The Concept of Multiplier
The Concept of Multiplier
The concept
of multiplier was first developed by F. A. Kahn in his article "The
Relation of Home Investment to Unemployment" in the Economic Journal of
June 1931. Kahn's multiplier was the Employment Multiplier. Keynes took the idea from Kahn and further
refined it and formulated the investment or income multiplier.
Investment
multiplier refers to the number of times by which the increase in output or
income exceeds the increase in investment.
According to
Keynes, “The multiplier establishes a precise relationship, given the
propensity to consume, between aggregate employment and income and the rate of
investment. It tells us that, when there is an increment of investment, income
will increase by an amount which is k times the increment of investment"
i.e., ∆Y=k∆I where Y is income, I is investment, ∆ is change and k is the
multiplier.
For example,
if investment is made of Rs 100 crore, then the income will not rise by 100
crores only but by a multiple of it. Suppose, if the national income increases
by Rs 200 crores, multiplier is equal to 2. The multiplier is, therefore, the
ratio of increment in income to the increment in investment. In the words of
Hansen, Keynes' investment multiplier is the coefficient relating to an
increment of investment to an increment of income, i.e., k=∆Y/∆I.
k refers to
the power by which any initial investment expenditure is multiplied to obtain a
final increase in income.
The
multiplier is the number by which the change in investment must be multiplied in
order to get the resulting change in income.
The value of
the multiplier is determined by the marginal propensity to consume. The higher
the marginal propensity to consume, the higher is the value of the multiplier,
and vice versa.
For example:
Government undertakes investment expenditure equal to Rs.100 crore on the
construction of roads. For this Government pays wages to the laborers engaged,
prices for the materials to the suppliers and remunerations to other factors
who make contribution to the work of road-building. The total cost will amount
to Rs 100 crore. This will increase incomes of the people equal to Rs 100
crore. These people will spend a good part of them on consumer goods. Suppose
marginal propensity to consume of the people is 1/2 0r 0.5. Then out of Rs 100 crore they will
spend Rs 50 crore on consumer goods, which would increase incomes of those
people who supply consumer goods equal to Rs 50 crore. People who receive these
Rs 50 crore will also spend these incomes, depending upon their marginal
propensity to consume. If their marginal propensity to consume is also 1/2 or
0.5, then they will spend Rs 25 crore on consumer goods. Thus, this will
further increase incomes of some other people equal to Rs 25 crore. In this
way, the chain of consumption expenditure would continue and the income of the
people will go on increasing. But every additional increase in income will be
progressively less since a part of the income received will be saved. Thus, the
income will not increase by only Rs 100 crore, which was initially invested in
the construction of roads, but by many times more.
Derivation
of Investment Multiplier:
The equation
for the equilibrium level of income in a two-sector economy:
Y = C + I
As in the multiplier analysis, we are
concerned with changes in income induced by changes in investment,
So, ∆Y = ∆C
+ ∆I
For simplicity, Keynes assumed that change in
investment is autonomous or independent of changes in income while changes in
consumption are function of changes in income.
In the
Keynesian consumption function,
C = a + bY
where a is a
constant term or considered as an autonomous consumption,
b is marginal propensity to consume which is
also assumed to remain constant. Therefore, change in consumption can occur
only if there is change in income.
So, ∆C = b∆Y
Thus,
∆Y = b∆Y + ∆I
∆Y – b∆Y = ∆I
∆Y (1 – b) =
∆I
As b stands for marginal propensity to consume
As 1-MPC= MPS
So, we can write:
Thus, the
value of multiplier can be obtained if we know either the value of MPC or MPS.
