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Page 1
MULTIPLIES
INSTITUTE OF LIFELONG LEARNING, UNIVERSITY OF DELHI
SUBJECT: MACROECONOMICS
LESSON : MULTIPLIES
LESSON DEVELOPER: MANJUL SINGH
COLLEGE/ DEPARTMENT: SATYAWATI COLLEGE (E), DEPARTMENT OF ECONOMICS,
UNIVERSITY OF DELHI
Page 2
MULTIPLIES
INSTITUTE OF LIFELONG LEARNING, UNIVERSITY OF DELHI
SUBJECT: MACROECONOMICS
LESSON : MULTIPLIES
LESSON DEVELOPER: MANJUL SINGH
COLLEGE/ DEPARTMENT: SATYAWATI COLLEGE (E), DEPARTMENT OF ECONOMICS,
UNIVERSITY OF DELHI
MULTIPLIES
INSTITUTE OF LIFELONG LEARNING, UNIVERSITY OF DELHI
MULTIPLIER
The theory of multiplier occupies a very important role in the analysis of national income
behavior with response to the change in its determinants. Multiplier is also helpful to
analyses the effect of change in monetary and budgetary policies of the government.
According to Shapiro: The ratio of the change in income and output to the change in
the level of the spending function is called Multiplier
There are two theories of multiplier given by two renowned economists
British Economist R.F. Kahn, his multiplier was an employment multiplier which measures
the ratio of increment of total employment in the capital goods industries.
Economist J.M. Keynes: his multiplier is also known as investment multiplier or income
multiplier, it is the ratio of the increment to total income associated with a given increment
in investment.
The theory of multiplier has been used generally to explain the cumulative upward and
downward swings of the trade cycles that occur in a free enterprise capitalist economy.
Increase in investment leads to multiple and cumulative effect on national income, output
and employment.
For example: Investment increases by Rs.100 crores. If this causes an increases in output
of Rs. 500 Crores, then the multiplier is 5 .If instead the resulting increase in output is
Rs.800, then multiplier is 8.So increase in income is many times more than the initial
increase in investment.
So, Basically, multiplier is the ratio of increment in income to the increment in investment.
K =
(?I stands for increment in investment, ?Y stands for resultant increase in income, K is
multiplier)
If we take an example of government spending for some public works i.e. construction of a
Central University. For this government provides Rs.100 crores for construction of
university, In this process the Rs.100 crores will go to the various field like wages to the
workers, purchasing building materials, etc. It will increase income of the people by Rs.1000
crores. The people who receive this amount spent some part of it on various consumer
goods but it depends on Marginal Propensity to Consume(MPC). If they all have Marginal
Propensity to Consume of 2/3, they will now spend Rs.666.67cr on new consumption goods.
So the producer of the goods will now get extra income of Rs.666.67 cr. But story is not
Page 3
MULTIPLIES
INSTITUTE OF LIFELONG LEARNING, UNIVERSITY OF DELHI
SUBJECT: MACROECONOMICS
LESSON : MULTIPLIES
LESSON DEVELOPER: MANJUL SINGH
COLLEGE/ DEPARTMENT: SATYAWATI COLLEGE (E), DEPARTMENT OF ECONOMICS,
UNIVERSITY OF DELHI
MULTIPLIES
INSTITUTE OF LIFELONG LEARNING, UNIVERSITY OF DELHI
MULTIPLIER
The theory of multiplier occupies a very important role in the analysis of national income
behavior with response to the change in its determinants. Multiplier is also helpful to
analyses the effect of change in monetary and budgetary policies of the government.
According to Shapiro: The ratio of the change in income and output to the change in
the level of the spending function is called Multiplier
There are two theories of multiplier given by two renowned economists
British Economist R.F. Kahn, his multiplier was an employment multiplier which measures
the ratio of increment of total employment in the capital goods industries.
Economist J.M. Keynes: his multiplier is also known as investment multiplier or income
multiplier, it is the ratio of the increment to total income associated with a given increment
in investment.
The theory of multiplier has been used generally to explain the cumulative upward and
downward swings of the trade cycles that occur in a free enterprise capitalist economy.
Increase in investment leads to multiple and cumulative effect on national income, output
and employment.
For example: Investment increases by Rs.100 crores. If this causes an increases in output
of Rs. 500 Crores, then the multiplier is 5 .If instead the resulting increase in output is
Rs.800, then multiplier is 8.So increase in income is many times more than the initial
increase in investment.
So, Basically, multiplier is the ratio of increment in income to the increment in investment.
