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Multipliers in Economics
ConceptofMultiplier
The concept of multiplier was first of all developed by F.A. Kahn in the early 1930s with reference to
the increase in employment,. But Keynes later further refined it. In economics, a multiplier is a factor
that measures how much an economic variable (Income, Output) changes in response to a change in
some other variable (Investment, Govt spending, tax, export etc). For example, suppose variable x
changes by 1 unit, which causes another variable y to change by M units. Then the multiplier is M.
In the economy, there is a circular flow of income and spending where everything is
connected and one’s spending/expenditure becomes earning of income to others. Money that is
earned by one person from another, gets spent again - not just once, but many times. What it means is
that small increase in spending by consumers or investment by government lead to much larger
increase in economic income/output. Economists use Multiplier to measure how much income gets
multiplied. Money spent in the economy doesn't stop with the first transaction only, rather flows
through the economy one person at a time, like a ripple effect when a rock gets thrown into the water.
An injection of extra income leads to more spending, which creates more income, and so on. The
multiplier effectrefers to the increase in final income arising fromany new injection of spending.
If ΔI stands for increment in investment and ΔY stands for the resultant increase in income,
then multiplier is equal to the ratio of increment in income (ΔY) to the increment in investment (ΔI).
Therefore k = ΔY/ΔI where k stands for multiplier. For example, if investment in an economy of Rs.
100 crores is made, then the income will not rise by Rs. 100 crores only but a multiple of it say by Rs.
300 crores, then the multiplier is equal to 3. The multiplier is, therefore, the ratio of increment in
income to the increment in investment. The size of the multiplier depends upon the marginal
propensityto consume (MPC)or to save called the marginalpropensityto save (MPS).
WorkingofMultiplier
Suppose Government undertakes investment expenditure equal to Rs. 100 crores on some public
works, say the construction of rural roads. For this Government will pay wages to the labourers
engaged, prices for the materials to the suppliers and remunerations to other factors that make
contribution to the work of road-building. The people who receive Rs. 100 crores will spend a good
part of them on consumer goods. Suppose marginal propensity to consume of community is 4/5 or
80%. Then out of Rs. 100 crores they will spend Rs. 80 crores on consumer goods, which would
increase incomes of those people who supply consumer goods equal to Rs. 80 crores. But those who
receive these Rs. 80 crores will also in turn spend these incomes, they will spend Rs. 64 crores (80%
of 80) on consumer goods. Thus, this will further increase incomes of some other people equal to Rs.
64 crores. In this way, the chain of consumption expenditure would continue and the income in the
economy 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, we see that the total income in the economy
due to initial investment of 100 crores will not increase by only Rs. 100 crores, but by many time
more.
Therefore total Increase in income denoted by ΔY
ΔY = 100 + 100 x 4/5 + 100(4/5)2 + 100(4/5)3 + 100(4/5)4 + …..
= 100[1 + (4/5) + (4/5)2 + (4/5)3 + (4/5)4+……]
But the aboveseries is an infinite geometric progression. Therefore, increase in income
(ΔY) = 100 [1/ (1-4/5)] =100 x [1/ (1/5)] = 100 x 5 = 500
Therefore here multiplier is 5
MultiplierAssumptions
(i) That there is no change in the marginal propensity to consume but remains constant.
(ii) That there is no induced investment (i.e., acceleratoris not operating).
(iv)That the output of consumer goods is responsive to effectivedemand for these.
(v)That there is complete absence of government taxation.
(vi)That there is no time lag between the receipt of income and its expenditure.
(vii)That there is a closed economy.
TheMultiplierCanBeDerivedAlgebraicallyAsFollows:
Writing the equation forthe equilibrium level of income we have -
Y = C + I ………………. [1]
As in the multiplier analysis we are concerned with changes in income induced by changes in
investment, rewriting the above equation in terms of changes in the variables wehave -
ΔY = ΔC + ΔI……………. [2]
In the simple Keynesian model of income determination, change in investment is considered to be
autonomous or independent of changes in income while changes in consumption are function of
changes in income. In the consumption function,
C = a + bY……………….[3]
Where a is a constant term, b is marginal propensity to consume which is also assumed to remain
constant. Therefore, change in consumption can occuronly if there is change in income. Thus
ΔC = bΔY…………………[4]
Substituting (4)into (2) we have
ΔY = bΔY + ΔI
Or ΔY – bΔY = ΔI
Or ΔY (1 – b) = ΔI
Or ΔY =ΔI [1/ (1-b)]
Or ΔY/ΔI= 1/ (1 – b)
As b stands for marginal propensity to consume
Investment Multiplier, KI = ΔY/ΔI= 1/ [1 – MPC] = 1/MPS
It follows from above that the size or value of multiplier is the reciprocal of marginal propensity to
save.
Two LimitingCasesofthe ValueofMultiplier:
(i) One limiting case occurs when the Marginal Propensity to Consume (MPC) is equal to one,
that is, when the whole of the increment in income is consumed and nothing is saved. In this case, the
size of multiplier will be equal to infinity, that is, a small increase in investment will bring about a
very large increase in income and employment. However, this is unlikely to occur since marginal
propensity to consume in the real world is less than one.
(ii) The other limiting case occurs when Marginal Propensity to Consume (MPC) is equal to
zero, that is, when nothing out of the increment in income is consumed; whole increment in income is
saved. In this case, the value of the multiplier will be equal to one. That is, in this case, the increment
in income will be equal to the original increase in investment and not a multiple of it. But in actual
practice the marginal propensity to consume is less than one but more than zero (1 > ΔC/ΔY > 0).
Therefore, the value of the multiplier is greater than one but less than infinity.
Applying the‘MultiplierEffect’:Themultiplier conceptcan be used any situation where there is a
new injection into an economy.Examples of such situations include:
1. When the government funds building of a new public works
2. When there is an increase in exports abroad
3. When there is a reduction in interest rates or tax rates, or when the exchange rate falls.
DiagrammaticRepresentationofMultiplier
We know that, the level of equilibrium national income is fixed at the level where C + I curve
intersects the 45° income curve. The multiplier is illustrated in Figure below. In this figure line C
represents consumption function. Marginal propensity to consume has been here assumed to be
equal to 1/2 i.e., 0.5. Therefore, the slope of the curve C equals to 0.5. C + I represents aggregate
demand curve. It will be seen from figure that the aggregate demand curve C + I intersects the 45°
line at point E resulting equilibrium levelof income equal to OY1.
