# The concept of Multiplier in Economics.

The  concept of Multiplier  was first  developed  by R. F. Kahn’s . Kahn’s  multiplier was the Employment Multiplier. Keynes  took the idea from  Kahn and formulated the Investment Multiplier .

THE  INVESTMENT MULTIPLIER :-   Keynes considers his theory of multiplier as an integral  part of  of his theory of employment.  The Multiplier , according to Keynes, ” establishes a precise  relationship  , given the propensity  to consume, between aggregate employment and income and the rate of investment .It tells us that , when there is an increment  of investment , income will increase by an amount  which is k times the increment of investment ,

i.e.let change is denoted by  ‘a’ , then aY = KaI.

or ,  k   =  aY/ aI .

In the multiplier theory  , the important  element is the multiplier co-efficient , K which refers to the power  by  which any initial  investment expenditure  is multiplied  to obtain a final  increase in income . the value  of the multiplier is determined by the marginal propensity  to consume. The higher the marginal propensity  to consume  , the higher is the  value of the multiplier , the vice- versa. The relationship between  the multiplier and the marginal propensity to  consume is as follows – As  change is denoted   by ‘a’,

aY = aC + aI .

aY-CaY = aI .                   [  Because  C= CaY]

aY[1-c] =  aI,

aY = aI/1-c.

aY/aI  = 1/1-c.

k =  1/1-c[k= aY/aI].

Since   c  is the marginal propensity to  consume  ,  the  multiplier k  is  equal to 1- 1/c . The  multiplier  can be derived from the marginal propensity to save [ MPS] and it is the reciprocal of MPS .

k = 1/MPS .

The size  of the  Multiplier varies directly with the MPC and inversely  with the MPS. Since the MPC is always greater than zero and less than one. The Multiplier is always between one and infinity. If the multiplier  is one , it means that the whole increment of income  is saved and nothing is spent because the MPC is zero . On the other hand an infinite multiplier implies that  MPC is equal to one and the entire of income is spent on consumption. —– #——

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