K =
(?I stands for increment in investment, ?Y stands for resultant increase in income, K is
multiplier)
If we take an example of government spending for some public works i.e. construction of a
Central University. For this government provides Rs.100 crores for construction of
university, In this process the Rs.100 crores will go to the various field like wages to the
workers, purchasing building materials, etc. It will increase income of the people by Rs.1000
crores. The people who receive this amount spent some part of it on various consumer
goods but it depends on Marginal Propensity to Consume(MPC). If they all have Marginal
Propensity to Consume of 2/3, they will now spend Rs.666.67cr on new consumption goods.
So the producer of the goods will now get extra income of Rs.666.67 cr. But story is not
MULTIPLIES
INSTITUTE OF LIFELONG LEARNING, UNIVERSITY OF DELHI
finished here. If their Marginal Propensity to consume is also 2/3 then they in turn spend
Rs.444.44 cr or 2/3 of 666.67(2/3 of 2/3 of Rs 1000cr).This process will go on. This is an
endless chain of consumption spending but on diminishing rate at every stage.
Using arithmetic formula, we can analyze total increase in spending as given:
Rs. 1000.00 1 x 1000
Rs. 666.67 2/3 x 1000
Rs. 444.44 (2/3)
2
x 1000
Rs. 296.30 (2/3)
3
x 1000
Rs. 197.53 (2/3)
4
x1000
….. …..
….. …..
Rs. 3000.00 1/1-2/3 x 1000, or 3x1000
It shows that with an Marginal Propensity to Consume (MPC)of 2/3,multilier is 3.If we
change(MPC) to 3/4 ,then multiplier is 2.So it is clear by the above given example that size
of multiplier depends upon the size of MPC.If in any case MPC =1 ,then it means multiplier
will be infinity and economy will be on full employment. This is the case when increment in
income is consumed wholly and nothing is saved. And if in another case MPC = 0, then the
multiplier will be equal to 1, this is the situation in which whole of the increment in income
is saved. But in actual practice the MPC is less than one but more than zero. [1>
>0]Therefore, the value of multiplier is greater than one but less than infinity.
In algebraic term, ?Y = ?I
=
, measures the size of multiplier
DERIVATION OF MULTIPLIER
The equilibrium level of income is Y= C+I …………(1)Expenditure Method
If investment increases by ?I then ?Y, which results change in ?C. So the post equilibrium
level of income equals Y+?Y =C+?C+I+?I ………………………… (2)
After subtraction equation (1) and (2) we get ?Y=?C+?I.
The consumption function is C= a+b?Y, ?C= b?Y …………………. (3)
Page 4
MULTIPLIES
INSTITUTE OF LIFELONG LEARNING, UNIVERSITY OF DELHI
SUBJECT: MACROECONOMICS
LESSON : MULTIPLIES
LESSON DEVELOPER: MANJUL SINGH
COLLEGE/ DEPARTMENT: SATYAWATI COLLEGE (E), DEPARTMENT OF ECONOMICS,
UNIVERSITY OF DELHI
MULTIPLIES
INSTITUTE OF LIFELONG LEARNING, UNIVERSITY OF DELHI
MULTIPLIER
The theory of multiplier occupies a very important role in the analysis of national income
behavior with response to the change in its determinants. Multiplier is also helpful to
analyses the effect of change in monetary and budgetary policies of the government.
According to Shapiro: The ratio of the change in income and output to the change in
the level of the spending function is called Multiplier
There are two theories of multiplier given by two renowned economists
British Economist R.F. Kahn, his multiplier was an employment multiplier which measures
the ratio of increment of total employment in the capital goods industries.
Economist J.M. Keynes: his multiplier is also known as investment multiplier or income
multiplier, it is the ratio of the increment to total income associated with a given increment
in investment.
The theory of multiplier has been used generally to explain the cumulative upward and
downward swings of the trade cycles that occur in a free enterprise capitalist economy.
Increase in investment leads to multiple and cumulative effect on national income, output
and employment.
For example: Investment increases by Rs.100 crores. If this causes an increases in output
of Rs. 500 Crores, then the multiplier is 5 .If instead the resulting increase in output is
Rs.800, then multiplier is 8.So increase in income is many times more than the initial
increase in investment.
So, Basically, multiplier is the ratio of increment in income to the increment in investment.