If investment increases by the amount EH (ΔI) then as a consequence of such increase in investment,
the aggregate demand curve shifts upward to the new position C + I’. This new aggregate demand
curve C + I’ intersects the 45° income line at point F so that the equilibrium level of income increases
to OY2. Hence as a result of net increase in investment equal to EH, the income has increased by Y1Y2.
It will be seen from the figure that Y1Y2 is greater than EH. On measuring, it will be found that Y1Y2 is
twice the length of EH. This is as it is expected because the marginal propensity to consume is here
equal to 1/2 and therefore the size of multiplier willbe equal to 2.
Five MajorLeakagewithMultiplier
The five major leakages with multiplier in income generation process which reduce the size of
multiplier are -
1. Paying off debts: The first leakage in the multiplier process occurs in the form of payment of debts
by the people, especially by businessmen. In the real world, all income received by the people as a
result of some increase in investment is not consumed. A part of the increment in income is used for
paying back the debts which the people have taken from moneylenders, banks or other financial
institutions. The incomes used for paying back the debts do not get spent on consumer goods and
services and therefore leak away fromthe income stream. This reduces the size of the multiplier.
2. Holding of idle cash balances: If the people hold a part of their increment in income as idle cash
balances and do not use them for consumption, they also constitute leakage in the multiplier process.
As we have seen, people keep a part of their income for satisfying their precautionary and speculative
motives, money kept for such purposes is not consumed and therefore does not appear in the
successive rounds of consumption expenditure and therefore reduces the increment in total income
and output.
3. Imports: In our above analysis if it is an open economy as is usually the case, then a part of
increment in income will also be spent on financing the imports of consumer goods. The proportion
of increments in income spent on the imports of consumer goods will generate income in other
countries and will not help in raising income and output in the domestic economy. Therefore, imports
constitute another important leakage in the multiplier process.
4. Taxation: Taxation is another important leakage in the multiplier process. The increments in
income which the people receive as a result of increase in investment are also in part used for pay-
ment of taxes. Therefore, the money used for payment of taxes does not appear in the successive
rounds of consumption expenditure in the multiplier process, and therefore multiplier is reduced to
that extent. However, if the money raised through taxation is spent by the Government, the leakage
through taxation will be offset by the increase in Government expenditure.
When will themultipliereffectbe large?
In short – the multiplier effectwillbe largerwhen
1. The propensity to spend extra income on domestic goods and services is high
2. The marginal rate of tax on extra income is low
3. The propensity to spend extra income rather than save is high
4. Consumer confidence is high (this affectswillingness to spend gains in income)
5. Businesses in the economy have the capacity to expand production to meet increases in
demand
FactorsaffectingMultiplier
1. Propensity To Consume: The higher is the propensity to consume domestically produced
goods and services, the greater is the multiplier effect. The government can influence the size
of the multiplier through changes in direct taxes. For example, a cut in the rate of income tax
will increase the amount of extra income that can be spent on further goods and services
2. Propensity To Imports: Another factor affecting the size of the multiplier effect is the
propensity to purchase imports. If, out of extra income, people spend their money on imports,
this demand is not passed on in the form of fresh spending on domestically produced output.
It leaks away from the circular flow of income and spending, reducing the size of the
multiplier.
3. Spare capacity in Economy: The multiplier process also requires that there is sufficient
spare capacity for extra output to be produced. If short-run aggregate supply is inelastic, the
full multiplier effect is unlikely to occur, because increases in AD will lead to higher prices
rather than a full increase in real national output. In contrast, when SRAS is perfectly elastic a
rise in aggregate demand causes a large increase in national output.
4. Crowdingout – this is where (for example) increased government spending or lower taxes
can lead to a rise in government borrowing and/or inflation which causes interest rates to
rise and has the effectof slowing down economic activity.
TypesofMultipliers
1. Employment Multiplier: It refers to type of a multiplier measure by Kahn’s where the number of
employment is created, activated and supplied from the base or primary jobs. let’s suppose in
cosmetic products the multiplier is 1.5, means that if employment increases by one job in cosmetic
company, then 1.5 other jobs are created throughout the economy.
2. Fiscal Multiplier: It’s referring to that type of multiplier where an increment of government
spending tends to leave a larger impact on the national income (GDP).
3. Money Multiplier: Money Multiplier is generally the amount of money that banks generate with
each unit of reserves which is the amount of deposit that banks keep. The money multiplier is the
ratio of deposits to reserves in the banking system. The higher the reserve ratio, the tighter will be
the money supply, which will result lesser excess reserve and larger the money supply, the lower the
reserve requirements which means more money is being generated for every unit deposited.
4. Income Multiplier: An injection of investment will ultimately result many times higher increase in
the income of an individual or to nation caused by that initial investment. That is why it’s called
income multiplier or investment multiplier at the same time.
5. Negative/Reverse Multiplier: The negative multiplier refers to such situation in the economy
where a minor decline in investment will trigger a huge decline in the business activity. A withdrawal
of income from the circular flow will lead to a downward multiplier effect. Therefore, whenever there
is an increased withdrawal, such as a rise in savings, import spending or taxation, there is a potential
downwardmultiplier effecton the rest of the economy.
6. Tax Multiplier: Tax multiplier can be thought in negative or downward multiplier because if an
increase in government spending leads in ever larger increase in GDP, then a contradictory case
would be an increase in tax, decreasing GDP or spending. Obviously higher taxes reduce the amount
of money people used to consume and this reduction indicates less spending in the market and a
leakage from the circular flow of income.
7. BalancedBudgetMultiplier
Balanced budget means change in government expenditure is exactly matched by a change in taxes.
Here in BBM an increase in government spending matched by an increase in taxes results in a net
increase in income by the same amount. The balanced budget multiplier is used to show an
expansionary fiscal policy. In this the increase in taxes (∆T) and in government expenditure (∆G) are
of an equal amount (∆T=∆G). The balanced-budget multiplier, as such, is actually the sum of the
EXPENDITURESMULTIPLIER (forgovernmentpurchases) and the TAXMULTIPLIER.
Meaning of BBM = 1: If the government increases its purchases by Rs X and also increases its
autonomous taxes so that the total change in taxes (both autonomous and induced) equals Rs X, the
level of equilibrium income (GDP) willincrease by precisely Rs X.
