The Quantity Theory of Money
The hallmark of classical macroeconomic theory is the separation of real and
nominal variables. This classical dichotomy enables us to examine the behaviour
of the real variables in the economic system while ignoring the nominal
variables. In the stylized classical model we have developed, the quantity of
money is irrelevant for the determination of the real variables. Long-run
money neutrality is a crucial property of the classical model.
To explain the determination of the nominal variables in the system, the
classical economists subscribed to the quantity theory of money. A long line
of famous economists have either contributed to the development of this
theory or have been associated with its policy prescriptions. The list includes
Cantillon, Hume, Ricardo, Mill, Marshall, Fisher, Pigou, Hayek and even
Keynes. More recently the quantity theory of money has been associated with
the development of monetarism and the work of Milton Friedman, perhaps
the most influential economist in the past quarter-century. Although the term
‘monetarism’ did not emerge until 1968 (see Brunner, 1968), its main core
proposition, the quantity theory of money, was well established in classical
macroeconomics following the publication of David Hume’s influential essay,
Of Money, in 1752. Indeed, Mayer (1980) has argued that the salient date
for the birth of monetarist ideas was 1752, since most of the fundamental
propositions which characterize monetarism date back to Hume’s essay. Here
we will present only a short exposition of the quantity theory in order to
complete the classical scheme. For a more detailed discussion, see Laidler
(1991).
The dominant macroeconomic theory prior to the 1930s was the quantity
theory of money. Two highly influential versions of the quantity theory can
be identified in the literature. The first version, associated with Marshall and
Pigou, is known as the Cambridge cash-balance approach. The second version
is associated with Irving Fisher.
The Cambridge economists drew a clear distinction in their version of the
quantity theory between the demand for money (Md) and the supply of
money (M). The demand for money was primarily determined by the need to
conduct transactions which will have a positive relationship to the money
value of aggregate expenditure. Since the latter is equal to money national
income we can represent the Cambridge money demand function as equation
(2.13):
Md = kPY (2.13)
where Md is the demand to hold nominal money balances, and k is the
fraction of the annual value of money national income (PY) that agents (firms
and households) wish to hold. The reader should be aware that the Cambridge
monetary approach did recognize that k could vary in the short run
(see Laidler, 1993) but, in the stylized presentation we consider in equation
(2.13), the coefficient k is assumed to be constant. As it stands, the Cambridge
equation is a theory of the demand for money. In order to explain the
price level we must introduce the supply of money. If we assume that the
supply of money is determined by the monetary authorities (that is, M is
exogenous), then we can write the condition for monetary equilibrium as
equation (2.14):
M = Md (2.14)
Substituting (2.14) into (2.13) we obtain (2.15):
M = kPY (2.15)
To obtain the quantity theory result that changes in the quantity of money
have no real effects in the long run but will determine the price level, we
simply need to remember from our earlier discussion that Y is predetermined
at its full employment value by the production function and the operation of a
competitive labour market. With k and Y constant, M determines P. If the
money market is initially in equilibrium, then an increase in the money
supply creates disequilibrium (M > Md). Since the values of Y and k are fixed,
equilibrium in the money market can only be restored if the price level rises.
The reason why prices rise in the classical model is that, if households and
firms find themselves holding more money than they desire, the excess money
balances are used to purchase goods and services. Since the supply of goods
and services is constrained by the predetermined full employment level of
output, excess demand in the goods market causes the general price level to
rise in proportion to the initial increase in the money supply.
The second approach uses the income version of Fisher’s equation of
exchange. This relationship is given by equation (2.16):
MV = PY (2.16)
where V is the income velocity of circulation of money and represents the
average number of times a unit of money is used in the course of conducting
final transactions which constitute nominal GDP. Since V can be defined as
the reciprocal of k, the constancy of V can be justified because institutional
factors which determine the frequency of the transactions carried out by
agents are likely to change slowly over time. That V is the reciprocal of k can
be seen by comparing (2.15) with (2.16) and noting that both V and 1/k equal
PY/M. That the price level is dependent on the nominal money supply is
clearly brought out if we examine equation (2.17), which rearranges (2.16):
P = MV / Y (2.17)
With V and Y constant, it is easy to see that P depends on M and that ΔM
equals ΔP.