K =
(?I stands for increment in investment, ?Y stands for resultant increase in income, K is
multiplier)
If we take an example of government spending for some public works i.e. construction of a
Central University. For this government provides Rs.100 crores for construction of
university, In this process the Rs.100 crores will go to the various field like wages to the
workers, purchasing building materials, etc. It will increase income of the people by Rs.1000
crores. The people who receive this amount spent some part of it on various consumer
goods but it depends on Marginal Propensity to Consume(MPC). If they all have Marginal
Propensity to Consume of 2/3, they will now spend Rs.666.67cr on new consumption goods.
So the producer of the goods will now get extra income of Rs.666.67 cr. But story is not
MULTIPLIES
INSTITUTE OF LIFELONG LEARNING, UNIVERSITY OF DELHI
finished here. If their Marginal Propensity to consume is also 2/3 then they in turn spend
Rs.444.44 cr or 2/3 of 666.67(2/3 of 2/3 of Rs 1000cr).This process will go on. This is an
endless chain of consumption spending but on diminishing rate at every stage.
Using arithmetic formula, we can analyze total increase in spending as given:
Rs. 1000.00 1 x 1000
Rs. 666.67 2/3 x 1000
Rs. 444.44 (2/3)
2
x 1000
Rs. 296.30 (2/3)
3
x 1000
Rs. 197.53 (2/3)
4
x1000
….. …..
….. …..
Rs. 3000.00 1/1-2/3 x 1000, or 3x1000
It shows that with an Marginal Propensity to Consume (MPC)of 2/3,multilier is 3.If we
change(MPC) to 3/4 ,then multiplier is 2.So it is clear by the above given example that size
of multiplier depends upon the size of MPC.If in any case MPC =1 ,then it means multiplier
will be infinity and economy will be on full employment. This is the case when increment in
income is consumed wholly and nothing is saved. And if in another case MPC = 0, then the
multiplier will be equal to 1, this is the situation in which whole of the increment in income
is saved. But in actual practice the MPC is less than one but more than zero. [1>
>0]Therefore, the value of multiplier is greater than one but less than infinity.
In algebraic term, ?Y = ?I
=
, measures the size of multiplier
DERIVATION OF MULTIPLIER
The equilibrium level of income is Y= C+I …………(1)Expenditure Method
If investment increases by ?I then ?Y, which results change in ?C. So the post equilibrium
level of income equals Y+?Y =C+?C+I+?I ………………………… (2)
After subtraction equation (1) and (2) we get ?Y=?C+?I.
The consumption function is C= a+b?Y, ?C= b?Y …………………. (3)
MULTIPLIES
INSTITUTE OF LIFELONG LEARNING, UNIVERSITY OF DELHI
Substituting the equation (3) in (2) we get ?Y=b?Y +?I
?Y =
?I,
=
= m (
gives the value of the Investment multiplier)
(b=MPC and 1-MPC=MPS), so multiplier can be stated as:
m =
=
=
=
Two Sector Model
In two sector economy model, a change in aggregate demand is the sum of consumption
and investment. Aggregate demand may be caused by change in consumption expenditure
or in business investment or in both. Consumption expenditure is however a more stable
function of income. According to Keynes, consumption is a function of income, it changes
only with changes in income, and a change in aggregate demand is often associated with
changes in investment which is exogenous. Now we assume ? ? as increased in autonomous
spending and the aggregate output remaining constant.AD > AO, (AO=AS) which results
lead to decrease in inventories.
Round Increase in Demand Increase in Production Total
increase in income
1 ? ? ? ? ? ?
2 c? ? c? ? (1+c) ? ?
3 c
2
? ? c
2
? ? (1+c+c
2
) ? ?
4 c
3
? ? c
3
? ? (1+c+c
2
+c
3
) ? ?
.. …… …… ……
.. …… …… ……
.. …… …… 1/1-c ? ?
Starting with the initial increase in autonomous demand with increase spending
?AD = ? ? + c? ? +c
2
? ? +c
3
? ?+……….
?AD = ? ? (1+c+c
2
+c
3
+……..) after simplification we obtain,
?AD = 1/1-c ? ? = ?Y
o
(c =MPC)
Page 5
MULTIPLIES
INSTITUTE OF LIFELONG LEARNING, UNIVERSITY OF DELHI
SUBJECT: MACROECONOMICS
LESSON : MULTIPLIES
LESSON DEVELOPER: MANJUL SINGH
COLLEGE/ DEPARTMENT: SATYAWATI COLLEGE (E), DEPARTMENT OF ECONOMICS,
UNIVERSITY OF DELHI
MULTIPLIES
INSTITUTE OF LIFELONG LEARNING, UNIVERSITY OF DELHI
MULTIPLIER
The theory of multiplier occupies a very important role in the analysis of national income
behavior with response to the change in its determinants. Multiplier is also helpful to
analyses the effect of change in monetary and budgetary policies of the government.