AlgebraicDerivationoftheBalancedBudgetMultiplier
The balanced budget multiplier is based on the combined operation of the Tax Multiplier [measures
changes in aggregate production caused by changes in taxes] and the Government Expenditure
Multiplier [measures changes in aggregate production caused by changes in an autonomous
expenditure]. In the balanced budget multiplier, the tax multiplier is smaller than the government
expenditure multiplier.
(a) The government expenditure multiplier is given by the following:-
This indicates that the change in income (∆Y) will equal the multiplier (1/1—c) times the change in
autonomous government expenditure.
(b)Similarly, the tax multiplier is given by:-
It shows that the change in income (∆Y) will equal multiplier (1/1-c) times the product of the
marginal propensity to consume (c)and the change in taxes (∆T).
(c) Now a simultaneous change in public expenditure and taxes may be expressed as a combination of
equations (1) and (2) whichis balanced budget multiplier,
It can also be expressed in the followingway:
Graphical ExplanationofBalancedBudgetMultiplier
We can explain BBM in terms of the Figure below where C1 is the consumption line before the
launching of the tax-expenditure programme. C2 is the post-tax consumption line, DE being the tax
receipt. If the entire DE amount of tax receipt is spent by the government, the aggregate demand
curve would be represented by C2 + I + G, where investment and government expenditure are
assumed to be autonomous. This curve intersects the 45° line at point F. As a result, national income
rises from OA to OB. Note that AB = DE = EF.
National Incomeand the ForeignTradeMultiplier
The Import Function: In an open economy consumers of a country also spend some income on
imported goods. The imports of a country depend on its level of income. The higher the level of
income, the prices of imported goods and tastes of consumers remaining the same, the greater will be
its imports. The relationship between imports and level of income of a country is called the import
functionand is written as: M = f(Y);whereM stands forimports and Y for income of a country.
It will be seen from above figure that even at zero national income some imports are undertaken by
exporting some capital accumulated in the past or by borrowingfrom abroad.
There are twoconcepts of Propensityto Importwhich should be understood –
(a) Marginal Propensity to Import (MPM) denoted by m
(b) Average Propensity to Import (APM)
Average Propensity to Import is defined as the proportion or percentage of national income
spent on imports, that is, it is rupee value of imports divided by national income or M/Y. Large
countries such as the U.S.A., Russia and India have low average propensity to import and small
countries such as Great Britain and Holland have high average propensity to import. The average
propensity to import in India is between 0.02 and 0.03.
Marginal Propensity to Import measures the change in import as a result of increase in
national incomes and is algebraically expressed as ΔM/ΔY where ΔM is the change in value of imports
and ΔY is the increase in national income. If imports increase by Rs. 3 when national income rises by
Rs. 100, the marginal propensity to import (ΔM/ΔI) will be equal to 3/100 = 0.03 or 3 per cent. If
increase in income by Rs. 100 leads to the increase in imports by Rs. 10, the marginal propensity to
imports is 10/100 = 0.1 or 10 per cent.
ForeignTradeMultiplier
It may be defined as the amount by which the national income of a nation will be raised by a
unit increase in domestic investment on exports. As exports increase, there is an increase in the
income of all persons associated with export industries. These in turn create demand for goods. But
this is dependent upon their marginal propensity to save (MPS) and the marginal propensity to
import (MPM). The smaller these two marginal propensities are, the larger will be the value of
multiplier and viceversa.
Equilibrium level of national income in an open economy is determined at the level at which
total leakage, that is, savings plus imports (S + M) equals total injection, that is, domestic investment
plus exports (I + X) into the income stream. Thus, in an open economy, national income is in
equilibrium at the level at which;S + M = I + X
When a change in any of the above four variables occurs, then the change on the left side of the above
equation must equal the change on the right side if the new equilibrium is to be achieved.
Hence, ΔS + ΔM = ΔI + ΔX … (1)
Now, change in saving, ΔS = s. ΔY; Where s = marginal propensity to save and ΔY= change in national
income. Likewise, change in imports, ΔM = m. ΔY;where m = marginal propensity to import.
Or Foreign Trade Multiplier = 1/ [1 – MPC (b) + MPM(m)] since MPS = 1 - MPC
Thus, foreign trade multiplier is equal to the reciprocal of marginal propensity to save (s) plus
marginal propensity to import (m). It is evident that smaller the leaks, that is, smaller the values of
marginal propensity to save (s) and marginal propensity to import (m) the greater the value of
foreign trade multiplier.
Example:An economy is characterised by the followingequations:
Consumption, C = 120 + 0.9Yd
Investment, I = 20 Crores
Government Expenditure, G = 20 Crores
Tax, T = 0
Exports, X = 40 Crores
Imports, M = 20 + 0.05 Y
What is the equilibrium income? Calculate trade balance and the value of foreign trade multiplier?
Solution
1. National Income
Y = C + I + G + NX
= 120 + 0.9Yd + 20 + 20 + 40 – (20 – 0.05Y)
= 120 + 0.9 (Y – T) + 20 + 20 + 40 – 20 – 0.05Y
= 120 + 0.9Y – 0 + 60 – 0.05Y
Y = 180 + 0.85Y
Y – 0.85Y = 180
0.15Y = 180
Y = 180 / 0.15
Y = 1,200
2. Trade Balance
X – M = 40 – (20 + 0.05Y)
Substituting the value of Y, we have
Trade balance = 40 – [20 + 0.5(1,200)]
= 40 – 20 – 60
= - 40
Tradebalanceis in deficit.
3. Value of foreign trade multiplier = 1
1 – b + m
Where b is marginal propensity to consumer and m is marginal propensity to import.
Foreign Trade Multiplier = 1
1 – 0.9 + 0.05
= 1
0.15
= 6.67
Example:Behavioural and Structural equations of an economy are given below:
C = 200 + b (Y – 100 – tY)
I = 100 & G = 100
X = 20 & M = 10 + 0.1Y
The marginal propensity to consume ‘b’ is equal to 0.8 and proportional income tax rate, t = 0.25.
1. Find the equilibrium national income
2. Find foreign trade multiplier
3. Find equilibrium value of imports
4. If equilibrium national income falls short of full employment income by Rs 100, how much
government should increase its expenditure to attain full – employment?
