purchasing Power of Money (1911). According to Fisher, “Other things remaining
unchanged, as the quantity of money in circulation increases, the price level also increases in direct
proportion and the value of money decreases and vice versa”.
Fisher’s quantity theory is best explained with the help of his famous equation of exchange:

MV = PT or P = MV/T
Like other commodities, the value of money or the price level is also determined by the demand and
supply of money.
i. Supply of Money:
The supply of money consists of the quantity of money in existence (M) multiplied by the number of times
this money changes hands, i.e., the velocity of money (V). In Fisher‟s equation, V is the transactions
velocity of money which means the average number of times a unit of money turns over or changes hands
to effectuate transactions during a period of time.

Thus, MV refers to the total volume of money in circulation during a period of time. Since money is only
to be used for transaction purposes, total supply of money also forms the total value of money
expenditures in all transactions in the economy during a period of time.
ii. Demand for Money:
Money is demanded not for its own sake (i.e., for hoarding it), but for transaction purposes. The demand
for money is equal to the total market value of all goods and services transacted. It is obtained by
multiplying total amount of things (T) by average price level (P).
Thus, Fisher‟s equation of exchange represents equality between the supply of money or the total value of
money expenditures in all transactions and the demand for money or the total value of all items
transacted.
Supply of money = Demand for Money
Or
Total value of money expenditures in all transactions = Total value of all items transacted
MV = PT
or
P = MV/T
Where,
M is the quantity of money
V is the transaction velocity

P is the price level.

T is the total goods and services transacted.
The equation of exchange is an identity equation, i.e., MV is identically equal to PT (or MV = PT). It
means that in the ex-post or factual sense, the equation must always be true. The equation states the fact
that the actual total value of all money expenditures (MV) always equals the actual total value of all items
sold (PT).
What is spent for purchases (MV) and what is received for sale (PT) are always equal; what someone
spends must be received by someone. In this sense, the equation of exchange is not a theory but rather a
truism.

Irving Fisher used the equation of exchange to develop the classical quantity theory of money, i.e., a
causal relationship between the money supply and the price level. On the assumptions that, in the long
run, under full-employment conditions, total output (T) does not change and the transactions velocity of
money (V) is stable, Fisher was able to demonstrate a causal relationship between money supply and price
level.
In this way, Fisher concludes, “… the level of price varies directly with the quantity of money in circulation
provided the velocity of circulation of that money and the volume of trade which it is obliged to perform
are not changed”. Thus, the classical quantity theory of money states that V and T being unchanged,
changes in money cause direct and proportional changes in the price level.
Irving Fisher further extended the equation of exchange so as to include demand (bank) deposits (M‟) and
their velocity, (V‟) in the total supply of money.
Thus, the equation of exchange becomes:
Thus, according to Fisher, the level of general prices (P) depends exclusively on five
definite factors:
(a) The volume of money in circulation (M);
(b) Its velocity of circulation (V) ;
(c) The volume of bank deposits (M‟);
(d) Its velocity of circulation (V‟); and
ADVERTISEMENTS:

(e) The volume of trade (T).

The transactions approach to the quantity theory of money maintains that, other things remaining the
same, i.e., if V, M‟, V‟, and T remain unchanged, there exists a direct and proportional relation between M
and P; if the quantity of money is doubled, the price level will also be doubled and the value of money
halved; if the quantity of money is halved, the price level will also be halved and the value of money
doubled.
Example:
Fisher‟s quantity theory of money can be explained with the help of an example. Suppose M = Rs. 1000.
M‟ = Rs. 500, V = 3, V‟ = 2, T = 4000 goods.
Thus, when money supply in doubled, i.e., increases from Rs. 4000 to 8000, the price level is doubled.
i.e., from Re. 1 per good to Rs. 2 per good and the value of money is halved, i.e., from 1 to 1/2.

Thus, when money supply is halved, i.e., decreases from Rs. 4000 to 2000, the price level is halved, i.e.,
from 1 to 1/2, and the value of money is doubled, i.e., from 1 to 2.
The effects of a change in money supply on the price level and the value of money are
graphically shown in Figure 1-A and B respectively:
(i) In Figure 1-A, when the money supply is doubled from OM to OM1, the price level is also doubled from
OP to OP1. When the money supply is halved from OM to OM2, the price level is halved from OP to OP2.
Price curve, P = f(M), is a 45° line showing a direct proportional relationship between the money supply
and the price level.
(ii) In Figure 1-B, when the money supply is doubled from OM to OM1; the value of money is halved from
O1/P to O1/P1 and when the money supply is halved from OM to OM2, the value of money is doubled from
O1/P to O1/P2. The value of money curve, 1/P = f (M) is a rectangular hyperbola curve showing an inverse
proportional relationship between the money supply and the value of money.
Assumptions of Fisher’s Quantity Theory:
Fisher’s transactions approach to the quantity theory of money is based on the following
assumptions:
ADVERTISEMENTS:

1. Constant Velocity of Money:

According to Fisher, the velocity of money (V) is constant and is not influenced by the changes in the
quantity of money. The velocity of money depends upon exogenous factors like population, trade
activities, habits of the people, interest rate, etc. These factors are relatively stable and change very slowly
over time. Thus, V tends to remain constant so that any change in supply of money (M) will have no effect
on the velocity of money (V).
2. Constant Volume of Trade or Transactions:
Total volume of trade or transactions (T) is also assumed to be constant and is not affected by changes in
the quantity of money. T is viewed as independently determined by factors like natural resources,
technological development, population, etc., which are outside the equation and change slowly over time.
Thus, any change in the supply of money (M) will have no effect on T. Constancy of T also means full
employment of resources in the economy.
3. Price Level is a Passive Factor:
According to Fisher the price level (P) is a passive factor which means that the price level is affected by
other factors of equation, but it does not affect them. P is the effect and not the cause in Fisher‟s equation.
An increase in M and V will raise the price level. Similarly, an increase in T will reduce the price level.
ADVERTISEMENTS:

4. Money is a Medium of Exchange:

The quantity theory of money assumed money only as a medium of exchange. Money facilitates the
transactions. It is not hoarded or held for speculative purposes.
5. Constant Relation between M and M’:
Fisher assumes a proportional relationship between currency money (M) and bank money (M‟). Bank
money depends upon the credit creation by the commercial banks which, in turn, are a function of the
currency money (M). Thus, the ratio of M‟ to M remains constant and the inclusion of M‟ in the equation
does not disturb the quantitative relation between quantity of money (M) and the price level (P).
6. Long Period:
The theory is based on the assumption of long period. Over a long period of time, V and T are considered
constant.
Thus, when M‟, V, V‟ and T in the equation MV + M‟Y‟ = PT are constant over time and P is a passive
factor, it becomes clear, that a change in the money supply (M) will lead to a direct and proportionate
change in the price level (P).
Broad Conclusions of Fisher’s Quantity Theory:
(i) The general price level in a country is determined by the supply of and the demand for money.
(ii) Given the demand for money, changes in money supply lead to proportional changes in the price level.
(iii) Since money is only a medium of exchange, changes in the money supply change absolute (nominal),
and not relative (real), prices and thus leave the real variables such as employment and output unaltered.
Money is neutral.
(iv) Under the equilibrium conditions of full employment, the role of monetary (or fiscal) policy is limited.
(v) During the temporary disequilibrium period of adjustment, an appropriate monetary policy can
stabilise the economy.
(vi) The monetary authorities, by changing the supply of money, can influence and control the price level
and the level of economic activity of the country.
Criticisms of Quantity Theory of Money:
The quantity theory of money as developed by Fisher has been criticised on the following
grounds:
1. Interdependence of Variables:
The various variables in transactions equation are not independent as assumed by the
quantity theorists:
(i) M Influences V – As money supply increases, the prices will increase. Fearing further rise in price in
future, people increase their purchases of goods and services. Thus, velocity of money (V) increases with
the increase in the money supply (M).
(ii) M Influences V‟ – When money supply (M) increases, the velocity of credit money (V‟) also increases.
As prices increase because of an increase in money supply, the use of credit money also increases. This
increases the velocity of credit money (V‟).
(iii) P Influences T – Fisher assumes price level (P) as a passive factor having no effect on trade (T). But,
in reality, rising prices increase profits and thus promote business and trade.
(iv) P Influences M – According to the quantity theory of money, changes in money supply (M) is the
cause and changes in the price level (P) is the effect. But, critics maintain that a change in the price level
occurs independently and this later on influences money supply.
(v) T Influences V – If there is an increase in the volume of trade (T), it will definitely increase the velocity
of money (V).
(vi) T Influences M – During prosperity growing volume of trade (T) may lead to an increase in the money
supply (M), without altering the prices.
(vii) M and T are not Independent – According to Keynes, output remains constant only under the
condition of full employment. But, in reality less-than-full employment prevails and an increase in the
money supply increases output (T) and employment.
2. Unrealistic Assumption of Long Period:
The quantity theory of money has been criticised on the ground that it provides a long-term analysis of
value of money. It throws no light on the short-run problems. Keynes has aptly remarked that “in the
long-run we are all dead”. Actual problems are short-run problems. Thus, quantity theory has no practical
value.
3. Unrealistic Assumption of full Employment:
Keynes‟ fundamental criticism of the quantity theory of money was based upon its unrealistic assumption
