Class 12 Macro Economics Notes · CBSE

Working and Diagrammatic Multiplier

Working and Diagrammatic Multiplier — understand how the multiplier works step by step with diagrammatic representation. CBSE Class 12 Macroeconomics notes.

Last updated: 16 Aug 2026

Notes

The Multiplier Process — Round by Round

Setup: Initial investment = ₹100 crores, MPC = 0.90. Click through each round to see how the multiplier works:

Round 1

1/6

Initial investment of ₹100 crores directly generates income of ₹100 crores for workers and suppliers.

Investment₹100 Cr

Income₹100 Cr

Saved₹0

Multiplier Table

Amount in Crores. MPC = 0.90. k = 1/(1-0.90) = 10. Total ΔY = 10 × 100 = 1,000 crores.
Round	Increase in Investment (ΔI)	Increase in Income (ΔY)	Increase in Consumption (ΔC)	Increase in Saving (ΔS)
1st	100	100	90 (100 × 0.9)	10
2nd	0	90	81 (90 × 0.9)	9
3rd	0	81	72.90 (81 × 0.9)	8.10
4th	0	72.90	65.61 (72.90 × 0.9)	7.29
5th	0	65.61	59.05 (65.61 × 0.9)	6.56
...	...	...	...	...
Total	100	1,000	900	100

Geometric Series Derivation

Total increase in income is the sum of a geometric series:

Total increase in income

Total ΔY = ΔI + ΔI × MPC + ΔI × MPC² + ΔI × MPC³ + …

= \Delta I(1 + MPC + MPC^2 + MPC^3 + \ldots)

Sum of infinite geometric series 1 + r + r² + ... = 1/(1-r) where |r| < 1. Here r = MPC.

Closed form

Total ΔY = ΔI × 1 / (1 − MPC)

This confirms: k = 1/(1-MPC) and ΔY = k × ΔI

Using example: Total ΔY = 100 × 10 = 1,000 crores.

Diagrammatic Presentation

Multiplier Effect on AD-AS Diagram

AS (45°)

AD (C + I)

AD₁ (C + I + ΔI)

Explanation

Initial equilibrium at E: AD (C + I) intersects 45-degree line at income OY = ₹1,000 crores
Investment increases by ΔI = ₹100 crores, shifting AD upward to AD₁ (C + I + ΔI)
New equilibrium at F with income OY₁ = ₹2,000 crores
Increase in income (ΔY = ₹1,000 crores) > initial increase in investment (ΔI = ₹100 crores)
ΔI = vertical distance between AD and AD₁ at income Y; k = ΔY / ΔI = 10