To see how the price level is determined in the classical model and how
real output, real wages and employment are invariant to the quantity of
money, consider Figure 2.4. In quadrants (a) and (b) we reproduce Figure 2.2.
Here a competitive labour market generates equilibrium employment of L0
and an equilibrium real wage of W0/P0. From the production function we can
see that full employment in this model leads to an output of Y0. In quadrant
(c) we have the classical aggregate demand (AD) and aggregate supply (AS)
functions. The AS function is perfectly inelastic, indicating that real output is
invariant to the general price level. The classical AD curve is derived from
equation (2.16). With a constant supply of money (for example, M0) and V
constant, a higher price level must be associated with a lower level of real
output. AD0(M0) shows how, for a given money supply, MV can be split up
among an infinite number of combinations of P and Y. Since we have assumed
V is fixed, the nominal value of all transactions in the economy is
determined by the supply of money. With higher prices each transaction
requires more units of currency and therefore the quantity of goods and
services that can be bought must fall. Since the AD curve is drawn for a given
quantity of money, an increase in the money supply will shift the AD curve to
the right, as shown by AD1(M1). Finally, in quadrant (d) we show the relationship
between the real wage and the price level for a given nominal wage. If
the nominal wage is W0 then a higher price level will reduce the real wage.
Let us assume that the initial equilibrium values in the model associated
with the quantity of money M0 are Y0, W0/P0, and L0. Suppose the monetary
Figure 2.4 The determination of the price level in the classical model
authorities increase the supply of money to M1 in an attempt to increase real
output and employment. We can see that such a policy will be completely
ineffectual in the classical model. The increase in the quantity of money, by
creating disequilibrium in the money market (Md < M), will lead to an
increase in the demand for goods and services. Since Y is constrained at Y0 by
labour market equilibrium employment (L0), prices rise to P1. For a given
nominal wage of W0, an increase in the price level lowers the real wage and
creates disequilibrium in the labour market. An excess demand for labour of
ZX emerges at a real wage of W0/P1. Competitive bidding by employers will
drive the nominal wage up until it reaches a value of W1, which restores the
real wage to its equilibrium value (that is, W0/P0 = W1/P1). Irving Fisher
(1907) also demonstrated how monetary expansion would raise the nominal
rate of interest through the ‘Fisher effect’. In the classical model, the real
interest rate adjusts to equate saving and investment in the loanable funds
market. Since the real rate of interest is equal to the nominal interest rate
minus the inflation rate and is determined by the real forces of productivity
and thrift, the nominal rate of interest will adjust to reflect the influence of
variations in both the real interest rate and the rate of inflation. Monetary
expansion, by raising the rate of inflation, will also raise the nominal interest
rate. To summarize, the end result of a monetary expansion is that the price
level, nominal wages and the nominal interest rate will increase but all the
real values in the system remain unaffected (that is, money is neutral). In the
language of David Hume (1752), ‘’tis evident that the greater or less plenty
of money is of no consequence since the prices of commodities are always
proportional to the plenty of money’.
Before moving on to examine Keynes’s objections to the classical model
we should note that the stylized version of the quantity theory presented
above does not do justice to the complexities and sophistication of the theories
developed by pre-Keynesian economists working in the quantity theory
tradition. Classical economists such as Ricardo were concerned with longrun
equilibrium states and utilized a comparative-static method of analysis in
order to compare one equilibrium state with another. Some classical economists
were well aware that the neutrality of money proposition would not
hold in the short run (see Corry, 1962). Indeed, Ralph Hawtrey, who strayed
from the classical nest even earlier than Keynes, throughout his career advocated
a purely monetary theory of the business cycle where money was far
from neutral in the short run (see Haberler, 1963; Deutscher, 1990). But
viewed from the vantage point of the early 1930s, during the depths of the
Great Depression, the Ricardian long-run equilibrium might just as well have
been located on Mars. In his Tract on Monetary Reform (1923), Keynes
declared, ‘In the long run we are all dead. Economists set themselves too
easy, too useless a task if in tempestuous seasons they can only tell us that
when the storm is long past the ocean is flat again.’ We now turn to consider
Keynes’s objections to classical theory, which culminated in the publication
of his most influential book in 1936.
