Multiplier and Accelerator

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showing how large an increase in income will result from each increase in
investment. The multiplier is the number by which the change in
investment must be multiplied in order to get the resulting change in
income. It is the ratio of change in income to the change in investment.
If an investment of Rs. 50 million increases income by Rs. 150 million,
the income multiplier is 3 and if Rs. 200 million, the multiplier is 4
and so on.

In the following multiplier equation, the relationship between income and
investment is determined through marginal propensity to consume:

  EMBED Equation.3      ------------------------------------(ii)

Where:
  EMBED Equation.3

(mps: Marginal Propensity to Save)

Therefore, the third multiplier equation is:

  EMBED Equation.3      --------------------------------------(iii)

It should be noted that the size of multiplier varies directly with the
size of mpc. When the mpc is high, the multiplier is high and when the
mpc is low, the multiplier is also low.

The multiplier works not only in money terms but also in real terms. In
other words, the increase in income takes place not only in the form of
money but in the form of goods and services.

Example 1:
mpc is ¾
Initial investment is Rs. 1,000 million

Required:
Multiplier,
Marginal propensity to save,
Increase in the level of national income, and
Conclusion.

Solution:
(a) Multiplier (K):
  EMBED Equation.3

(b) Marginal Propensity to Save (mps):
  EMBED Equation.3

(c) Increase in the level of NI:
  EMBED Equation.3

(d) Conclusion:
From the above example, we can see that with an initial primary
investment of Rs. 1,000 million, with an mpc at ¾ and multiplier at 4,
gives rise to an increase of Rs. 4,000 million in the level of national
income.



Example 2:
Calculate mpc, mps and multiplier (K):

mpc
mps
K

4/6
?
?

½
?
?

?
¼
4

?
1/7
?

1
?
?

0
?
?


Solution:
  EMBED Equation.3

mpc
mps
K

4/6
2/6      EMBED Equation.3
 3          E M B E D   E q u a t i o n . 3

    ½
    ½       E M B E D   E q u a t i o n . 3
    2       E M B E D   E q u a t i o n . 3

    ¾       E M B E D   E q u a t i o n . 3
    ¼
    4

    6 / 7      E M B E D    E q u a t i o n . 3
    1 / 7
    7       E M B E D   E q u a t i o n . 3

    1
    0
    ±   ( i n f i n i t y ) *

    0
    1
    1 * *

 *      I f   t h e   m p c   i s   1 ,   t h e   m p s   w i l l   b e
 z e    r o   a n d   t h e   m u ltiplier will be infinity; and a given
dose    of investment (let say, Rs. 1,000 million) will automatically create
full    employment.

** If the mpc is 0, the mps will be 1 and the multiplier will be 1 so
that total increase in income will just equal the increase in primary
investment.



Keynes multiplier theory is also very helpful in the determination of
national income. In his book, ‘General Theory of Employment, Interest
and Money’, he has contradicted the viewpoint of the classical
economists. He is of the opinion that if an economy operates at a level
of equilibrium it is not necessary that there should be a high level of
employment in a country. It is just possible that there may be millions
of people unemployed. So according to Keynes, if any country wishes to
achieve level of employment, it can only do so through the changes in the
magnitude of investment.

According to Keynes’ theory, there are two main methods of measuring the
equilibrium level of NI, i.e.:

The AD-AS Approach, and

The Saving Investment Approach

AD-AS Approach: For explaining the determination of level of income in a
two-sector economy, we assume an economy in which there is no
international trade, no government role and in which corporations retain
no earnings. In this simplest model of economy, the level of income is
determined at a point where the AD intersects the AS. It is depicted as
below:




In the above diagram, the national income is determined at the point
where AD curve (C+I) cuts the AS curve (C+S), i.e., at E. The multiplier
effect is also shown in this diagram. The curve C represents the mpc
which is assumed to be ½. That is why the slope of curve C is 0.5.
Since the AD curve (C + I) cuts the 45o angle line at E, OY1 is the level
of income determined. If now investment is increased to EH
(

