The document discusses the concept of the multiplier, which refers to the total change in aggregate income resulting from a change in autonomous expenditures. It provides examples to show how an initial $1 million injection is multiplied through subsequent rounds of spending, consumption, and savings. The multiplier depends on the marginal propensity to consume (MPC), with a higher MPC resulting in a larger multiplier. The document also discusses different types of multipliers, such as the investment, consumption, government and tax multipliers, and how they are calculated. It provides a practice question as an example.

1.  Multiplier means any numeric number which
shows a change in dependent variable due to
one unit change in Independent variable. For
example how much change is required in
consumption to increase 400 million in GNP.
It is based on consumption Multiplier.

2. Multiplier means a change in autonomous
expenditures (e.g. investment) leads to an even
larger change in aggregate income (GNP).
►An increase in spending by one party
increases the income of others. Thus,
growth in spending can expand output by a
multiple of the original increase.
►The multiplier is the number by which the
initial change in spending is multiplied to
obtain the total amplified increase in
National income.
►The size of the multiplier increases with the
marginal propensity to consume (MPC).

3. Significance of Multiplier
►In evaluating the importance of the
multiplier, one should remember:
 taxes and spending on imports will
dampen the size of the multiplier;
 it takes time for the multiplier to work;
and,
 the amplified effect on real output will
be valid only when the additional
spending brings idle resources into
production without price changes.

4. ► Here, a $1,000,000 injection is spent, received as
payment, saved and spent, received as payment,
saved and spent … etc. … until … effectively, $4 million
is spent in the economy.
Expenditure
stage
Additional income
(dollars)
Marginal propensity
to consume
Additional consumption
(dollars)
For simplicity (here) it is assumed that all additions to income are either spent domestically or saved.
1,000,000
750,000
562,500
421,875
316,406
949,219
750,000
562,500
421,875
316,406
237,305
711,914
Round 1
Round 2
Round 3
Round 4
Round 5
Total 4,000,000 3,000,000
All others
3/4
3/4
3/4
3/4
3/4
3/4
3/4
The Multiplier Principle
► The multiplier concept is fundamentally based upon
the proportion of additional income that households
choose to spend on consumption: the marginal propensity
to consume (here assumed to be 75% = 3/4).

5. MPC
Size of
multiplier
9/10
4/5
3/4
2/3
1/2
1/3
10.0
5.0
4.0
3.0
2.0
1.5
A Higher MPC Means a Larger Multiplier
► As the MPC increases more and more money of every
injection is spent (and so received as payment and
then spent again, received as payment and spent
again, etc.).
► The effect is that for higher MPCs, higher multipliers
result, specifically the relationship follows this
equation:
MPC
KM


1
1

6.  Consumption Multiplier
 Investment Multiplier
 Government Multiplier
 Tax Multiplier
◦ Lump sum Tax Multiplier
◦ Income Tax Multiplier

7. (Expenditure Multipliers)
 Consumption Multiplier
 Investment Multiplier
 Government Multiplier
K = 1/1- MPC
Tax Multiplier
Lump sum tax Multiplier: -MPC/1-MPC
Income tax Multiplier (K)=
-MPC/1-MPC+MPC * Tax Rate

8. 0
0
1
0
, G
G
I
I
Y
c
C
C
where
G
I
C
Y







Then
1. find equilibrium output (Y*), consumption level and savings
of a country.
2. Find Investment multiplier and consumption multiplier

9.  
0
0
0
1
0
,
, G
G
I
I
T
T
T
Y
c
C
C
where
G
I
C
Y









Then
1. find equilibrium output (Y*), consumption level and savings of
a country.
2. Find Investment multiplier, consumption multiplier and Tax
Multiplier

10.  
0
0
0
1
0
,
, G
G
I
I
tY
T
T
T
Y
c
C
C
where
G
I
C
Y










Then
1. Find equilibrium output (Y*), consumption level and savings
of a country.
2. Find Investment multiplier, consumption multiplier and
Income Tax Multiplier

11. Practice Question
Suppose
Then
1. Find equilibrium output, level of consumption
and saving from the above information
2. Find Income Tax Multiplier, lump sum tax and
Expenditure Multiplier.
3. Suppose Government has imposed tax by 15%
on Output then what would be the effect on
equilibrium output, consumption and savings.
100
)
(
340
150
3
.
0
130
)
(
67
.
0
200










M
X
G
I
Y
T
T
Y
C

12.  
500
,
1000
,
15
.
0
240
65
.
0
100










G
I
Y
T
T
Y
C
where
G
I
C
Y
Then
1. Find equilibrium output (Y*), consumption level and
savings of a country.
2. Find Investment multiplier, consumption multiplier
and Income Tax Multiplier

13.  Presume the consumption function is C = 100 + 0.8Yd and
investment is I = 200 millions. The government expenditure
at $ 180 millions where as the tax function is a proportional
income tax function where T = 0.10Y.
1. Find the equilibrium level of income in an economy
2. Find the revenue from taxes at the equilibrium level of
income. Is the government budget balanced?
3. Suppose there is an increase in investment from 200 to 240
million dollars, what is the equilibrium level income
4. What is the revenue from taxes at the new equilibrium level of
income? Is there a balanced government budget?