Multiplier and Super multiplier by Hicks, Lecture notes of Economics

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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

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.

 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 ).

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

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. 40. - - - - 80 64 40. 32. - - - - 20 16 12. 10. - - - - 

Total 100 500 400 100

 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

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).

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.

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

Derivation of Super multiplier

Let, the equilibrium of a two sector economy be

expressed as:

Y = C+I .... ..... ..... ..... ...... (i)

We know,

I = I

a

+ I

i

∴ I = I

a

+ V.Y ..... ...... ...... (ii) ( ∵ I

i

= V.Y)

Similarly

C = a + b Y............. ...... .......... (iii)

Where, a = autonomous consumption

b= ∆C/∆Y

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

If V = 0, Ks = 1/1-b-0 = 1/1-b =K Where, K = Simple multiplier Let, b = 0.5, V= 0. ∴ 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

When we introduce the induced investment in autonomous investment, the total investment will have two components: a)autonomous investment(Ia) and b)induced investment(I i )

I = I

a

+ I

i

 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?