Solution
1. Reduced form of the equation for equilibrium income is
Y = 1 (a - bT + I + G + X - Ḿ)
1 – b (1-t) + m
Substituting the values of the variables and parameters we have
Y = 1 [200 – (100*0.8) + 100 + 100 + 20 – 10]
1 – 0.8 (1-0.25) + 0.1
Y = 1 (330)
0.5
Y = 330 / 0.5
Y = 660
2. Foreign Trade Multiplier
= 1
1 – b (1-t)+ m
= 1
1 – 0.8 (1-0.25) + 0.1
=2
3. Equilibrium value of imports can be obtained by substituting the equilibrium income 660 in the
import function.Thus
M = 10 + 0.1Y
M = 10 + 0.1(660)
M = 10 + 66 = 76
4. Required increase in Government expenditures to attain Rs 100 increase in income can be
obtained as under:
Δ Y = Foreign Trade Multiplier * Δ G
Δ Y = 2 * DG
Or Δ G = ΔY/2 = 100/2 = 50
Example:The equations in the economy are given as:
C = 400 + bYd
I = 140; Tax T = 120
Government Expenditure G = 140
Exports X = 40
Imports M = 20 + 0.1Y
Marginal Propensity to consumer b = 0.8.
1. Find the equilibrium level of income
2. The value of the foreign trade multiplier
3. The equilibrium level of imports
Solution
The consumption functionis
C = 400 + 0.8Yd
C = 400 + 0.8(Y – T)
C = 400 + 0.8(Y – 120)
The equilibrium condition is given as Y = C + I + G + X – M; Thus,
Y = 400 + 0.8(Y – 120) + 140 + 140 + 40 – 20 – 0.1Y
Y = 400 + 0.8Y – 96 + 140 + 140 + 40 – 20 – 0.1Y
Y = 604 + 0.7Y
Y – 0.7Y = 60; 0.3Y= 604
Y = 604 /0.3
Thus equilibrium levelof income is 2,013.33.
2. Foreign Trade Multiplier
Δ Y = 1
Δ X 1 – b + m
= 1 = 3.33
1 – 0.8 + 0.1
3. Imports at the equilibrium level
M = 20 + 0.1Y = 20 + 0.1 (2,013.33) = 221.333
The equilibrium level of imports is 221.333.
WorkingofForeignTradeMultiplier
The foreign trade multiplier works in the same way as Keynes’ investment multiplier. When
there is increase in exports, it will cause the increase in income of the exporters and those employed
in the export industries. They will save some of the increase in their incomes and will spend a good
part of the increases in their incomes on consumer goods, both domestic and imported ones.
While savings do not generate further income and represent leakage from the income stream,
expenditure on imports leads to the increase in the incomes of the foreign countries from which
goods are imported. Thus expenditure on imports also represents a leakage from the income stream
as far as domestic economy is concerned. But the increased expenditure on domestic goods as a result
of increase in exports will go on increasing incomes in various successive rounds of spending till the
multiplier fully works itself out.
It may be noted that increase in exports of a country can occur due to several reasons. There
may be change in tastes or demand of the people of foreign countries for goods of a country. To begin
with, the exporters may meet the demand for exported goods by selling their inventories and enjoy
higher incomes. But in the next periods, they will make efforts to increase the production of exported
goods and employ more workers. This will generate new income and employment in the export
industries. But the working of multiplier does not stop here. Those employed in export industries will
spend a good part of their increased incomes on goods produced by other industries and in this way
increases in income, production and employment will spread in the wholeof the domestic economy.
TheForeignTradeMultiplier:WithbothExportsandDomesticInvestment
In an open economy when there is positive investment the level of equilibrium national income is
reached when sum of domestic investment and net exports equals saving. Thus, in an open economy
the condition for the equilibrium level of national income is:
Id + Xn = S … (1);
Where Id is domestic investment, Xn is net exports and S is the saving.
Net exports (Xn)is the net of exports over imports, that is, Xn = X – M
Substituting X – M forXn in equation (1) we get
Id + (X – M) = S
Or Id + X = S + M
In the case when there is positive domestic investment the determination of the equilibrium level of
national income is graphically shown in Fig. below. The curve Id represents autonomous domestic
investment which remains constant. S is the saving function curve showing that saving is the
increasing function of income.
Over the domestic investment curve (Id) we have added the exports (X) of the economy to get
the Id + X curve. To the saving function curve we have added the import function curve to obtain the
aggregate of saving and import functions curve(S + M).
It will be observed from Figure that Id + X equals S+M at point E and thus the equilibrium level
of national income Y0 is determined. Note that at Y0 level of income saving (S) and domestic
investment (Id)are also equal. Thus, at equilibrium income Y0; Id + X = S + M and Id = S
The equality of exports (X) with imports (M) implies that there is equilibrium in the balance on the
current account. However, it is important to note that it is not necessary that at equilibrium level of
national income exports (X) equal imports (M). This equilibrium in the current account balance along
with equilibrium of saving and domestic investment occurs only when exports are equal to imports at
the equilibrium level of income determined by the equality of saving and domestic investment. In Fig.
above at equilibrium income Y0 at which saving equals domestic investment, imports are equal to DE.
If exports happen to be equal to DE, the equilibrium in the current account balance will also occur.
However,this is not necessary because exports may be greater or less than the imports DE.
MoreExamples onMultiplier
Problem: Suppose C = Rs. 40 + 0.75Y and I = Rs. 60. Find the equilibrium levels of income,
consumption and savings. Now, if investment rises to Rs. 90, what will be the new levels of
equilibrium income, consumption and savings?
Solution: Usingaggregate demand- aggregate approach,
Problem:Suppose the level of autonomous investment in an economy is Rs. 200 crores and
consumption function of the economy is: C = 80 + 0.75Y
(a) What willbe the equilibrium level of income?
(b)What will be the increase in national income if investment increases by Rs. 25 crores
Solution,
(a) For equilibrium level of income,
Y = C + I……….[1];
Where C = 80 + 0.75; I = 200 crores
Substituting the values of C and I in (1) we have
Y = 80 + 0.75Y + 200
Or (Y – 0.75F) = 80 + 200 = 280
Or 0.25 Y = 280
Or Y = 280 x 100/25 = 1120
Equilibrium level of income is therefore equal to 1120 crores.
b) How much increase in income will occuras a result of increase in investment by Rs. 25?
The size of multiple is determined by the value of marginal prepensely to consume.