The hallmark of classical macroeconomic theory is the separation of real and
nominal variables. This classical dichotomy enables us to examine the behaviour
of the real variables in the economic system while ignoring the nominal
variables. In the stylized classical model we have developed, the quantity of
money is irrelevant for the determination of the real variables. Long-run
money neutrality is a crucial property of the classical model.
To explain the determination of the nominal variables in the system, the
classical economists subscribed to the quantity theory of money. A long line
of famous economists have either contributed to the development of this
theory or have been associated with its policy prescriptions. The list includes
Cantillon, Hume, Ricardo, Mill, Marshall, Fisher, Pigou, Hayek and even
Keynes. More recently the quantity theory of money has been associated with
the development of monetarism and the work of Milton Friedman, perhaps
the most influential economist in the past quarter-century. Although the term
‘monetarism’ did not emerge until 1968 (see Brunner, 1968), its main core
proposition, the quantity theory of money, was well established in classical
macroeconomics following the publication of David Hume’s influential essay,
Of Money, in 1752. Indeed, Mayer (1980) has argued that the salient date
for the birth of monetarist ideas was 1752, since most of the fundamental
propositions which characterize monetarism date back to Hume’s essay. Here
we will present only a short exposition of the quantity theory in order to
complete the classical scheme. For a more detailed discussion, see Laidler
(1991).
The dominant macroeconomic theory prior to the 1930s was the quantity
theory of money. Two highly influential versions of the quantity theory can
be identified in the literature. The first version, associated with Marshall and
Pigou, is known as the Cambridge cash-balance approach. The second version
is associated with Irving Fisher.
The Cambridge economists drew a clear distinction in their version of the
quantity theory between the demand for money (Md) and the supply of
money (M). The demand for money was primarily determined by the need to
conduct transactions which will have a positive relationship to the money
value of aggregate expenditure. Since the latter is equal to money national
income we can represent the Cambridge money demand function as equation
(2.13):
Md = kPY (2.13)
where Md is the demand to hold nominal money balances, and k is the
fraction of the annual value of money national income (PY) that agents (firms
and households) wish to hold. The reader should be aware that the Cambridge
monetary approach did recognize that k could vary in the short run
(see Laidler, 1993) but, in the stylized presentation we consider in equation
(2.13), the coefficient k is assumed to be constant. As it stands, the Cambridge
equation is a theory of the demand for money. In order to explain the
price level we must introduce the supply of money. If we assume that the
supply of money is determined by the monetary authorities (that is, M is
exogenous), then we can write the condition for monetary equilibrium as
equation (2.14):
M = Md (2.14)
Substituting (2.14) into (2.13) we obtain (2.15):
M = kPY (2.15)
To obtain the quantity theory result that changes in the quantity of money
have no real effects in the long run but will determine the price level, we
simply need to remember from our earlier discussion that Y is predetermined
at its full employment value by the production function and the operation of a
competitive labour market. With k and Y constant, M determines P. If the
money market is initially in equilibrium, then an increase in the money
supply creates disequilibrium (M > Md). Since the values of Y and k are fixed,
equilibrium in the money market can only be restored if the price level rises.
The reason why prices rise in the classical model is that, if households and
firms find themselves holding more money than they desire, the excess money
balances are used to purchase goods and services. Since the supply of goods
and services is constrained by the predetermined full employment level of
output, excess demand in the goods market causes the general price level to
rise in proportion to the initial increase in the money supply.
The second approach uses the income version of Fisher’s equation of
exchange. This relationship is given by equation (2.16):
MV = PY (2.16)
where V is the income velocity of circulation of money and represents the
average number of times a unit of money is used in the course of conducting
final transactions which constitute nominal GDP. Since V can be defined as
the reciprocal of k, the constancy of V can be justified because institutional
factors which determine the frequency of the transactions carried out by
agents are likely to change slowly over time. That V is the reciprocal of k can
be seen by comparing (2.15) with (2.16) and noting that both V and 1/k equal
PY/M. That the price level is dependent on the nominal money supply is
clearly brought out if we examine equation (2.17), which rearranges (2.16):
P = MV / Y (2.17)
With V and Y constant, it is easy to see that P depends on M and that ΔM
equals ΔP.
