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Static Multiplier

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Topics

Estimated time: 17 minutes
  • Introduction to Static Multiplier
  • Forward Working of the Multiplier
  • Reverse (Backward) Working of the Multiplier
  • Saving-Investment Equality Approach
  • Key Points: Static Multiplier
CISCE: Class 12

Introduction to Static Multiplier

In the static multiplier, there is no time lag between the original and the new equilibrium. The increase in investment leads to an increase in income in the same period. All economic variables — investment, income, and consumption — are related to the same period. The time interval between the two equilibria (known as the generation period) is not considered.

Gardner Ackley described this as a "fixed period analysis" — it compares the starting equilibrium with the final equilibrium without tracking what happens in between.

Prof. Samuelson's Warning 
The multiplier is a two-edged sword. It will cut for you or go against you." — This means the multiplier works both in forward and backward directions, i.e., to raise or reduce income.

CISCE: Class 12

Forward Working of the Multiplier

The forward working of the multiplier states that an increase in investment leads to a multiplied increase in the level of income.

Multiplier Table (MPC = 0.5)

Round ΔI (Investment) ΔY (Income) ΔC (Consumption) ΔS (Saving)
1 ₹200 Cr ₹200 Cr ₹100 Cr ₹100 Cr
2 ₹100 Cr ₹50 Cr ₹50 Cr
3 ₹50 Cr ₹25 Cr ₹25 Cr
4 ₹25 Cr ₹12.50 Cr ₹12.50 Cr
5 ₹12.50 Cr ₹6.25 Cr ₹6.25 Cr
6 ₹6.25 Cr ₹3.12 Cr ₹3.12 Cr
Total ₹200 Cr ₹400 Cr ₹200 Cr ₹200 Cr
Key Observation: Investment was ₹200 Cr, but total income generated is ₹400 Cr — exactly 2 times the investment. Multiplier K = 1/(1−0.5) = 2.

Mathematical Derivation

ΔY = ΔI + c·ΔI + c²·ΔI + c³·ΔI + …
ΔY = ΔI × (1 + c + c² + c³ + …) = ΔI / (1 − c)
Substituting: ΔY = 200 / (1 − 0.5) = 200 / 0.5 = ₹400 crores

Keynesian Cross Diagram (AD-AS Approach)

Keynesian Cross diagram showing the forward multiplier effect
Fig. 2 — Keynesian Cross: Forward Working of the Multiplier (C + I shifts to C + I + ΔI)

How to Read This Diagram

  1. Axes: X-axis = National Income (Y); Y-axis = Aggregate Expenditure (C + I). The 45° line shows where Income = Expenditure (equilibrium condition).
  2. Original Equilibrium: C + I line intersects the 45° line at point E₀ → Equilibrium income = OY₀. At this point, OY₀ = E₀Y₀.
  3. Investment Increases: When investment rises by ΔI, expenditure line shifts upward to C + I + ΔI.
  4. New Equilibrium: New expenditure line intersects 45° line at Eₙ → New income = OYₙ.
  5. Multiplier Effect: The increase from OY₀ to OYₙ is greater than ΔI. This is the forward multiplier effect.
CISCE: Class 12

Reverse (Backward) Working of the Multiplier

Just as an increase in investment causes a multiplied rise in income, a decrease in investment causes a multiplied fall in income.

How Reverse Multiplier Works

  1. Starting from equilibrium at Eₙ where income = OYₙ.
  2. Investment falls → Expenditure line shifts downward from C + I + ΔI back to C + I.
  3. Equilibrium shifts back to E₀ → Income falls from OYₙ to OY₀.
  4. The fall in income is a multiple of the fall in investment.
Numerical Example
If investment falls by ₹200 Cr and MPC = 0.5 (K = 2), then income falls by ₹200 × 2 = ₹400 Cr.
CISCE: Class 12

Saving-Investment Equality Approach

This is an alternative method to demonstrate the multiplier, using the condition that equilibrium occurs where Saving = Investment.

Saving-Investment equality diagram for the multiplier
Fig. 3 — Saving-Investment Equality: Forward and Reverse Multiplier

How to Read This Diagram

  • X-axis: National Income (Y); Y-axis: Saving (S) & Investment (I)
  • S-curve (Saving function): Upward sloping — savings increase with income. This is an induced function.
  • I-line (Investment): Horizontal — autonomous investment that does not depend on income (e.g., government welfare spending).
CISCE: Class 12

Key Points: Static Multiplier

  • In a static multiplier, there is no time lag; increase in investment raises income in the same period.
  • All variables (income, consumption, investment) belong to the same time period.
  • Multiplier works in two directions:
    Forward: Increase in investment → multiple increase in income.
    Reverse: Decrease in investment → multiple fall in income.
  • Size of income change depends on MPC and saving–investment equality.

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