# 2.5 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 M

equals P.

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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