The process of investment multiplier is as under:

It can be illustrated with the help of a simple example. We know that one man’s expenditure is another man’s income.
Suppose, the government of a country spends ₹100 crores on building roads. This is the increase in investment. The national income of the country automatically rises by ₹100crore in Round 1.
Now suppose MPC is 0.5, consumption will increase by ₹ 50 crores on new consumption goods and the remaining Rs 50 crore will be saved.
In round 2, the consumer goods industry will have an extra income of ₹ 50 crores. Since MPC=0.5 people will again spend 50% of their additional income of ₹50 crores (which works out to be 25 crores) on more consumer goods and the rest 25 crores will be saved.
These ₹ 25 crores will, thus, become the income for others. This will continue till the total increase in income becomes k times the increase in investment.
The process of income generation has been shown in the following table:

Round Number	Increase in Investment (∆I)	Increase in Income (∆Y)	Increase in Consumption ∆(C)
1	100	100	50 (100 × 0.5)
2	.	50 = b ∆I	25 (50 × 0.5)
3	.	25 = b² ∆I	12.5 (25×0.5)
4	.	12.5 = b³ ∆I	6.25 (12.5 × 0.5)
5	.	6.25 = b⁴ ∆I	3.125 (6.25 × 0.5)
6	.	3.125 = b⁵ ∆I	1.56 (3.125 × 0.5)
7	.	1.56 = b⁶ ∆I	0.78 (1.56 × 0.5)
-	-	-	-
-	-	-	-
-	-	-	-
Total increase in Income = 200 crore

Since increase in investment is 100 crores and an increase in income is 200 crores.
Multiplier (K) = $ \bigtriangleup Y\over \bigtriangleup I$ = $ 200\over 100$ = 2
Or
K = $ 1\over 1-MPC$ = $ 1\over 1-0.5$ = 2.
There is a positive relationship between MPC and multiplier. A higher MPC would cause a greater increase in income implying a higher value of the multiplier.

Briefly, the working of the multiplier assumes the following process: change in investment causes a change in income. As a result, there is a change in consumption. Consumption expenditure of one person is an income of the other. Hence, the change in consumption leads to a change in income. This process continues till ∆C reduces to zero.

Short Run Equilibrium & Multiplier Questionbank