                                                                              ”I )
 w e   c a n     f i n d     o u t        t h   e   i   n c r e a s e   i n
 i n c o m e     ( ”Y )   .      A   s     a     r e   s u l t   o f
 i n v e s t   m e n t     E H ,      t   h e     A D     c u r v e   s h i   f t s
 u p w a r d   s   t o     C   +      I     .       T   h i s   n e w   A D
 c u r v e     c u t s     t h e      A   S     c u r   v e   ( 4 5 o   a n   g l e
 l i n e )     a t   F ,     s o      t   h a   t   O   Y 2   i n c o m e     i s
 d e t e r m   i n e d .       T h    u   s ,     i n   c o m e   i n c r e   a s e s
 b y   Y 1 Y   2   a s     a   r e    s   u l   t of    investment increase   of EH,
which (Y1Y2)   is double   of EH.
It is clear, therefore, that the multiplier is 2.   It is also calculated
as below:

  EMBED Equation.3
  EMBED Equation.3

Saving-Investment Approach: In order to simplify the analysis of income
determination we imagine an economy (1) where there are no taxes levied
by the government, (2) the corporations retain no earnings, and (3) there
are no changes in the level of prices. The equilibrium level of NI is
determined at a point where planned or intended saving is equal to
planned or intended investment, or in other words, where the saving
intersect the investment. It is further explained with the help of
following diagram:




The above diagram shows the multiplier effect of an increase in
investment on the equilibrium level of income. SS is the supply curve
and II is the investment curve showing the total level of investment of
OI. These two curves intersect each other at the equilibrium point E
where is income is OY1. If now there is a change in investment from OI
to OI’, i.e., an increase of II’, then the II curve will shift to the
position of I’I’ and the two curves I’I’ and SS intersect each other at
the new equilibrium point E’, where the income is OY2. Now it is clear
that when mps is ½, an increase in investment by II’ (let say Rs. 10
million) has led to the increase in income by Y1Y2 (let say Rs. 30
million). Obviously the value of the multiplier is equal to 3.

Limitations of Multiplier:
Efficiency of production: If the production system of the country cannot
cope with increased demand for consumption goods and make them readily
available, the incomes generated will not be spent as visualised. As a
result, the mpc may decline.

Regular investment: The value of the multiplier will also depend on
regularly repeated investments. A steadily increasing investment is
essential to maintain the tempo of economic activity.

Multiplier period: Successive doses of investment must be injected at
suitable intervals if the multiplier effect is not to be lost.

Full employment ceiling: As soon as full employment of the idle resources
is achieved, further beneficial effect of the multiplier will practically
cease.

Leakages of Income Stream and Their Effect on the Multiplier:
As we know that as income increases, consumption does not increase to the
same extent or proportionately, because a part of the income is saved.
The part of the income that is saved is as if a leakage from the flow of
income stream. These leakages obstruct the growth of national income.
In the absence of these leakages, mpc would have been unity. The
consumption expenditure would have increased 100 per cent of the increase
in income and there would have been full employment. The following are
the principal leakages:

Paying off debts: It generally happens that a person has to pay a debt to
a bank or to another person. A part of his income goes out in repaying
such debts and is not utilised either in consumption or in productive
activity. Income used to pay off debts disappears from the income
stream. If, however, the creditor uses this amount in buying consumer
goods or in some productive activity, then this sum will generate some
income, otherwise not.

Idle cash balances: It is well known that people keep with them ready
cash which is neither used productively nor in purchasing consumer goods.
Keynes has mentioned three motives for holding ready cash for liquidity
preference, viz., transactions motive, precautionary motive and
speculative motive. This means that the re-spent part of income goes on
decreasing. In this way, a part of the initial expenditure leaks out of
the income stream.

Imports: The part of the money spent by country for importing goods also
leaks out of the country’s income stream. It does not encourage or
support any business or industry in the country. This is specially so if
the imports do not help the trade and industry of the country or if they
are not used for export promotion. The net import is a leakage.

Purchase of existing securities: Some people purchase securities (saving
certificates) from others and the seller of securities can hoard this
money. This money also leaks out of the income stream. This may also be
valid in case of purchase of shares, debentures, bonds, insurance policy,
or some other financial investment. If this invested money is not used
in productive areas, there will be a leakage in the income stream.