According to Shapiro: The ratio of the change in income and output to the change in
the level of the spending function is called Multiplier
There are two theories of multiplier given by two renowned economists
British Economist R.F. Kahn, his multiplier was an employment multiplier which measures
the ratio of increment of total employment in the capital goods industries.
Economist J.M. Keynes: his multiplier is also known as investment multiplier or income
multiplier, it is the ratio of the increment to total income associated with a given increment
in investment.
The theory of multiplier has been used generally to explain the cumulative upward and
downward swings of the trade cycles that occur in a free enterprise capitalist economy.
Increase in investment leads to multiple and cumulative effect on national income, output
and employment.
For example: Investment increases by Rs.100 crores. If this causes an increases in output
of Rs. 500 Crores, then the multiplier is 5 .If instead the resulting increase in output is
Rs.800, then multiplier is 8.So increase in income is many times more than the initial
increase in investment.
So, Basically, multiplier is the ratio of increment in income to the increment in investment.
K =
(?I stands for increment in investment, ?Y stands for resultant increase in income, K is
multiplier)
If we take an example of government spending for some public works i.e. construction of a
Central University. For this government provides Rs.100 crores for construction of
university, In this process the Rs.100 crores will go to the various field like wages to the
workers, purchasing building materials, etc. It will increase income of the people by Rs.1000
crores. The people who receive this amount spent some part of it on various consumer
goods but it depends on Marginal Propensity to Consume(MPC). If they all have Marginal
Propensity to Consume of 2/3, they will now spend Rs.666.67cr on new consumption goods.
So the producer of the goods will now get extra income of Rs.666.67 cr. But story is not
MULTIPLIES
INSTITUTE OF LIFELONG LEARNING, UNIVERSITY OF DELHI
finished here. If their Marginal Propensity to consume is also 2/3 then they in turn spend
Rs.444.44 cr or 2/3 of 666.67(2/3 of 2/3 of Rs 1000cr).This process will go on. This is an
endless chain of consumption spending but on diminishing rate at every stage.
Using arithmetic formula, we can analyze total increase in spending as given:
Rs. 1000.00 1 x 1000
Rs. 666.67 2/3 x 1000
Rs. 444.44 (2/3)
2
x 1000
Rs. 296.30 (2/3)
3
x 1000
Rs. 197.53 (2/3)
4
x1000
….. …..
….. …..
Rs. 3000.00 1/1-2/3 x 1000, or 3x1000
It shows that with an Marginal Propensity to Consume (MPC)of 2/3,multilier is 3.If we
change(MPC) to 3/4 ,then multiplier is 2.So it is clear by the above given example that size
of multiplier depends upon the size of MPC.If in any case MPC =1 ,then it means multiplier
will be infinity and economy will be on full employment. This is the case when increment in
income is consumed wholly and nothing is saved. And if in another case MPC = 0, then the
multiplier will be equal to 1, this is the situation in which whole of the increment in income
is saved. But in actual practice the MPC is less than one but more than zero. [1>
>0]Therefore, the value of multiplier is greater than one but less than infinity.
In algebraic term, ?Y = ?I
=
, measures the size of multiplier
DERIVATION OF MULTIPLIER
The equilibrium level of income is Y= C+I …………(1)Expenditure Method
If investment increases by ?I then ?Y, which results change in ?C. So the post equilibrium
level of income equals Y+?Y =C+?C+I+?I ………………………… (2)
After subtraction equation (1) and (2) we get ?Y=?C+?I.
The consumption function is C= a+b?Y, ?C= b?Y …………………. (3)
MULTIPLIES
INSTITUTE OF LIFELONG LEARNING, UNIVERSITY OF DELHI
Substituting the equation (3) in (2) we get ?Y=b?Y +?I
?Y =
?I,
=
= m (
gives the value of the Investment multiplier)
(b=MPC and 1-MPC=MPS), so multiplier can be stated as:
m =
=
=
=
Two Sector Model
In two sector economy model, a change in aggregate demand is the sum of consumption
and investment. Aggregate demand may be caused by change in consumption expenditure
or in business investment or in both. Consumption expenditure is however a more stable
function of income. According to Keynes, consumption is a function of income, it changes
only with changes in income, and a change in aggregate demand is often associated with
changes in investment which is exogenous. Now we assume ? ? as increased in autonomous
spending and the aggregate output remaining constant.AD > AO, (AO=AS) which results
lead to decrease in inventories.
