The reader will recall that in the classical model, consumption, saving and

investment are all functions of the interest rate “ see equations (2.10) and

(2.11). In Keynes™s model, consumption expenditure is endogenous and es-

sentially passive, depending as it does on income rather than the interest rate.

Keynes™s theory of the consumption function develops this relationship.

Investment expenditure depends on the expected pro¬tability of investment

and the interest rate which represents the cost of borrowing funds. Keynes

called expected pro¬ts the ˜marginal ef¬ciency of capital™. Thus, unavoid-

ably, in Keynes™s model employment becomes dependent on an unstable

factor, investment expenditure, which is liable to wide and sudden ¬‚uctua-

tions. The dependence of output and employment on investment would not be

so important if investment expenditure were stable from year to year. Unfor-

tunately the investment decision is a dif¬cult one because machinery and

buildings are bought now to produce goods that will be sold in a future that is

inevitably uncertain. Expectations about future levels of demand and costs

are involved in the calculation, allowing hopes and fears, as well as hard

facts, to in¬‚uence the decision. Given the volatility of expectations, often

driven by ˜animal spirits™, the expected pro¬tability of capital must also be

highly unstable. That investment decisions could be in¬‚uenced by tides of

irrational optimism and pessimism, causing large swings in the state of busi-

ness con¬dence, led Keynes to question the ef¬cacy of interest rate adjustments

as a way of in¬‚uencing the volume of investment. Expectations of the future

pro¬tability of investment are far more important than the rate of interest in

linking the future with the present because: ˜given the psychology of the

public, the level of output and employment as a whole depends on the

amount of investment™, and ˜it is those factors which determine the rate of

investment which are most unreliable, since it is they which are in¬‚uenced by

our views of the future about which we know so little™ (Keynes, 1937).

The ˜extreme precariousness™ of a ¬rm™s knowledge concerning the pro-

spective yield of an investment decision lies at the heart of Keynes™s explanation

of the business cycle. In his analysis of instability, ˜violent ¬‚uctuations™ in the

marginal ef¬ciency of capital form the shocks which shift real aggregate

demand; that is, the main source of economic ¬‚uctuations comes from the

real side of the economy, as described by the IS curve; see Chapter 3, section

3.3.1. From his analysis of the consumption function Keynes developed the

concept of the marginal propensity to consume which plays a crucial role in

60 Modern macroeconomics

determining the size of the multiplier. Because of the multiplier any distur-

bance to investment expenditure will have a magni¬ed impact on aggregate

output. This can be shown quite easily as follows. Letting c equal the mar-

ginal propensity to consume (∆C/∆Y) and a equal autonomous consumption,

we can write the behavioural equation for consumption as (2.19):

C = a + cY (2.19)

Remember in Keynes™s model the amount of aggregate consumption is (mainly)

dependent on the amount of aggregate income. Substituting (2.19) into (2.18)

we get the equilibrium condition given by (2.20):

Y = a + cY + I (2.20)

Since Y “ cY = a + I and Y “ cY = Y(1 “ c), we obtain the familiar reduced-

form equation (2.21):

Y = ( a + I ) /(1 ’ c) (2.21)

where 1/1 “ c represents the multiplier. Letting κ symbolize the multiplier,

we can rewrite equation (2.21) as Y = (a + I)κ. It follows that for a given

change in investment expenditure (∆I):

∆Y = ∆Iκ (2.22)

Equation (2.22) tells us that income (output) changes by a multiple of the

change in investment expenditure. Keynes de¬nes the investment multiplier

(κ) as the ratio of a change in income to a change in autonomous expenditure

which brought it about: ˜when there is an increment of aggregate investment,

income will increase by an amount which is κ times the increment in invest-

ment™ (Keynes, 1936, p. 115).