Price inflation: Inflationary situation is also responsible for leakage.
In such a situation, investment does not help in generating employment or
increasing income. If there is already full employment in the country,
increase in investment, far from increasing demand for consumer goods, it
decreases it as a result of which employment in the consumer goods
industries contracts and demand for capital goods decreases. Whatever
increase in income there is, it is spent in high prices and it does not
help in creating income and employment.
As a result of leakages of income from the main income stream of the
country, the multiplier effect of the primary or initial investment in
increasing income is reduced. If somehow these leakages are plugged, the
multiplier effect of investment in generating income and employment would
increase. If they cannot be plugged altogether, they should be reduced
or the propensity to consume should be increased or propensity to save
should be reduced, otherwise the new investment will not have full effect
in increasing income and employment.

Importance of Multiplier:
Keynes’ principle of multiplier has a great role in removing the Great
Depression of 1929-34. These days governments are actively interfere in
the economic affairs of the community through multiplier. Its importance
is further explained as below:

The multiplier principle focuses on the importance of public investment,
which is the key to remove unemployment during the days of depression.
An investment of Rs. 1 million can create income and employment worth
many times, and can help the government to remove unemployment from the
country.

During the days of depression, the private entrepreneurs are discouraged
to invest in the economy. Therefore, to fill this gap, the government
comes forward and undertakes the investment in her own hands. Hence, the
demand for consumer goods increases and also the level of NI and
employment increases on account of the working of the multiplier.

When the demand for goods increases and incomes rise owing to government
investment, the profit expectations of the entrepreneurs go up and as a
result the MEC rises.

When the government makes investment in public works to fight depression
and unemployment, private investment is encouraged on account of the
operation of the multiplier. The confidence of private investors is
restored, and hence helps in further removing the economic depression of
the country.

Assumptions of Multiplier:
The following certain essential conditions / assumptions for the
operation of multiplier:

The supply curve of output should be elastic. In other words, when
demand for certain goods or services increases, its supply can be
increased without much difficulty.

There is excess productive capacity in consumer goods industries, so that
the supply of goods can be easily increased when demand increases.

The supply of raw materials and working capital should also be elastic.

There should be ‘involuntary unemployment’. That is, there are people
who want work at the prevailing wage rate, but are not getting it.

Criticism on Keynes’ Multiplier Theory:
Many economists including the classical economists and the economists
from third world countries have strongly criticise the Keynes’ Multiplier
Theory. It is explained in brief as below:

Keynes’ multiplier theory assumes that the supply of output, raw
materials and working capital is elastic, i.e., it can be increased
whenever required. But, according to critics, this condition cannot be
fulfilled in an under-developed country (UDC), where there is a
continuous vicious cycle of poverty. The whole economy is based on
agriculture, and there is a dearth of capital equipment, skill labour and
technology. The existing industries cannot fulfil the increased demand.
Moreover, the government is so poor to invest in public works.

According to Keynes’ multiplier theory, there is excess productive
capacity in consumer goods industries. But according to critics, there
is a little excess productive capacity in poor countries; therefore, this
theory cannot be applied to UDCs.

Another condition of Keynes’ theory is that there should be ‘involuntary
unemployment’. That is, there are people who want work at the prevailing
wage rate, but are not getting it. Whereas, in UDCs, there is ‘disguised
unemployment’, and most of the workers are self-employed, therefore, this
condition cannot be fulfilled in such countries.

According to critics, this theory can only be applied to economically
advanced and highly industrialised countries, and cannot be applied to
under-developed countries, which are pre-dominantly agricultural
countries. In UDCs, the heavy plant and machineries, and skilled labour
are not easily available and the supply cannot be increased quickly.

The Accelerator:
The multiplier describes the relationship between investment and income,
i.e., the effect of investment on income. The multiplier concept is
concerned with original investment as a stimulus to consumption and
thereby to income and employment. But in this concept, we are not
concerned about the effect of income on investment. This effect is
covered by the ‘accelerator’. The term ‘accelerator’ should not be
confused with the accelerator in cars. It does not make the investment
to grow faster and faster.

The term ‘accelerator’ is associated with the name of J.M. Clark in the
year 1914. it has been proved a powerful tool of economic analysis since
then. Keynes, astonishingly, has altogether ignored this concept. That
is why, the concept of accelerator is not considered the part of
Keynesian theory.

