The multiplier process can be explained with the help of an imaginary example. Suppose that in an economy an additional investment of Rs. 1,000 crores is made in the construction industry. As a result, more workers get employment and an additional income of Rs. 1,000 crores is generated in the economy. This is called the immediate or first round effect of additional investment.

A part of this income will be spent on consumption and the remaining amount will be saved. Assuming MPC as 50% or 0.5, Rs. 500 crores will be spent on consumption and the remaining Rs. 500 crores will be saved.

Since one man’s expenditure is another’s income, consumption of Rs. 500 crores in the second round of which Rs. 250 crores is consumed and the remaining Rs. 250 crores is saved.

In the next round, out of an income of Rs. 250 crores, Rs. 125 crores will be spent on consumption and the remaining amount of Rs. 125 crores will be saved.

In fact, this process-the multiplier process continues indefinitely. But, since the increase in consumption becomes progressively smaller, the total increase in income is finite. The multiplies process.

The process of Income Propagation (Assumption MPC =0.5)

The total change in income can be calculated as the sum f the change in income at each round. In algebraic term, the total change in income may be given by

                   ΔY = ΔI + bΔI + b²ΔI + b³ΔI +...
or              ΔY = ΔI (I + b + b² + b³ +...)
where      ΔI = Change in investment,
                 ΔY = Change in income, and
                 Δb = marginal propesnity to consume.
(I + b + b² + b³...) is an infinite geometric series. The addition of the series I + b + b² + b³ + ...
adds up to 1/1-b

Therefore, the total change in income will be
      
    ΔY = ΔI (1/1-b)
or        Δy = Δi (1/1-0.5) = Δi (1/0.5)
or         ΔY= ΔI X 2

Since the additional investment is Rs. 1,000 crores, it will increase the level of income to Rs. 2, 000 crores (i.e., ΔY Rs. 1,000 crores x 2 = Rs. 2,000 crores).

Also shows that an additional investmetn of Rs. 1,000 crores result into an increase of Rs. 2,000 in the income the income. As an additonal income is created in a particular round, apart of it is pent on consumption which becomes income for the next round. The successive rounds generate more and more income. Consequently, the total income generated is more than the additional investmetn by the multiple of the value of multiplier (K = 2).

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