To see how the price level is determined in the classical model and how
real output, real wages and employment are invariant to the quantity of
money, consider Figure 2.4. In quadrants (a) and (b) we reproduce Figure 2.2.
Here a competitive labour market generates equilibrium employment of L0
and an equilibrium real wage of W0/P0. From the production function we can
see that full employment in this model leads to an output of Y0. In quadrant
(c) we have the classical aggregate demand (AD) and aggregate supply (AS)
functions. The AS function is perfectly inelastic, indicating that real output is
invariant to the general price level. The classical AD curve is derived from
equation (2.16). With a constant supply of money (for example, M0) and V
constant, a higher price level must be associated with a lower level of real
output. AD0(M0) shows how, for a given money supply, MV can be split up
among an infinite number of combinations of P and Y. Since we have assumed
V is fixed, the nominal value of all transactions in the economy is
determined by the supply of money. With higher prices each transaction
requires more units of currency and therefore the quantity of goods and
services that can be bought must fall. Since the AD curve is drawn for a given
quantity of money, an increase in the money supply will shift the AD curve to
the right, as shown by AD1(M1). Finally, in quadrant (d) we show the relationship
between the real wage and the price level for a given nominal wage. If
the nominal wage is W0 then a higher price level will reduce the real wage.
Let us assume that the initial equilibrium values in the model associated
with the quantity of money M0 are Y0, W0/P0, and L0. Suppose the monetary
Figure 2.4 The determination of the price level in the classical model
authorities increase the supply of money to M1 in an attempt to increase real
output and employment. We can see that such a policy will be completely
ineffectual in the classical model. The increase in the quantity of money, by
creating disequilibrium in the money market (Md < M), will lead to an
increase in the demand for goods and services. Since Y is constrained at Y0 by
labour market equilibrium employment (L0), prices rise to P1. For a given
nominal wage of W0, an increase in the price level lowers the real wage and
creates disequilibrium in the labour market. An excess demand for labour of
ZX emerges at a real wage of W0/P1. Competitive bidding by employers will
drive the nominal wage up until it reaches a value of W1, which restores the
real wage to its equilibrium value (that is, W0/P0 = W1/P1). Irving Fisher
(1907) also demonstrated how monetary expansion would raise the nominal
rate of interest through the ‘Fisher effect’. In the classical model, the real
interest rate adjusts to equate saving and investment in the loanable funds
market. Since the real rate of interest is equal to the nominal interest rate
minus the inflation rate and is determined by the real forces of productivity
and thrift, the nominal rate of interest will adjust to reflect the influence of
variations in both the real interest rate and the rate of inflation. Monetary
expansion, by raising the rate of inflation, will also raise the nominal interest
rate. To summarize, the end result of a monetary expansion is that the price
level, nominal wages and the nominal interest rate will increase but all the
real values in the system remain unaffected (that is, money is neutral). In the
language of David Hume (1752), ‘’tis evident that the greater or less plenty
of money is of no consequence since the prices of commodities are always
proportional to the plenty of money’.
Before moving on to examine Keynes’s objections to the classical model
we should note that the stylized version of the quantity theory presented
above does not do justice to the complexities and sophistication of the theories
developed by pre-Keynesian economists working in the quantity theory
tradition. Classical economists such as Ricardo were concerned with longrun
equilibrium states and utilized a comparative-static method of analysis in
order to compare one equilibrium state with another. Some classical economists
were well aware that the neutrality of money proposition would not
hold in the short run (see Corry, 1962). Indeed, Ralph Hawtrey, who strayed
from the classical nest even earlier than Keynes, throughout his career advocated
a purely monetary theory of the business cycle where money was far
from neutral in the short run (see Haberler, 1963; Deutscher, 1990). But
viewed from the vantage point of the early 1930s, during the depths of the
Great Depression, the Ricardian long-run equilibrium might just as well have
been located on Mars. In his Tract on Monetary Reform (1923), Keynes
declared, ‘In the long run we are all dead. Economists set themselves too
easy, too useless a task if in tempestuous seasons they can only tell us that
when the storm is long past the ocean is flat again.’ We now turn to consider
Keynes’s objections to classical theory, which culminated in the publication
of his most influential book in 1936.
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