In the given consumption function (C = 80 + 0.75 Y) marginal propensity to consume or MPC is equal
to 0.75 or 3/4
Thus, multiplier = 1/1-MPC = 1/1-3/4 = 4
Thus, with increase in investment by Rs. 25 crores, national income will rise by 25 x 4 = 100 crores.

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Multiplier Theory in Economics

  • 1. Multipliers in Economics ConceptofMultiplier The concept of multiplier was first of all developed by F.A. Kahn in the early 1930s with reference to the increase in employment,. But Keynes later further refined it. In economics, a multiplier is a factor that measures how much an economic variable (Income, Output) changes in response to a change in some other variable (Investment, Govt spending, tax, export etc). For example, suppose variable x changes by 1 unit, which causes another variable y to change by M units. Then the multiplier is M. In the economy, there is a circular flow of income and spending where everything is connected and one’s spending/expenditure becomes earning of income to others. Money that is earned by one person from another, gets spent again - not just once, but many times. What it means is that small increase in spending by consumers or investment by government lead to much larger increase in economic income/output. Economists use Multiplier to measure how much income gets multiplied. Money spent in the economy doesn't stop with the first transaction only, rather flows through the economy one person at a time, like a ripple effect when a rock gets thrown into the water. An injection of extra income leads to more spending, which creates more income, and so on. The multiplier effectrefers to the increase in final income arising fromany new injection of spending. If ΔI stands for increment in investment and ΔY stands for the resultant increase in income, then multiplier is equal to the ratio of increment in income (ΔY) to the increment in investment (ΔI). Therefore k = ΔY/ΔI where k stands for multiplier. For example, if investment in an economy of Rs. 100 crores is made, then the income will not rise by Rs. 100 crores only but a multiple of it say by Rs. 300 crores, then the multiplier is equal to 3. The multiplier is, therefore, the ratio of increment in income to the increment in investment. The size of the multiplier depends upon the marginal propensityto consume (MPC)or to save called the marginalpropensityto save (MPS). WorkingofMultiplier Suppose Government undertakes investment expenditure equal to Rs. 100 crores on some public works, say the construction of rural roads. For this Government will pay wages to the labourers engaged, prices for the materials to the suppliers and remunerations to other factors that make contribution to the work of road-building. The people who receive Rs. 100 crores will spend a good part of them on consumer goods. Suppose marginal propensity to consume of community is 4/5 or 80%. Then out of Rs. 100 crores they will spend Rs. 80 crores on consumer goods, which would increase incomes of those people who supply consumer goods equal to Rs. 80 crores. But those who receive these Rs. 80 crores will also in turn spend these incomes, they will spend Rs. 64 crores (80% of 80) on consumer goods. Thus, this will further increase incomes of some other people equal to Rs. 64 crores. In this way, the chain of consumption expenditure would continue and the income in the economy 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, we see that the total income in the economy due to initial investment of 100 crores will not increase by only Rs. 100 crores, but by many time more. Therefore total Increase in income denoted by ΔY ΔY = 100 + 100 x 4/5 + 100(4/5)2 + 100(4/5)3 + 100(4/5)4 + ….. = 100[1 + (4/5) + (4/5)2 + (4/5)3 + (4/5)4+……] But the aboveseries is an infinite geometric progression. Therefore, increase in income (ΔY) = 100 [1/ (1-4/5)] =100 x [1/ (1/5)] = 100 x 5 = 500 Therefore here multiplier is 5 MultiplierAssumptions (i) That there is no change in the marginal propensity to consume but remains constant. (ii) That there is no induced investment (i.e., acceleratoris not operating). (iv)That the output of consumer goods is responsive to effectivedemand for these. (v)That there is complete absence of government taxation. (vi)That there is no time lag between the receipt of income and its expenditure.
  • 2. (vii)That there is a closed economy. TheMultiplierCanBeDerivedAlgebraicallyAsFollows: Writing the equation forthe equilibrium level of income we have - Y = C + I ………………. [1] As in the multiplier analysis we are concerned with changes in income induced by changes in investment, rewriting the above equation in terms of changes in the variables wehave - ΔY = ΔC + ΔI……………. [2] In the simple Keynesian model of income determination, change in investment is considered to be autonomous or independent of changes in income while changes in consumption are function of changes in income. In the consumption function, C = a + bY……………….[3] Where a is a constant term, b is marginal propensity to consume which is also assumed to remain constant. Therefore, change in consumption can occuronly if there is change in income. Thus ΔC = bΔY…………………[4] Substituting (4)into (2) we have ΔY = bΔY + ΔI Or ΔY – bΔY = ΔI Or ΔY (1 – b) = ΔI Or ΔY =ΔI [1/ (1-b)] Or ΔY/ΔI= 1/ (1 – b) As b stands for marginal propensity to consume Investment Multiplier, KI = ΔY/ΔI= 1/ [1 – MPC] = 1/MPS It follows from above that the size or value of multiplier is the reciprocal of marginal propensity to save. Two LimitingCasesofthe ValueofMultiplier: (i) One limiting case occurs when the Marginal Propensity to Consume (MPC) is equal to one, that is, when the whole of the increment in income is consumed and nothing is saved. In this case, the size of multiplier will be equal to infinity, that is, a small increase in investment will bring about a very large increase in income and employment. However, this is unlikely to occur since marginal propensity to consume in the real world is less than one. (ii) The other limiting case occurs when Marginal Propensity to Consume (MPC) is equal to zero, that is, when nothing out of the increment in income is consumed; whole increment in income is saved. In this case, the value of the multiplier will be equal to one. That is, in this case, the increment in income will be equal to the original increase in investment and not a multiple of it. But in actual practice the marginal propensity to consume is less than one but more than zero (1 > ΔC/ΔY > 0). Therefore, the value of the multiplier is greater than one but less than infinity. Applying the‘MultiplierEffect’:Themultiplier conceptcan be used any situation where there is a new injection into an economy.Examples of such situations include: 1. When the government funds building of a new public works 2. When there is an increase in exports abroad 3. When there is a reduction in interest rates or tax rates, or when the exchange rate falls. DiagrammaticRepresentationofMultiplier We know that, the level of equilibrium national income is fixed at the level where C + I curve intersects the 45° income curve. The multiplier is illustrated in Figure below. In this figure line C represents consumption function. Marginal propensity to consume has been here assumed to be equal to 1/2 i.e., 0.5. Therefore, the slope of the curve C equals to 0.5. C + I represents aggregate demand curve. It will be seen from figure that the aggregate demand curve C + I intersects the 45° line at point E resulting equilibrium levelof income equal to OY1.