Ceteris paribus the multiplier will be larger the smaller the marginal pro-

pensity to save. Therefore the size of the multiplier will depend on the value

of c, and 1 > c > 0. The multiplier effect shows that for an autonomous

demand shift (∆I) income will initially rise by an equivalent amount. But this

rise in income in turn raises consumption by c∆I. The second-round increase

in income again raises expenditure by c(c∆I), which further raises expendi-

ture and income. So what we have here is an in¬nite geometric series such

that the full effect of an autonomous change in demand on output is given by

(2.23):

∆Y = ∆I + c∆I + c 2 ∆I + = ∆I (1 + c + c 2 + c 3 + ¦) (2.23)

Keynes v. the ˜old™ classical model 61

and (1 + c + c2 + c3 + ¦) = 1/1 “ c. Throughout the above analysis it is

assumed that we are talking about an economy with spare capacity where

¬rms are able to respond to extra demand by producing more output. Since

more output requires more labour input, the output multiplier implies an

employment multiplier (Kahn, 1931). Hence an increase in autonomous spend-

ing raises output and employment. Starting from a position of less than full

employment, suppose there occurs an increase in the amount of autonomous

investment undertaken in the economy. The increase in investment spending

will result in an increase in employment in ¬rms producing capital goods.

Newly employed workers in capital-goods industries will spend some of their

income on consumption goods and save the rest. The rise in demand for

consumer goods will in turn lead to increased employment in consumer-

goods industries and result in further rounds of expenditure. In consequence

an initial rise in autonomous investment produces a more than proportionate

rise in income. The same multiplier process will apply following a change

not only in investment expenditure but also in autonomous consumer ex-

penditure. In terms of Samuelson™s famous Keynesian cross model, a larger

multiplier will show up as a steeper aggregate expenditure schedule, and vice

versa (see Pearce and Hoover, 1995). Within the Keynesian IS“LM model the

multiplier affects the slope of the IS curve. The IS curve will be ¬‚atter the

larger the value of the multiplier, and vice versa (see Chapter 3).

Keynes was well aware of the various factors that could limit the size of

the multiplier effect of his proposed public expenditure programmes, includ-

ing the effect of ˜increasing the rate of interest™ unless ˜the monetary authority

take steps to the contrary™ thus crowding out ˜investment in other directions™,

the potential for an adverse effect on ˜con¬dence™, and the leakage of expen-

ditures into both taxation and imports in an open economy such as the UK

(see Keynes, 1936, pp. 119“20). In the case of a fully employed economy,

Keynes recognized that any increase in investment will ˜set up a tendency in

money-prices to rise without limit, irrespective of the marginal propensity to

consume™.

Although the concept of the multiplier is most associated with Keynes and

his General Theory, the concept made its ¬rst in¬‚uential appearance in a

memorandum from Richard Kahn to the Economic Advisory Council during

the summer of 1930. Kahn™s more formal presentation appeared in his fa-

mous 1931 paper published in the Economic Journal. This article analysed

the impact of an increase in government investment expenditure on employ-

ment assuming that: (1) the economy had spare capacity, (2) there was

monetary policy accommodation, and (3) money wages remained stable.

Kahn™s article was written as a response to the Treasury™s ˜crowding-out™

objections to loan-¬nanced public works expenditures as a method of reduc-

ing unemployment. The following year Jens Warming (1932) criticized, re¬ned

62 Modern macroeconomics

and extended Kahn™s analysis. It was Warming who ¬rst brought the idea of a

consumption function into the multiplier literature (see Skidelsky, 1992,

p. 451). The ¬rst coherent presentation of the multiplier by Keynes was in a

series of four articles published in The Times in March 1933, entitled ˜The

Means to Prosperity™, followed by an article in the New Statesman in April

entitled ˜The Multiplier™. However, the idea of the multiplier met with con-

siderable resistance in orthodox ¬nancial circles and among fellow economists

wedded to the classical tradition. By 1933, Keynes was attributing this oppo-

sition to the multiplier concept to

the fact that all our ideas about economics ¦ are, whether we are conscious of it

or not, soaked with theoretical pre-suppositions which are only applicable to a

society which is in equilibrium, with all its productive capacity already employed.

Many people are trying to solve the problem of unemployment with a theory

which is based on the assumption that there is no unemployment ¦ these ideas,

perfectly valid in their proper setting, are inapplicable to present circumstances.

(Quoted by Meltzer, 1988, p. 137; see also Dimand, 1988, for an excellent survey

of the development of the multiplier in this period)

There is no doubt that the multiplier process plays a key role in Keynesian

economics. In Patinkin™s (1976) view the development of the multiplier rep-

resented a ˜major step towards the General Theory™ and Skidelsky (1992)

describes the concept of the multiplier as ˜the most notorious piece of