For example, if marginal propensity to consume (b) is 0.5, investment multiplier is:
If marginal propensity to consume is equal to 0.5, with the increase in investment by Rs 100 crore, the increase in income will be:
|
Round |
Increment in investment[∆I] [In crore] |
Increment in income[∆Y] [In crore] |
Increment in consumption[∆C] MPC=.5 [In crore] |
Increment in saving[∆S] MPS=.5 [In crore] |
|
1 |
100 |
100 |
50 |
50 |
|
2 |
--- |
50 |
25 |
25 |
|
3 |
--- |
25 |
12.5 |
12.5 |
|
4 |
--- |
12.5 |
6.25 |
6.25 |
|
5 |
--- |
6.25 |
3.12 |
3.12 |
|
6 |
--- |
3.12 |
1.56 |
1.56 |
|
7 |
--- |
1.56 |
.78 |
.78 |
|
8 |
--- |
.78 |
.39 |
.39 |
|
0 |
--- |
0 |
0 |
0 |
|
Finally |
100 |
200 |
100 |
100 |
The multiplier
theory explains the cumulative effect of a change in investment on income via
its effect on consumption expenditure. An increase in investment leads to
increased production which creates income and generates consumption
expenditure. This process continues in dwindling series till no further
increase in income and expenditure is possible.
Suppose that
in an economy MPC is .5 and investment is raised by Rs 100 crores as shown in
the above table. This will immediately lead to a rise in production and income
by Rs 100 crores. It reveals that an increment of Rs 100 crores of investment
in the primary round leads to the same increase in income. Of this, Rs 50
crores are saved and Rs 50 crores are spent on consumption which go to increase
income by the same amount in the second round. This dwindling process of income
generation continues in the secondary rounds till the total income generated
from Rs 100 crores of investment rises to Rs 200 crores.
∆Y = K∆I
200=2 × 100
where K = 2 (MPC = .5) and ∆I = Rs 100 crores.
Diagrammatic Representation of Investment Multiplier
The multiplier can be illustrated through saving-investment
diagram also as shown in the diagram. when income increases, savings also
increase to equal the new investment at a new equilibrium level of income.
Saving function slope 0.5 that show MPS
of one-half. I is the old investment curve which cuts S at E1 so that OY1 is
the old equilibrium level of income. The increase in investment ∆I shown by a
new investment curve I + ∆I which is intersected by the S curve at E2 the new
equilibrium point that shows OY2 a new equilibrium level of income. The rise in
income Y1Y2 shown as ∆Y is exactly double the increase in investment ∆I, as the
MPS is one-half.
Leakages
of Multiplier-The
various leakages that occur in the income stream and reduce the size of
multiplier in the real world are given below:
1-Leakages from the Income Stream: The multiplier theory assumes that people would continue to spend a constant proportion of additional income that they have earned as a result of certain autonomous investment depending on the aggregate MPC. In practical, this assumption is not so true as people tend to spend their additional income on many other non-consumption and non-investment items. These expenses are known as leakages from the income stream in the working process of the multiplier. These kinds of leakages and their effect on the multiplier are given below.
· Saving: whole incremental income is
not consumed but a part of it is saved and the higher the marginal propensity
to save, the smaller the size of the multiplier and the greater the amount of
leakage out of the income stream, and vice versa.
· Payment of the past debts: When a consumers use a part of their additional income to
repay their past debts, such as to pay a debt to a bank or to another person, instead of consuming it. It decreases marginal
propensity to consume. This reduces the generation of additional income over
the working process of the multiplier.
· Purchase of existing wealth: When people spend the whole or a part
of their additional income on purchasing existing wealth and property, and
purchase of shares and bonds from the share and bond holders, then another kind
of leakage in the multiplier process arises.
· Import of goods and services: The
part of increased income spent by country on imported goods and services also leaks out of the country's income stream. It does not encourage any business or industry in the country. The imports which make incomes flow out of the country
reduce the value of multiplier.
· Holding of idle cash balances: If the people hold a part of their increment in income as idle cash balances which is neither used productively nor in purchasing consumer goods. Instead, they hold it for satisfying their precautionary and speculative motives, it creates leakage in the multiplier process. Therefore, reduces the increments in total income and output.
· Price Inflation: Inflationary situation is also responsible for leakage. A rise in the prices of consumption goods implies increased expenditure on them. As a result, increased income is absorbed by higher prices and the real consumption and income fall.
· Undistributed Profits: If profits accruing to joint stock
companies are not distributed to the shareholders in the form of dividend but
are kept in the reserve fund, it is a leakage from the income stream.