of fall employment. Full employment is a rare phenomenon in the actual world. In a modern capitalist
economy, less than full employment and not full employment is a normal feature. According to Keynes, as
long as there is unemployment, every increase in money supply leads to a proportionate increase in
output, thus leaving the price level unaffected.
4. Static Theory:
The quantity theory assumes that the values of V, V‟, M‟ and T remain constant. But, in reality, these
variables do not remain constant. The assumption of constancy of these factors makes the theory a static
theory and renders it inapplicable in the dynamic world.
5. Simple Truism:
The equation of exchange (MV = PT) is a mere truism and proves nothing. It is simply a factual statement
which reveals that the amount of money paid in exchange for goods and services (MV) is equal to the
market value of goods and services received (PT), or, in other words, the total money expenditure made by
the buyers of commodities is equal to the total money receipts of the sellers of the commodities. The
equation does not tell anything about the causal relationship between money and prices; it does not
indicate which the cause is and which is the effect.
6. Technically Inconsistent:
Prof. Halm considers the equation of exchange as technically inconsistent. M in the equation is a stock
concept; it refers to the stock of money at a point of time. V, on the other hand, is a flow concept, it refers
to velocity of circulation of money over a period of time, M and V are non-comparable factors and cannot
be multiplied together. Hence the left-hand side of the equation MV = PT is inconsistent.
7. Fails to Explain Trade Cycles:
The quantity theory does not explain the cyclical fluctuations in prices. It does not tell why during
depression the prices fall even with the increase in the quantity of money and during the boom period the
prices continue to rise at a faster rate in spite of the adoption of tight money and credit policy.
The proper explanation for the decline.in prices during depression is the fall in the velocity of money and
for the rise in prices during boom period is the increase in the velocity of money. Thus, the quantity theory
of money fails to explain the trade cycles. Crowther has remarked, “The quantity theory is at best, an
imperfect guide to the causes of the cycle.”
8. Ignores Other Determinants of Price Level:
The quantity theory maintains that price level is determined by the factors included in the equation of
exchange, i.e. by M, V and T, and unrealistically establishes a direct and proportionate relationship
between the quantity of money and the price level. It ignores the importance of many other determinates
of prices, such as income, expenditure, investment, saving, consumption, population, etc.
9. Fails to Integrate Monetary Theory with Price Theory:
The classical quantity theory falsely separates the theory of value from the theory of money. Money is
considered neutral and changes in money supply are believed to affect the absolute prices and not relative
prices. Keynes criticises this view and maintains that money plays an active role and both the theory of
money and the theory of value are essential parts of the general theory of output, employment and money.
He integrated the two theories through the rate of interest.
10. Money as a Store of Value Ignored:
The quantity theory of money considers money only as a medium of exchange and completely ignores its
importance as a store of value. Keynes recognised the stores of value function of money and laid emphasis
on the demand for money for speculative purpose as against the classical emphasis on the transactions
and precautionary demand for money.
11. No Discussion of Velocity of Money:
The quantity theory of money does not discuss the concept of velocity of circulation of money, nor does it
throw light on the factors influencing it. It regards the velocity of money to be constant and thus ignores
the variation in the velocity of money which are bound to occur in the long period.
12. One-Sided Theory:
Fisher‟s transactions approach is one- sided. It takes into consideration only the supply of money and its
effects and assumes the demand for money to be constant. It ignores the role of demand for money in
causing changes in the value of money.
13. No Direct and Proportionate Relation between M and P:
Keynes criticised the classical quantity theory of money on the ground that there is no direct and
proportionate relationship between the quantity of money (M) and the price level (P). A change in the
quantity of money influences prices indirectly through its effects on the rate of interest, investment and
output.
The effect on prices is also not predictable and proportionate. It all depends upon the nature of the
liquidity preference function, the investment function and the consumption function. The quantity theory
does not explain the process of causation between M and P.
14. A Redundant Theory:
The critics regard the quantity theory as redundant and unnecessary. In fact, there is no need of a
separate theory of money. Like all other commodities, the value of money is also determined by the forces
of demand and supply of money. Thus, the general theory of value which explains the value determination
of a commodity can also be extended to explain the value of money.
15. Crowther’s Criticism:
Prof. Crowther has criticised the quantity theory of money on the ground that it explains only „how it