Round Increase in Demand Increase in Production Total
increase in income
1 ? ? ? ? ? ?
2 c? ? c? ? (1+c) ? ?
3 c
2
? ? c
2
? ? (1+c+c
2
) ? ?
4 c
3
? ? c
3
? ? (1+c+c
2
+c
3
) ? ?
.. …… …… ……
.. …… …… ……
.. …… …… 1/1-c ? ?
Starting with the initial increase in autonomous demand with increase spending
?AD = ? ? + c? ? +c
2
? ? +c
3
? ?+……….
?AD = ? ? (1+c+c
2
+c
3
+……..) after simplification we obtain,
?AD = 1/1-c ? ? = ?Y
o
(c =MPC)
MULTIPLIES
INSTITUTE OF LIFELONG LEARNING, UNIVERSITY OF DELHI
Now with the expansion in production to meet that increase in demand .Production will
expand by ? ?.Increase in production will lead to rise an increase in income via MPC.And
increase in income will in turn lead to an increase in expenditure’s size c? ?, As AD >AO
(aggregate demand is greater than aggregate output) then production increase by c? ? in
3
rd
round. Again if production expands to meet this increase in spending, this give rise of
induced spending equals to MPC time the increase in income c (c? ?) =c
2
? ?, which results
increase in income, AD will increase by c
2
? ?.And again AD>AO.Here the MPC is less than 1
so the term c
2
is less than c.As a result of this induced expenditures in third round is
smaller than the second round.
Cumulative change in aggregate spending equals multiple increases in autonomous
spending. In some particular case, if omitting the government sector, and foreign trade the
multiplier is as a defined a = 1/1-c
The level of national income is determined by the equilibrium between aggregate demand
and aggregate supply. It is to be noted that in equilibrium AD equals income or output.
From one to another equilibrium change in income, ?Y
o
is equal to the change in aggregate
demand ?AD. Aggregate demand split into the change in autonomous spending, ? ?, and
the change in expenditure induced by change in income i.e. c?Y
0.
So the change in income is
Y
0=
? ?+c?Y
0
.
In all we get ?Y
0
=
? ?
DIAGRAMMATIC REPRESENTATION OF MULTIPLIER
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FAQs on Lecture 4 - Multiplier - Macroeconomics- Learning and Analysis
| 1. What is the multiplier effect in economics? |  |
Ans. The multiplier effect in economics refers to the phenomenon where an initial increase in spending or investment leads to a larger increase in national income and output. This occurs because the increased spending stimulates further economic activity, as the income generated from the initial spending is spent and respent by individuals and businesses in the economy.
| 2. How is the multiplier effect calculated? | |
Ans. The multiplier effect can be calculated using the formula: Multiplier = 1 / (1 - Marginal Propensity to Consume). The Marginal Propensity to Consume (MPC) represents the proportion of additional income that individuals spend, rather than save. By dividing 1 by 1 minus the MPC, we can determine the total increase in national income resulting from an initial increase in spending or investment.
| 3. What factors can influence the size of the multiplier effect? | |
Ans. Several factors can influence the size of the multiplier effect. One key factor is the Marginal Propensity to Consume (MPC), as a higher MPC leads to a larger multiplier. The size of the multiplier can also be affected by leakages, such as savings and taxes, which reduce the amount of income that is respent in the economy. Additionally, the presence of imports can decrease the size of the multiplier, as some of the increased spending leaks out of the domestic economy.
| 4. How does government spending affect the multiplier effect? | |
Ans. Government spending can have a significant impact on the multiplier effect. When the government increases its spending, it injects money into the economy, which leads to increased income and consumption. This initial increase in government spending can have a multiplier effect, as the increased income leads to further spending and economic activity. Therefore, government spending can be used as a tool to stimulate economic growth and recovery.
| 5. Can the multiplier effect have negative consequences? | |
Ans. While the multiplier effect is generally seen as a positive phenomenon that stimulates economic growth, it can also have negative consequences in certain situations. For example, if the economy is already operating at full capacity, an increase in spending can lead to inflationary pressures. Additionally, if the initial increase in spending is financed through borrowing, it can lead to a higher debt burden in the long term. Therefore, it is important for policymakers to carefully consider the timing and magnitude of their actions to avoid potential negative consequences of the multiplier effect.
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