Download Multiplier

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Definition
Calculating the value of multiplier
Importance of multiplier
Uses of multiplier
Limitations of multiplier
Mathematics
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A number which indicates the magnitude of a
particular macroeconomics policy measure. In
other words, the multiplier attempts to quantify
the additional effects of a policy beyond those
that are immediately measurable. This is true of
most macroeconomics policy measures, because
the actual effect of the measure cannot be
quantified by the effect of the measure itself.
What is a simple definition of the multiplier?
It is the number of times a rise in national
income exceeds the rise in injections of demand
that caused it
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We propose to study how much or how many
times income increases as investment is
done. This can be known from the concept of
Multiplier.
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Marginal propensity to consume.
In economics the marginal propensity to consume
(MPC) is an empirical metric that quantifies induced
consumption the concept that the increase in
personal consumer spending consumption occurs
with an increase in disposable income (income after
taxes and transfers).
The proportion of the disposable income which
individuals desire to spend on consumption is known
as propensity to consume. MPC is the proportion of
additional income that an individual desires to
consume. For example, if a household earns one
extra dollar of disposable income, and the marginal
propensity to consume is 0.65, then of that dollar,
the household will spend 65 cents and save 35 cents.
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Mathematically, the function is expressed as the
derivative of the consumption function with respect
to disposable income .
or
, where is the change in consumption, and is the
change in disposable income that produced the
consumption.
Marginal propensity to consume can be found by
dividing change in consumption by a change in
income, or . The MPC can be explained with the
simple example:
INCOME
CONSUMPTION
120
120
180
170
Here
;
Therefore,
or 83%.
For example, suppose you receive a bonus with your paycheck, and it's $500 on top of your
normal annual earnings. You suddenly have $500 more in income than you did before. If you
decide to spend $400 of this marginal increase in income on a new business suit, your marginal
propensity to consume will be 0.8 (
).
MPC and the Multiplier
MPC’s importance depends on the multiplier theory. The value of the multiplier—is determined
by MPC. The higher the MPC, the higher the multiplier and vice-versa. The relationship between
the multiplier and the propensity to consume is as follows:We know
(i.e.,total national income=total Consumption)
(where is
(where ,
)
is multiplier and
Since is the MPC, the multiplier is, by definition, equal to
. The multiplier
can also be derived from MPS (marginal propensity to save) and it is the reciprocal of MPS,
1. Saving Investment Equality
The multiplier theory highlights the importance of investment in theory of income and
employment. As the consumption function is stable during the short run, fluctuations in income
and employment are result of the fluctuations in the level of investment. A rise in investment
causes a cumulative rise in income and employment through the multiplier process and viceversa. The multiplier theory not only explains the process of income propagation as a result of
rise in the level of investment, it also helps in bringing equality between saving and investment.
In case of divergence between the two, change in the level of investment leading to a change in
the level of income via the multiplier process, ultimately equalizes saving and investment
2. Business Cycles
The multiplier process explains and helps in controlling different phases of business cycles
occurring due to fluctuations in the level of income and employment. The boom period (high
level of income and employment) can be controlled by a reduction in investment, which leads to
a cumulative decline in income and employment in the multiplier process. On the other hand,
during the depression phase of business cycle (low level of income and employment), an
increase in investment leads to revival. If this process continues, boom may be the result.
3. Formulation of Economic Policies
The government can decide upon the amount of investment to be injected into the economy to
reduce unemployment. The multiplier theory helps the government in formulating an appropriate
employment policy during depression. During depression, Government’s public works
programmes are more effective than cheap money policy due to multiplier effect of
investment. It is important to note that any increase in the investment in one sector should not
be accompanied by a decrease in the investment in the other sector. An inter-sectoral transfer of
the investment will not raise the value of the multiplier. Further, it is necessary to ensure a steady
injection of the investment. That is, the increments in the investment should be repeated at
regular intervals so as to raise the level of the income and the employment to the full
employment level. Further, modifications in the Keynes theory of the Multiplier will enhance the
utility of the multiplier concept.
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The multiplier principles occupies a very important
place not only in economic theory but also in
shaping economic policy.
It plays a vital role as an instrument of income
building.
It tells us how a small increase in investment can
result in large increase in income.
Multiplier uses control of business cycles.
It furnishes guidelines for appropriate income and
employment policies.
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It also explains the expansion of public sector
in modern times.
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Efficiency of production: If the production
system of the country cannot cope with
increased demand for consumption goods
and make them readily available, the income
generated will not be spend as visualised. As
a result the MPC may decline.
Regular investment: The value of multiplier
will also depend on regularity repeated
investment.
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Multiplier period: Successive doses of
investment must be injected at suitable
intervals if the multiplier effect is not be lost.
Full employment celling: As soon as full
employment of the idle resources is achieved,
further beneficial effect of the multiplier will
practically cease.
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Illustration 1
In an economy, the basic equations are as follows: the
consumption function is C = 300 + 0.8Y and investment is
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I= $ 360 millions. You are required to ascertain the following
1.
