Chapter 8: Income Determination & Multiplier

Determination of Equilibrium Income

In Keynesian economics, the equilibrium level of income is determined where planned aggregate demand equals aggregate supply. There are two equivalent approaches:

Approach 1 — AD = AS (Expenditure Approach):

• AD = C + I (two-sector economy); AS = C + S
• At equilibrium: C + I = C + S → I = S (planned investment = planned saving)
• On the 45° diagram: equilibrium is where the AD line intersects the 45° AS line.

Approach 2 — S = I (Saving-Investment Approach):

• Plot the saving function (S = –a + (1–b)Y) and the investment line (horizontal, since I is autonomous).
• Equilibrium is where the saving function intersects the investment line.
• If S > I: AD < AS → income falls. If S < I: AD > AS → income rises.

Both approaches yield the same equilibrium income. The algebraic solution: Y = (a + I) ÷ (1 – MPC) = (a + I) ÷ MPS.

Full employment equilibrium occurs when equilibrium income equals potential (full employment) output. If equilibrium income is below full employment output, the economy is at underemployment equilibrium — Keynes' key insight.

The Investment Multiplier

The investment multiplier (K) measures the total change in national income resulting from a unit change in autonomous investment. It shows the amplified effect of investment on income through successive rounds of spending.

K = ΔY ÷ ΔI = 1 ÷ MPS = 1 ÷ (1 – MPC)

• Higher MPC → lower MPS → higher multiplier (more of each round gets re-spent).
• Lower MPC → higher MPS → lower multiplier.
• If MPC = 0: K = 1 (no amplification). If MPC = 1: K = ∞ (theoretically infinite).
• In practice, MPC is between 0 and 1, so K is between 1 and ∞.

Numerical example (MPC = 0.8, ΔI = ₹100):

• K = 1 ÷ (1 – 0.8) = 1 ÷ 0.2 = 5
• ΔY = K × ΔI = 5 × 100 = ₹500

Working of the Multiplier — Round by Round

The multiplier works through successive rounds of spending and re-spending. Suppose investment increases by ₹100 and MPC = 0.8:

• Round 1: Investment ↑ ₹100 → Income ↑ ₹100 → Consumption ↑ ₹80 (80% of 100)
• Round 2: Income ↑ ₹80 → Consumption ↑ ₹64 (80% of 80)
• Round 3: Income ↑ ₹64 → Consumption ↑ ₹51.2 …
• Total: ΔY = 100 + 80 + 64 + 51.2 + … = 100 × (1 ÷ 0.2) = ₹500

Each round's addition gets smaller (MPC < 1), so the series converges to a finite total. The process continues until the total additional saving generated equals the initial investment (ΔS = ΔI at new equilibrium).

The multiplier works in reverse too — a fall in investment reduces income by a multiple of the initial fall.

Paradox of Thrift

The paradox of thrift is one of Keynes' most important insights — it states that what is individually rational (saving more) can be collectively self-defeating.

• If all households try to save more (shift up the saving function) → AD falls (less consumption).
• Falling AD → falling income → falling output and employment.
• As income falls, actual saving may not increase (or may even fall) — the attempt to save more leads to lower income, offsetting the higher saving rate.

This paradox applies specifically in a Keynesian underemployment context with idle resources. It does not apply when the economy is at full employment.

Policy implication: During a recession, encouraging more saving by households can worsen the recession. Government should boost spending (fiscal stimulus) to raise AD and pull the economy out of underemployment equilibrium.

Key Concepts at a Glance

Sample MCQs — Chapter 8: Income Determination & Multiplier