According the principle of accelerator, when income increases, people’s
spending power increases; their consumption increases and consequently
the demand for consumer goods increases. In order to meet this enhanced
demand, investment must increase to raise the productive capacity of the
community. Initially, however, the increased demand will be met by over-
working the existing plants and machinery. All this leads to increase in
profits which will induce entrepreneurs to expand their plants by
increasing their investments. Thus a rise in income leads to a further
induced investment. The accelerator is the numerical value of the
relation between an increase in income and the resulting increase in
investment.

(Figures in Rs. ‘000)
Years Demand Required
Stock of
Capital Replacement
Cost Net
Investment Gross
Investment 2007 500 5 machines
1500 1 machine
300 0 machine 300 2008 500 5 machines
1500 1 machine
300 0 machine 300 2009 800 8 machines
2400 1 machine
300 3 machines
900 1200 2010 1000 10 machines
3000 1 machine
300 2 machines
600 900 2011 1000 10 machines
3000 1 machine
300 0 machine 300 2012 800 8 machines
2400 1 machine
300 – 2 machines
600 – 300   Cost per machine: Rs. 300,000 per machine

In the above example, suppose we are living in a world, where the only
commodity produced is cloth. Further suppose that to produce cloth Rs.
100,000, we require one machine worth Rs. 300,000, which means that the
value of the accelerator is 3 (i.e., the capital-output ratio is 1:3).
That is, if demand rises by Rs. 100,000, additional investment worth Rs.
300,000 takes place. If the existing level of demand for cloth remains
constant, let us say, at Rs. 500,000, then to produce this much cloth we
need five machines worth Rs. 1.5 million. At the end of one year, let us
suppose, that one machine becomes useless as a result of wear and tear,
so that at the end of one year, a gross investment of Rs. 300,000 must
take place to replace the old machine in order that the stock of capital
is capable of producing output worth Rs. 500,000.

In the third period, i.e., the year 2009, demand rises to Rs. 800,000. To
produce output worth Rs. 800,000, we need 8 machines. But our previous
stock consisted of only 5 machines. Thus if we are to produce output
worth Rs. 800,000, we must install 3 new machines, worth Rs. 900,000.
The net investment for the year 2009 will be Rs. 900,000 and with the
replacement cost of one machine Rs. 300,000, our gross investment jumps
from Rs. 300,000 in the year 2008 to Rs. 1.2 million in the year 2009. A
60 per cent increase in demand led to a 400 per cent increase in gross
investment. Here we have a glimpse of the powerful destabilising role of
accelerator.

Assumptions of the Accelerator:
Under the principle of accelerator, it is assumed that there is no excess
capacity existing in the consumer goods industries. No machines are
lying idle and shift working is not possible.

In capital goods industries, it has been assumed that there is an
existence of surplus capacity. If there is no excess capacity in capital
goods industries, increased demand for machines could not lead to
increase in the supply of machines.

Output is flexible. The machine-making industry or capital goods
industry can increase its output whenever desired.

The size of the accelerator does not remain constant over time. It value
will be affected by the businessmen’s calculations regarding the
profitability of installing new plants to make more machines on the basis
of their probable working life.

The demand for machines will remain stable in the future, although the
increase in demand has suddenly cropped up.


O               Y1            Y2            X
Income

Y

Consumption and Investment

Y = C + S

F

H

C + I’

C + I

C

E

Figure 1 – Multiplier Effect (a)

45o

0.5

E’


Figure 2 – Multiplier Effect (b)

E

S
I

I’

I’

I

S

Saving / Investment

Y

O              Y1     Y2   X
Income




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0 4 9 2 2 4                                       ÿÿÿÿÿÿÿÿ
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1 5 9 9 4 6                                                          "           Î
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   ÿÿÿÿÿÿÿÿÿÿÿÿ                                    .                   C o m p
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ƒm ƒp ƒc †= ˆ1 †"ƒm ƒp ƒs ‚; ˜ë˜ëƒm ƒp ƒs †= ˆ1 †"
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DOCUMENT INFO
Description: bank reconcilation statement,circular flow of income, closing enteries, coefficient of correlation, concepts of National income, Consumption Functions, Determination of National income,Financial statement, Flow of Funds accounts, Index numbers, Introduction to statistics,investment, macro economics, measures of central tendency, measure of depersion, measure of shape distribution, merchandise inventory, micro macro economics, Micro Economics, multiplier and accelerator, probability, public finance, random variable,regression,sample distribution theory, statistics dynamics and comparative, theofy of employment, trade cycle