The equilibrium level of income
2.
The equilibrium level of income when planned investment
increases from 360 to 400 millions, a total increases of 40
millions
3.
The multiplier effect of the 40 millions increases in planned
investment.
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Solution
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The equilibrium condition is given as Y = C + I
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Y
=
300 + 0.8Y + 360
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Y – 0.8Y
=
300 + 360
0.2Y
=
660
=
3,300
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Y
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1.
The equilibrium level of income is Y
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The equilibrium condition is given as Y = C + I
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Thus,
Y
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2.
300 + 0.8Y + 400
Y – 0.8Y
=
300 + 400
0.2Y
=
700
=
700 / 0.2
Y
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=
=
Hence, the equilibrium level of income is 3,500
3,300
The equilibrium level of income increases from 3,300 to
3,500crores when planned investment increases from 360 to
400 millions. There is an increase in income by 200
millions. Hence the multiplier effect is
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m
=
1
1–b
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=
1
1 – 0.8
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=
1
0.2
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3.
The multiplier effect is m is 5
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Illustration 2
Presume in an economy the marginal propensity to
consume is 0.75 and the level of autonomous
investment decreases by 40 millions. Find,
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1.
The change in the equilibrium level of income
2.
The change in consumption expenditures
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Solution
We know
ΔY
ΔI
=
m
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Also,
m
=
1
1–b
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So
ΔY
ΔI
=
1
1–b
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ΔY
=
ΔI
1
1–b
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=
-40 x
1
1 – 0.75
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=
-160
(1)
Thus, the decrease in autonomous investment causes a decrease
in the equilibrium level of income by 160 millions. This effect occurs due
to the reverse multiplier.
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Y
=
C+I
ΔY
=
ΔC +ΔI
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-160
=
Δ C – 40
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ΔC
=
- 160 + 40
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ΔC
=
- 120
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Therefore,
(2)
The consumption expenditure decreases by
120 millions
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Illustration 3
Compute the value of the investment multiplier when
the marginal propensity to consume is
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(1) 0.80, (2) 0.65, (3) 0.40 and (4) 0.25
Find the effect of a decrease in the equilibrium income
when autonomous investment decreases by 60 millions
when the marginal propensity to consume is (1) 0.80,
(2) 0.65, (3) 0.40 and (4) 0.25
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Solution
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The value of m, the investment multiplier is
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m
=
1
1–b
m
=
1
1 – 0.8
Hence,
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(1)
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=
(2)
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1 / 0.2
m
=
=
=
m
=
5
=
m
=
1
1 – 0.65
1 / 0.35
2.87
(3)
m
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(4)
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m
=
1
1 – 0.4
=
1 / 0.2 =
=
m
=
1.67
m
=
1.33
1
1 – 0.25
= 1 / 0.75
=
Thus, the decrease in the equilibrium income when autonomous
investment decreases by 60 millions is
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ΔY
=
Δ Im
=
60 x 5
=
300
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=
60 x 2.87
=
172.2
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=
60 x 1.67
=
100.2
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=
60 x 1.33
=
79.8
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Illustration 4
In an economy the marginal propensity to consume is
0.50. The level of autonomous investment decreases by
60 millions. Find the following
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1.
The change in the equilibrium level of income
2.
The change in autonomous demand
3.
The induced change in the consumption expenditure
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Solution
ΔY
ΔI
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=
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But, m is the investment multiplier
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Also
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m
=
1
1–b
ΔY
=
ΔIm
m
Thus,
ΔI
=
1
1–b
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=
- 60 x
1
1 – 0.50
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=
- 120
1.
Hence, the decrease in autonomous investment
causes a decrease in the equilibrium level of
income by 120 millions.
2.
The decrease in investment by 60 millions is the
change in the level of autonomous demand.
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Y
+
I
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Therefore,
ΔY
=
Δ C + ΔI
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-120
=
ΔC – 60
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ΔC
=
-120 + 60
ΔC
=
-60
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=
C
3.The Consumption expenditure falls by 60 millions
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Illustration 5
Presume that in two sector economy, the income is $
1000 million while the marginal propensity to consume
is 0.40. Suppose the government wants to increase the
income to $ 1600 million, by an amount of $ 600
million.
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1.By how much should the autonomous investment be
increased?
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Solution
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The income level
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The planned income level is $1600 millions
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Change in income
=
=
$1000 millions
ΔY
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1600 – 1000
=
$600 millions
But
ΔY
ΔI
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=
ΔY
=
m
=
=
ΔI
1
1–b
1
1–b
= ΔI
600
1
1–b
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=
ΔI
1 / 1-0.4
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=
ΔI
1 / 0.6
1.66667
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600
=
ΔI
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ΔI
=
600 / 1.66667
Thus, the autonomous investment should be increased by $360
millions for the income to increase to $ 1600 millions. An increase
in income by $ 600 millions
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