· Taxation: Progressive taxes have the effect of lowering the disposable income of the taxpayers and reducing their consumption expenditure. Similarly, commodity taxation tends to raise the prices of goods, and a part of increased income may be dissoluted on higher prices. Thus, increased taxation reduces the income stream and lowers the size of the multiplier.
2- Non-availability of Consumer Goods and Services: The multiplier theory assumes an instant and matching supply of consumer goods and services. But, in reality, the supply of goods does not follow instantly the rise in demand. There is always a time lag. During the lag period, newly earned income creates additional demand for goods and services. As a result, prices of consumer goods rise, and it leads to inflation. This reduces the real consumer expenditure which limits the multiplier effect.
3- Full Employment Situation: The multiplier principle does not work in case of full employment because the resources of the production (capital and labour) are fully employed, and further production will not be possible. Therefore, additional investment will only lead to inflation, not to the generation of additional real income.
Criticism of Multiplier-
· Timeless Analysis: Keynes's logical theory of the multiplier is an instant process without time lag. But in reality, a time lag is always involved between the receipt of income and its expenditure on consumption goods and also in producing consumption goods. Therefore, it is unrealistic.
· Acceleration Effect Ignored: It only studies the effects of investment on income through changes in consumption expenditure and ignores the effect of consumption on investment which is known as the acceleration principle. Hicks, Samuelson and others have shown that it is the interaction of the multiplier and the accelerator which helps in controlling business fluctuations.
· MPC does not Remain Constant: Gordon points out that the multiplier concept fully emphasis on consumption. He endorses the use of the term 'marginal propensity to spend' in place of marginal propensity to consume to make this concept more realistic. According to him, this multiplier theory works on the constancy of the marginal propensity to consume, but in a dynamic economy, it does not remain constant.
· Relation between Consumption and Income: Gardner Ackley pointed out, "The relationship does not run simply from current income to current consumption, but rather involves some complex average of past and expected income and consumption. There are other factors than income to consider."
Prof. Hart considers it
"a useless fifth wheel."
According to Stigler, it
is the fuzziest part of Keynes's theory. Prof. Hutt calls it a "rubbish
apparatus" which should be expunged from text books.
Importance
of Multiplier- The
multiplier principle has considerable practical applicability to economic
problems as given below-
· Investment: The multiplier theory highlights the importance of investment in income and employment theory. Fluctuations in income and employment are due to fluctuations in the rate of investment as the consumption function is stable during the short-run. If there is a fall in investment, it leads to a cumulative decline in income and employment by the multiplier process and vice versa.
· Trade Cycle: The multiplier process shows the different phases of the trade cycle in the case of fluctuations in the level of income and employment due to fluctuations in the rate of investment,. A fall in investment declines income and employment in a cumulative manner leading to recession and ultimately to depression. On the contrary, an increase in investment leads to to a boom. Thus, the multiplier is considered as an indispensable tool in trade cycles.
· Saving-Investment Equality: It also helps in bringing the equality between saving and investment. In case of discrepancy between the two, change in level of investment leading to a change in the level of income via the multiplier process, ultimately equalizes saving and investment.
·
Formulation of Economic Policies: The multiplier is an important tool
in the hands of modern states in formulating economic policies.
The theory of multiplier
has also a great practical importance in the field of fiscal policy made by the
Government. Keynes supported Government investment in public works so that
the problem of depression and unemployment can be solved. When the public
investment is made in public works such as construction of road, building,
hospitals, schools, irrigation facilities it will increase aggregate demand by a
multiple amount. It will also encourage the increase in private investment. As
a result, a state of full employment will be restored.
The multiplier principle
highlights the importance of deficit budgeting. In a state of depression,
cheap money policy by lowering
the rate of interest is not helpful as the marginal efficiency of capital is so
low that a low rate of interest fails to encourage private investment. In this
situation, when public expenditure is increased through public investment by creating a budget deficit, it helps in increasing income and employment by
multiplier time the increase in investment.
Thus,
multiplier is one of the most important concepts developed by J.M. Keynes to
explain the determination of income and employment in an economy.
Dr. Swati Gupta
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