Investment Multiplier and Super Multiplier are very important concept of Macroeconomics to understand the effect of autonomous investment and induced investment in final increase in national income.

1. By:
Khemraj Subedi
Assistant Professor
Far Western University
PhD Scholar in Economics
M.Phill (Economics)
M.A. (Economics)
M.Ed. (Economics)
Simple Multiplier and Super
Multiplier

2. Simple Multiplier and Super
Multiplier
 The simple multiplier implies that investment is
the central determinant of output.
An investment multiplier similarly refers to the
concept that any increase in public or private
investment has a more than proportionate positive
impact on aggregate income and the general
economy.
The super multiplier combines the multiplier with
the accelerator that indicates that investment is not
autonomous, but is part of derived demand.
Hence, the super multiplier indicates that capacity
adjusted output is determined by autonomous
demand.

3.  Autonomous demand in the case of the super
multiplier would correspond to government spending,
exports and some elements of consumption
(particularly the wealthy whose consumption is not
constrained by income).
The practical difference is that not only demand
determines output in the short run, but also in the
long run.
The economic system is effectively demand driven
and Keynes' Principle of Effective Demand

4.  The concept of Multiplier occupies an important place
in Keynesian theory of income, output and employment.
 It is an important tool of income propagation and
business cycle analysis.
 According to Keynesian framework, employment
depends upon effective demand, which in turn, depends
upon consumption and investment(Y=C+I).
 Keynes designed framework to show the relationship of
a small increase in investment to final increase in
income.
 It is very closely connected with the concept of the
marginal propensity to consume(MPC).

5. F. Kahn ," Multiplier is the ratio of the final
change in income to the initial change in
investment."
Arithmetically,
∆Y = K. ∆I
Where, ∆Y = Change in income.
∆I = Change in investment.
K = Multiplier
Therefore , we get
K = ∆Y / ∆I

6. Example
Suppose , initial investment is Rs.100 Million
and multiplier coefficient is 5 ( MPC = 0.8) ,
then find out final increase in income.
Solution: Given, ∆I = 100 Million
Multiplier (K) = 5 (K= 1/1-MPC)
We have, Final increase in income, ∆Y = K.∆I
= 5 x Rs.100 Million
∆Y = Rs. 500 Million

7. Multiplier Formula Multiplier = K = 1/1-MPC or, K =
1/MPS
Calculation of multiplier or Income propagation in
multiplier ( MPC = 0.8)Period ∆I
( Rs. Crore)
∆Y
( Rs. Crore)
∆C
( Rs. Crore)
∆S=∆Y-∆C
( Rs. Crore)
1
2
3
4
-
-
(and so on)
100
-
-
-
-
-
-
-
100
80
51.2
40.96
-
-
-
-
80
64
40.96
32.768
-
-
-
-
20
16
12.8
10.24
-
-
-
-
Total 100 500 400 100

8.  The concept of supermultiplier is the
mathematical combination of multiplier of Keynes
and accelerator of Aftalian.
 Prof. J.R. Hicks has interacted both multiplier and
accelerator with a view to measuring the total
effect of initial investment on income.
 The combined effect of the multiplier and the
accelerator is also called the leverage effect.
Super multiplier

9.  The super multiplier is worked out by combining
both induced consumption (MPC) and induced
investment (MPI). Defined as;
 K’ = 1 / ( 1- MPC – MPI)
 The super multiplier is thus defined as the ratio of
change in income to a change in autonomous
investment when the induced investment is also
present.

10. Concept of Super Multiplier
 The concept of super multiplier was developed J.
R. Hicks in 1950 by combining the concept of
multiplier and accelerator to give new concept of
super multiplier.
The concept of super multiplier is derived by
combining both induced consumption
(∆C/∆Y=MPC) and induced investment
(∆I/∆Y=MPI).

11. The simple multiplier measures the
effect of autonomous investment
in the final increase in aggregate
income where as accelerator
measures the effect of induced
investment in the final increase in
aggregate income.

12. But, super multiplier measures
the effect of both induced
consumption and induced
investment in the final increase
in aggregate income.

13. Thus, super multiplier is
combination of both simple
multiplier and accelerator
designed to measure the final
effect of initial investment
outlays to the final increase in

14. Derivation of Super multiplier
Let, the equilibrium of a two sector economy be
expressed as:
Y = C+I .... ..... ..... ..... ...... (i)
We know,
I = Ia + Ii
∴ I = Ia+ V.Y ..... ...... ...... (ii) ( ∵ Ii
= V.Y)
Similarly
C = a + b Y............. ...... .......... (iii)
Where, a = autonomous consumption
b= ∆C/∆Y

15. Substituting (ii) and (iii) in equation (i)
Y = a + b Y + Ia + V.Y .... ..... ......
.....(iv)
Let, Ia changes by ∆I so that Y also
changes by ∆Y,
Y+∆Y=a +b(Y+∆Y)+ Ia+∆ Ia+ V(Y+∆Y
)...(V)
Subtracting equation (iv) from (v), we

16. Dividing both sides by ∆Y,
1 = b + ∆ Ia/∆Y +V
or, 1 - b- V = ∆ Ia/∆Y
or, ∆Y/∆ Ia = 1/1 - b- V
∴ Ks = 1/1-b-V
Where, b= ∆C/∆Y = MPC
V= ∆I/∆Y =MPI or Accelerator
coefficient.

17. If V = 0, Ks = 1/1-b-0 = 1/1-b =K
Where, K = Simple multiplier
Let, b = 0.5, V= 0.4
∴ K = 1/1-b = 1/1-0.5 = 2 ( i.e. V= 0)
∴ Ks = 1/1-b-V = 1/1-0.5-0.4 = 10

18. Period
Initial
Investment
Induced
consumption
(MPC = 0.50)
Induced
Investment
(MPI (Ii )= 0.4)
Increase in
income (Delta Y
= MPC + MPI)
Total increase
in income
1st - - - -
2nd 50.00 - - 50.00 50.00
3rd 25.00 20.00 45.00 95.00
4th 22.50 18.00 40.50 135.50
5th 20.25 16.20 36.45 171.95
6th 18.23 14.58 32.81 204.76
7th 16.40 13.12 29.52 234.28
8th 14.76 11.81 26.57 260.85
9th 13.29 10.63 23.91 284.77
10th 11.96 9.57 21.52 306.29
11th 10.76 8.61 19.37 325.66
12th 9.69 7.75 17.43 343.09
13th 8.72 6.97 15.69 358.79
14th 7.85 6.28 14.12 372.91
. . . . .
. . . . .
0 0 0 500.00
K' = 1 / (1-0.5-.4) K' = 10
Note: When K' is 10, the initial investment grow
equivalent to 10 fold in terms of national income
SUPERMULTIPLIER PROCESS

19. When we introduce the induced investment in
autonomous investment, the total investment will
have two components:
a)autonomous investment(Ia) and
b)induced investment(Ii )
I = Ia + Ii

20.  The simple multiplier implies that investment is the central
determinant of output.
 The super multiplier combines the multiplier with the accelerator
that indicates that investment is not only autonomous, but is part
of derived demand.
 Hence, the super multiplier indicates that capacity adjusted
output is determined by autonomous demand.
What are the practical differences between simple
multiplier and super multiplier?