  • 3. If investment increases by the amount EH (ΔI) then as a consequence of such increase in investment, the aggregate demand curve shifts upward to the new position C + I’. This new aggregate demand curve C + I’ intersects the 45° income line at point F so that the equilibrium level of income increases to OY2. Hence as a result of net increase in investment equal to EH, the income has increased by Y1Y2. It will be seen from the figure that Y1Y2 is greater than EH. On measuring, it will be found that Y1Y2 is twice the length of EH. This is as it is expected because the marginal propensity to consume is here equal to 1/2 and therefore the size of multiplier willbe equal to 2. Five MajorLeakagewithMultiplier The five major leakages with multiplier in income generation process which reduce the size of multiplier are - 1. Paying off debts: The first leakage in the multiplier process occurs in the form of payment of debts by the people, especially by businessmen. In the real world, all income received by the people as a result of some increase in investment is not consumed. A part of the increment in income is used for paying back the debts which the people have taken from moneylenders, banks or other financial institutions. The incomes used for paying back the debts do not get spent on consumer goods and services and therefore leak away fromthe income stream. This reduces the size of the multiplier. 2. Holding of idle cash balances: If the people hold a part of their increment in income as idle cash balances and do not use them for consumption, they also constitute leakage in the multiplier process. As we have seen, people keep a part of their income for satisfying their precautionary and speculative motives, money kept for such purposes is not consumed and therefore does not appear in the successive rounds of consumption expenditure and therefore reduces the increment in total income and output. 3. Imports: In our above analysis if it is an open economy as is usually the case, then a part of increment in income will also be spent on financing the imports of consumer goods. The proportion of increments in income spent on the imports of consumer goods will generate income in other countries and will not help in raising income and output in the domestic economy. Therefore, imports constitute another important leakage in the multiplier process. 4. Taxation: Taxation is another important leakage in the multiplier process. The increments in income which the people receive as a result of increase in investment are also in part used for pay- ment of taxes. Therefore, the money used for payment of taxes does not appear in the successive rounds of consumption expenditure in the multiplier process, and therefore multiplier is reduced to that extent. However, if the money raised through taxation is spent by the Government, the leakage through taxation will be offset by the increase in Government expenditure. When will themultipliereffectbe large? In short – the multiplier effectwillbe largerwhen 1. The propensity to spend extra income on domestic goods and services is high
  • 4. 2. The marginal rate of tax on extra income is low 3. The propensity to spend extra income rather than save is high 4. Consumer confidence is high (this affectswillingness to spend gains in income) 5. Businesses in the economy have the capacity to expand production to meet increases in demand FactorsaffectingMultiplier 1. Propensity To Consume: The higher is the propensity to consume domestically produced goods and services, the greater is the multiplier effect. The government can influence the size of the multiplier through changes in direct taxes. For example, a cut in the rate of income tax will increase the amount of extra income that can be spent on further goods and services 2. Propensity To Imports: Another factor affecting the size of the multiplier effect is the propensity to purchase imports. If, out of extra income, people spend their money on imports, this demand is not passed on in the form of fresh spending on domestically produced output. It leaks away from the circular flow of income and spending, reducing the size of the multiplier. 3. Spare capacity in Economy: The multiplier process also requires that there is sufficient spare capacity for extra output to be produced. If short-run aggregate supply is inelastic, the full multiplier effect is unlikely to occur, because increases in AD will lead to higher prices rather than a full increase in real national output. In contrast, when SRAS is perfectly elastic a rise in aggregate demand causes a large increase in national output. 4. Crowdingout – this is where (for example) increased government spending or lower taxes can lead to a rise in government borrowing and/or inflation which causes interest rates to rise and has the effectof slowing down economic activity. TypesofMultipliers 1. Employment Multiplier: It refers to type of a multiplier measure by Kahn’s where the number of employment is created, activated and supplied from the base or primary jobs. let’s suppose in cosmetic products the multiplier is 1.5, means that if employment increases by one job in cosmetic company, then 1.5 other jobs are created throughout the economy. 2. Fiscal Multiplier: It’s referring to that type of multiplier where an increment of government spending tends to leave a larger impact on the national income (GDP). 3. Money Multiplier: Money Multiplier is generally the amount of money that banks generate with each unit of reserves which is the amount of deposit that banks keep. The money multiplier is the ratio of deposits to reserves in the banking system. The higher the reserve ratio, the tighter will be the money supply, which will result lesser excess reserve and larger the money supply, the lower the reserve requirements which means more money is being generated for every unit deposited. 4. Income Multiplier: An injection of investment will ultimately result many times higher increase in the income of an individual or to nation caused by that initial investment. That is why it’s called income multiplier or investment multiplier at the same time. 5. Negative/Reverse Multiplier: The negative multiplier refers to such situation in the economy where a minor decline in investment will trigger a huge decline in the business activity. A withdrawal of income from the circular flow will lead to a downward multiplier effect. Therefore, whenever there is an increased withdrawal, such as a rise in savings, import spending or taxation, there is a potential downwardmultiplier effecton the rest of the economy. 6. Tax Multiplier: Tax multiplier can be thought in negative or downward multiplier because if an increase in government spending leads in ever larger increase in GDP, then a contradictory case would be an increase in tax, decreasing GDP or spending. Obviously higher taxes reduce the amount of money people used to consume and this reduction indicates less spending in the market and a leakage from the circular flow of income. 7. BalancedBudgetMultiplier Balanced budget means change in government expenditure is exactly matched by a change in taxes. Here in BBM an increase in government spending matched by an increase in taxes results in a net
  • 5. increase in income by the same amount. The balanced budget multiplier is used to show an expansionary fiscal policy. In this the increase in taxes (∆T) and in government expenditure (∆G) are of an equal amount (∆T=∆G). The balanced-budget multiplier, as such, is actually the sum of the EXPENDITURESMULTIPLIER (forgovernmentpurchases) and the TAXMULTIPLIER. Meaning of BBM = 1: If the government increases its purchases by Rs X and also increases its autonomous taxes so that the total change in taxes (both autonomous and induced) equals Rs X, the level of equilibrium income (GDP) willincrease by precisely Rs X. AlgebraicDerivationoftheBalancedBudgetMultiplier The balanced budget multiplier is based on the combined operation of the Tax Multiplier [measures changes in aggregate production caused by changes in taxes] and the Government Expenditure Multiplier [measures changes in aggregate production caused by changes in an autonomous expenditure]. In the balanced budget multiplier, the tax multiplier is smaller than the government expenditure multiplier. (a) The government expenditure multiplier is given by the following:- This indicates that the change in income (∆Y) will equal the multiplier (1/1—c) times the change in autonomous government expenditure. (b)Similarly, the tax multiplier is given by:- It shows that the change in income (∆Y) will equal multiplier (1/1-c) times the product of the marginal propensity to consume (c)and the change in taxes (∆T). (c) Now a simultaneous change in public expenditure and taxes may be expressed as a combination of equations (1) and (2) whichis balanced budget multiplier, It can also be expressed in the followingway: Graphical ExplanationofBalancedBudgetMultiplier We can explain BBM in terms of the Figure below where C1 is the consumption line before the launching of the tax-expenditure programme. C2 is the post-tax consumption line, DE being the tax receipt. If the entire DE amount of tax receipt is spent by the government, the aggregate demand curve would be represented by C2 + I + G, where investment and government expenditure are assumed to be autonomous. This curve intersects the 45° line at point F. As a result, national income rises from OA to OB. Note that AB = DE = EF.