works‟ of the fluctuations in the value of money and does not explain „why it works‟ of these fluctuations.
As he says, “The quantity theory can explain the „how it works‟ of fluctuations in the value of money… but
it cannot explain the „why it works‟, except in the long period”.
Merits of Quantity Theory of Money:
Despite many drawbacks, the quantity theory of money has its merits:
1. Correct in Broader Sense:
It is true that in its strict mathematical sense (i.e., a change in money supply causes a direct and
proportionate change in prices), the quantity theory may be wrong and has been rejected both
theoretically and empirically. But, in the broader sense, the theory provides an important clue to the
fluctuations in prices. Nobody can deny the fact that most of the changes in the prices of the commodities
are due to changes in the quantity of money.
2. Validity of the Theory:
Till 1930s, the quantity theory of money was used by the economists and policy makers to explain the
changes in the general price level and to form the basis of monetary policy. A number of historical
instances like hyper- inflation in Germany in 1923-24 and in China in 1947-48 have proved the validity of
the theory. In these cases large issues of money pushed up prices.
3. Basis of Monetary Policy:
The theory forms the basis of the monetary policy. Various instruments of credit control, like the bank
rate and open market operations, presume that large supply of money leads to higher prices. Cheap
money policy is advocated during depression to raise prices.
4. Revival of Quantity Theory:
In the recent times, the monetarists have revived the classical quantity theory of money. Milton Friedman,
the leading monetarist, is of the view that the quantity theory was not given full chance to fight the great
depression 1929-33; there should have been the expansion of credit or money or both.
He believes that the present inflationary rise in prices in most of the countries of the world is because of
expansion of money supply much more than the expansion in real income. The proper monetary policy is
to allow the money supply to grow in line with the growth in the country‟s output.
Implications of Quantity Theory of Money:
Various theoretical and policy implications of the quantity theory of money are given
below:
1. Proportionality of Money and Prices:
The quantity theory of money leads to the conclusion that the general level of prices varies directly and
proportionately with the stock of money, i.e., for every percentage increase in the money stock, there will
be an equal percentage increase in the price level. This is possible in an economy – (a) whose internal
mechanism is capable of generating a full-employment level of output, and (b) in which individuals
maintain a fixed ratio between their money holdings and money value of their transactions.
2. Neutrality of Money:
The quantity theory of money justifies the classical belief that money is neutral‟ or „money is a veil‟ or
„money does not matter‟. It implies that changes in the money supply are neutral in the sense that they
affect the absolute prices and not the relative prices. Since, consumer spending and business spending
decisions depend upon relative prices; changes in the money supply do not affect real variables such as
employment and output. Thus, money is neutral.
3. Dichotomisation of the Price Process:
The quantity theory also justifies the dichotomisation of the price process by the classical economists into
its real and monetary aspects. The relative (or real) prices are determined in the commodity markets and
the absolute (or nominal) prices in the money market. Since money is neutral and changes in money
supply affect only the monetary and not the real phenomena, the classical economists developed the
theory of employment and output entirely in real terms and separated it from their monetary theory of
absolute prices.
4. Monetary Theory of Prices:
The quantity theory of money upholds the view that the general level of prices is mainly a monetary
phenomenon. The non-monetary factors, like taxes, prices of imported goods, industrial structure, etc., do
not have lasting influence on the price level. These factors may raise the prices in the short run, but this
price rise will reduce actual money balances below their desired level. This will lead to fall in money
spending and a consequent fall in the price level until the original price is restored.
5. Role of Monetary Policy:
In a self-adjusting free-market economy in which changes in money supply do not affect the real macro
variables of employment and output, there is little room left for a monetary policy. But the classical
economists recognised the existence of frictional unemployment which represents temporary
disequilibrium situation.
Such a situation arises when wages and prices are rigid downward. To me such a situation of
unemployment, the classical economists advocated a stabilising monetary policy of increasing money
supply. An increase in the money supply increases total spending and the general price level.
Wage will rise less rapidly (or relative wages will fall) in the labour surplus areas, thereby reducing
unemployment Thus, through a judicious use of monetary policy, the time lag between disequilibrium and
adjustment can shortened; or, in the case of frictional unemployment, the duration of unemployment can
be reduce. Thus, the classical economists assigned a modest stabilising role to monetary policy to deal
with the disequilibrium situation.