Working of Multiplier: 

1. Suppose the Government undertakes investment expenditure equal to Rs 100 crore on some public works, by way of wages, price of materials etc. 

2. Thus income of labourers and suppliers of materials increases by Rs 100 crore. Suppose the MPC is 0.8 that is 80 %. 

3. A sum of Rs 80 crores is spent on consumption (A sum of Rs 20 Crores is saved). 

4. As a result, suppliers of goods get an income of Rs 80 crores.

5. They intum spend Rs 64 crores (80% of Rs 80 cr). In this manner consumption expenditure and increase in income act in a chain like manner.

The final result is ΔY = 100 + 100 × 4/5 + 100 × [4/5]² + 100 × [4/5]³ or, ΔY = 100 + 100 × 0.8 + 100 × (0.8)² + 100 × (0.8)³ = 100 + 80+ 64 + 51.2… = 500 that is 100 × 1/1 – 4/5

100 × 1/1/5

100 × 5 = Rs 500 crores

For instance if C = 100 + 0.8Y, I = 100,

Then Y = 100+ 0.8Y + 100

0. 2Y = 200

Y = 200/0.2 = 1000 → Point B

If I is increased to 110, then

0. 2Y = 210

Y = 210/0.2 = 1050 → Point D

For Rs 10 increase in I, Y has increased by Rs 50. 

This is due to multiplier effect.

At point A, Y = C = 500

C = 100 + 0.8 (500) = 500; S = 0

At point B, Y = 1000

C = 100 + 0.8 (1000) = 900; S = 100 = I

At point D, Y = 1050

C = 100 + 0.8 (1050) = 940; S = 110 = I

When I is increased by 10, Y increases by 50.

This is multiplier effect (K = 5)

K = 1 / 0.2 = 5