  • 6. National Incomeand the ForeignTradeMultiplier The Import Function: In an open economy consumers of a country also spend some income on imported goods. The imports of a country depend on its level of income. The higher the level of income, the prices of imported goods and tastes of consumers remaining the same, the greater will be its imports. The relationship between imports and level of income of a country is called the import functionand is written as: M = f(Y);whereM stands forimports and Y for income of a country. It will be seen from above figure that even at zero national income some imports are undertaken by exporting some capital accumulated in the past or by borrowingfrom abroad. There are twoconcepts of Propensityto Importwhich should be understood – (a) Marginal Propensity to Import (MPM) denoted by m (b) Average Propensity to Import (APM) Average Propensity to Import is defined as the proportion or percentage of national income spent on imports, that is, it is rupee value of imports divided by national income or M/Y. Large countries such as the U.S.A., Russia and India have low average propensity to import and small countries such as Great Britain and Holland have high average propensity to import. The average propensity to import in India is between 0.02 and 0.03. Marginal Propensity to Import measures the change in import as a result of increase in national incomes and is algebraically expressed as ΔM/ΔY where ΔM is the change in value of imports and ΔY is the increase in national income. If imports increase by Rs. 3 when national income rises by Rs. 100, the marginal propensity to import (ΔM/ΔI) will be equal to 3/100 = 0.03 or 3 per cent. If increase in income by Rs. 100 leads to the increase in imports by Rs. 10, the marginal propensity to imports is 10/100 = 0.1 or 10 per cent. ForeignTradeMultiplier It may be defined as the amount by which the national income of a nation will be raised by a unit increase in domestic investment on exports. As exports increase, there is an increase in the income of all persons associated with export industries. These in turn create demand for goods. But this is dependent upon their marginal propensity to save (MPS) and the marginal propensity to
  • 7. import (MPM). The smaller these two marginal propensities are, the larger will be the value of multiplier and viceversa. Equilibrium level of national income in an open economy is determined at the level at which total leakage, that is, savings plus imports (S + M) equals total injection, that is, domestic investment plus exports (I + X) into the income stream. Thus, in an open economy, national income is in equilibrium at the level at which;S + M = I + X When a change in any of the above four variables occurs, then the change on the left side of the above equation must equal the change on the right side if the new equilibrium is to be achieved. Hence, ΔS + ΔM = ΔI + ΔX … (1) Now, change in saving, ΔS = s. ΔY; Where s = marginal propensity to save and ΔY= change in national income. Likewise, change in imports, ΔM = m. ΔY;where m = marginal propensity to import. Or Foreign Trade Multiplier = 1/ [1 – MPC (b) + MPM(m)] since MPS = 1 - MPC Thus, foreign trade multiplier is equal to the reciprocal of marginal propensity to save (s) plus marginal propensity to import (m). It is evident that smaller the leaks, that is, smaller the values of marginal propensity to save (s) and marginal propensity to import (m) the greater the value of foreign trade multiplier. Example:An economy is characterised by the followingequations: Consumption, C = 120 + 0.9Yd Investment, I = 20 Crores Government Expenditure, G = 20 Crores Tax, T = 0 Exports, X = 40 Crores Imports, M = 20 + 0.05 Y What is the equilibrium income? Calculate trade balance and the value of foreign trade multiplier? Solution 1. National Income Y = C + I + G + NX = 120 + 0.9Yd + 20 + 20 + 40 – (20 – 0.05Y) = 120 + 0.9 (Y – T) + 20 + 20 + 40 – 20 – 0.05Y = 120 + 0.9Y – 0 + 60 – 0.05Y Y = 180 + 0.85Y Y – 0.85Y = 180 0.15Y = 180 Y = 180 / 0.15
  • 8. Y = 1,200 2. Trade Balance X – M = 40 – (20 + 0.05Y) Substituting the value of Y, we have Trade balance = 40 – [20 + 0.5(1,200)] = 40 – 20 – 60 = - 40 Tradebalanceis in deficit. 3. Value of foreign trade multiplier = 1 1 – b + m Where b is marginal propensity to consumer and m is marginal propensity to import. Foreign Trade Multiplier = 1 1 – 0.9 + 0.05 = 1 0.15 = 6.67 Example:Behavioural and Structural equations of an economy are given below: C = 200 + b (Y – 100 – tY) I = 100 & G = 100 X = 20 & M = 10 + 0.1Y The marginal propensity to consume ‘b’ is equal to 0.8 and proportional income tax rate, t = 0.25. 1. Find the equilibrium national income 2. Find foreign trade multiplier 3. Find equilibrium value of imports 4. If equilibrium national income falls short of full employment income by Rs 100, how much government should increase its expenditure to attain full – employment? Solution 1. Reduced form of the equation for equilibrium income is Y = 1 (a - bT + I + G + X - Ḿ) 1 – b (1-t) + m Substituting the values of the variables and parameters we have Y = 1 [200 – (100*0.8) + 100 + 100 + 20 – 10] 1 – 0.8 (1-0.25) + 0.1 Y = 1 (330) 0.5 Y = 330 / 0.5 Y = 660 2. Foreign Trade Multiplier = 1 1 – b (1-t)+ m = 1 1 – 0.8 (1-0.25) + 0.1 =2 3. Equilibrium value of imports can be obtained by substituting the equilibrium income 660 in the import function.Thus M = 10 + 0.1Y M = 10 + 0.1(660) M = 10 + 66 = 76 4. Required increase in Government expenditures to attain Rs 100 increase in income can be obtained as under: Δ Y = Foreign Trade Multiplier * Δ G
