Determination of Equilibrium Income in the Short Run - The Multiplier Mechanism

The ratio of the total increment in equilibrium value of final goods output to the initial increment in autonomous expenditure is called the investment multiplier of the economy.

• An autonomous increase in expenditure of 10 units raises equilibrium income by 50 units (from 250 to 300).
• The increase is more than proportionate because of the multiplier mechanism operating through repeated rounds of income, consumption and output.

• Production of final goods uses factors: labour, capital, land and entrepreneurship.
• In the absence of indirect taxes or subsidies, total factor payments (wages, interest, rent, profit) equal the value of final output (GDP).
• Therefore, national income equals the aggregate value of final goods output (GDP).

• Initial autonomous expenditure increases by 10, so output and income rise by 10.
• People spend 0.8 fraction of extra income on consumption; consumption and aggregate demand rise by 0.8 × 10.
• This creates excess demand of 0.8 × 10; producers increase output by the same amount, raising income again by 0.8 × 10.
• In the next round, income rise of 0.8 × 10 leads to extra consumption of (0.8)² × 10, creating further excess demand and output of (0.8)² × 10.
• This continues round after round, with increments:
• 10, (0.8) × 10, (0.8)² × 10, …

The Multiplier Mechanism in the Final Goods Market

Each column shows how consumption, aggregate demand and output grow in the same pattern each round.

• Total increase in output equals:
• 10 + (0.8) × 10 + (0.8)² × 10 + …
• This is an infinite geometric series:
• 10 {1 + 0.8 + (0.8)² + …}
• Sum of the series:

\[\frac{10}{1-0.8}=\frac{10}{0.2}=50\]

Hence total increase in equilibrium output (and income) is 50, greater than the initial autonomous increase of 10.

\[\frac{\Delta Y}{\Delta\bar{A}}=\frac{1}{1-c}=\frac{1}{s}\]

where,

• ΔY: Total increment in equilibrium value of final goods output (national income).
• ΔĀ: Initial increment in autonomous expenditure (e.g., ΔĪ).
• c: MPC (Marginal Propensity to Consume).
• s: MPS (Marginal Propensity to Save), equal to 1 − c.

• Investment Multiplier measures the ratio of the increase in equilibrium income to the initial increase in autonomous expenditure.
• An increase in autonomous expenditure raises income, consumption, and output through repeated rounds of spending.
• The size of the multiplier depends on the Marginal Propensity to Consume (MPC) - higher MPC results in a larger multiplier.
• Total increase in income is greater than the initial increase in autonomous expenditure due to the multiplier effect.
• Investment Multiplier Formula: \[K=\frac{\Delta Y}{\Delta\bar{A}}=\frac{1}{1-c}=\frac{1}{s}\]