  • 9. Δ Y = 2 * DG Or Δ G = ΔY/2 = 100/2 = 50 Example:The equations in the economy are given as: C = 400 + bYd I = 140; Tax T = 120 Government Expenditure G = 140 Exports X = 40 Imports M = 20 + 0.1Y Marginal Propensity to consumer b = 0.8. 1. Find the equilibrium level of income 2. The value of the foreign trade multiplier 3. The equilibrium level of imports Solution The consumption functionis C = 400 + 0.8Yd C = 400 + 0.8(Y – T) C = 400 + 0.8(Y – 120) The equilibrium condition is given as Y = C + I + G + X – M; Thus, Y = 400 + 0.8(Y – 120) + 140 + 140 + 40 – 20 – 0.1Y Y = 400 + 0.8Y – 96 + 140 + 140 + 40 – 20 – 0.1Y Y = 604 + 0.7Y Y – 0.7Y = 60; 0.3Y= 604 Y = 604 /0.3 Thus equilibrium levelof income is 2,013.33. 2. Foreign Trade Multiplier Δ Y = 1 Δ X 1 – b + m = 1 = 3.33 1 – 0.8 + 0.1 3. Imports at the equilibrium level M = 20 + 0.1Y = 20 + 0.1 (2,013.33) = 221.333 The equilibrium level of imports is 221.333. WorkingofForeignTradeMultiplier The foreign trade multiplier works in the same way as Keynes’ investment multiplier. When there is increase in exports, it will cause the increase in income of the exporters and those employed in the export industries. They will save some of the increase in their incomes and will spend a good part of the increases in their incomes on consumer goods, both domestic and imported ones. While savings do not generate further income and represent leakage from the income stream, expenditure on imports leads to the increase in the incomes of the foreign countries from which goods are imported. Thus expenditure on imports also represents a leakage from the income stream as far as domestic economy is concerned. But the increased expenditure on domestic goods as a result of increase in exports will go on increasing incomes in various successive rounds of spending till the multiplier fully works itself out. It may be noted that increase in exports of a country can occur due to several reasons. There may be change in tastes or demand of the people of foreign countries for goods of a country. To begin with, the exporters may meet the demand for exported goods by selling their inventories and enjoy higher incomes. But in the next periods, they will make efforts to increase the production of exported goods and employ more workers. This will generate new income and employment in the export industries. But the working of multiplier does not stop here. Those employed in export industries will spend a good part of their increased incomes on goods produced by other industries and in this way increases in income, production and employment will spread in the wholeof the domestic economy.
  • 10. TheForeignTradeMultiplier:WithbothExportsandDomesticInvestment In an open economy when there is positive investment the level of equilibrium national income is reached when sum of domestic investment and net exports equals saving. Thus, in an open economy the condition for the equilibrium level of national income is: Id + Xn = S … (1); Where Id is domestic investment, Xn is net exports and S is the saving. Net exports (Xn)is the net of exports over imports, that is, Xn = X – M Substituting X – M forXn in equation (1) we get Id + (X – M) = S Or Id + X = S + M In the case when there is positive domestic investment the determination of the equilibrium level of national income is graphically shown in Fig. below. The curve Id represents autonomous domestic investment which remains constant. S is the saving function curve showing that saving is the increasing function of income. Over the domestic investment curve (Id) we have added the exports (X) of the economy to get the Id + X curve. To the saving function curve we have added the import function curve to obtain the aggregate of saving and import functions curve(S + M). It will be observed from Figure that Id + X equals S+M at point E and thus the equilibrium level of national income Y0 is determined. Note that at Y0 level of income saving (S) and domestic investment (Id)are also equal. Thus, at equilibrium income Y0; Id + X = S + M and Id = S The equality of exports (X) with imports (M) implies that there is equilibrium in the balance on the current account. However, it is important to note that it is not necessary that at equilibrium level of national income exports (X) equal imports (M). This equilibrium in the current account balance along with equilibrium of saving and domestic investment occurs only when exports are equal to imports at the equilibrium level of income determined by the equality of saving and domestic investment. In Fig. above at equilibrium income Y0 at which saving equals domestic investment, imports are equal to DE. If exports happen to be equal to DE, the equilibrium in the current account balance will also occur. However,this is not necessary because exports may be greater or less than the imports DE. MoreExamples onMultiplier Problem: Suppose C = Rs. 40 + 0.75Y and I = Rs. 60. Find the equilibrium levels of income, consumption and savings. Now, if investment rises to Rs. 90, what will be the new levels of equilibrium income, consumption and savings? Solution: Usingaggregate demand- aggregate approach,
  • 11. Problem:Suppose the level of autonomous investment in an economy is Rs. 200 crores and consumption function of the economy is: C = 80 + 0.75Y (a) What willbe the equilibrium level of income? (b)What will be the increase in national income if investment increases by Rs. 25 crores Solution, (a) For equilibrium level of income, Y = C + I……….[1]; Where C = 80 + 0.75; I = 200 crores Substituting the values of C and I in (1) we have Y = 80 + 0.75Y + 200 Or (Y – 0.75F) = 80 + 200 = 280 Or 0.25 Y = 280 Or Y = 280 x 100/25 = 1120 Equilibrium level of income is therefore equal to 1120 crores. b) How much increase in income will occuras a result of increase in investment by Rs. 25? The size of multiple is determined by the value of marginal prepensely to consume. In the given consumption function (C = 80 + 0.75 Y) marginal propensity to consume or MPC is equal to 0.75 or 3/4 Thus, multiplier = 1/1-MPC = 1/1-3/4 = 4 Thus, with increase in investment by Rs. 25 crores, national income will rise by 25 x 4 = 100 crores.