Determination of Income and Employment

A. Aggregate Demand ($AD$) & Aggregate Supply ($AS$):

• Aggregate Demand ($AD$): Total planned (ex-ante) expenditure on final goods and services in an economy during an accounting year: $$AD = C + I$$
• Aggregate Supply ($AS$): Total monetary value of final output planned to be produced in an economy; exactly identical to National Income ($Y$): $$AS = Y = C + S$$ The 45-degree Line: Since $AS = Y$, the $AS$ curve is a straight $45^\circ$ line originating from the coordinate origin ($0,0$).

B. The Linear Consumption Function (Propensity to Consume):

The functional relationship between aggregate consumption expenditure ($C$) and national income ($Y$):

• $\bar{c}$ = Autonomous Consumption: Minimum consumption expenditure required for human survival at zero income level ($Y = 0$), financed by dissaving (drawing down past savings or borrowing).
• $b$ = Marginal Propensity to Consume (MPC): The proportion of additional income spent on consumption: $$MPC = b = \frac{\Delta C}{\Delta Y} \quad (0 < MPC < 1)$$
• Average Propensity to Consume (APC): The ratio of total consumption expenditure to total national income: $$APC = \frac{C}{Y}$$

A. The Linear Saving Function:

Since National Income is either consumed or saved ($Y = C + S \implies S = Y - C$):

• $-\bar{c}$ = Autonomous Dissaving at zero income.
• $(1 - b) = s$ = Marginal Propensity to Save (MPS): The ratio of change in savings to change in total income: $$MPS = \frac{\Delta S}{\Delta Y}$$
• Average Propensity to Save (APS): $APS = \frac{S}{Y}$.

B. Mathematical Proofs of Fundamental Identities:

1. Proof that $APC + APS = 1$: $$Y = C + S \implies \frac{Y}{Y} = \frac{C}{Y} + \frac{S}{Y} \implies \mathbf{1 = APC + APS}$$
2. Proof that $MPC + MPS = 1$: $$\Delta Y = \Delta C + \Delta S \implies \frac{\Delta Y}{\Delta Y} = \frac{\Delta C}{\Delta Y} + \frac{\Delta S}{\Delta Y} \implies \mathbf{1 = MPC + MPS}$$ $$\Longleftrightarrow MPS = 1 - MPC$$

A. Equilibrium Income Determination: Two Dual Approaches

1. 1. $AD = AS$ Approach: Equilibrium is achieved where planned Aggregate Demand equals Aggregate Supply: $$Y = C + I \Longleftrightarrow Y = \bar{c} + bY + I \Longleftrightarrow Y^* = \frac{\bar{c} + I}{1 - b}$$
2. 2. $S = I$ Approach: Equilibrium occurs where planned ex-ante Saving equals planned ex-ante Investment.
   Disequilibrium Adjustment: If $S > I$, planned saving exceeds planned investment. Unsold stocks accumulate in warehouses; firms cut production and employment, causing income ($Y$) to fall until $S$ drops back to equal $I$.

B. The Investment Multiplier ($k$):

The multiplier measures the factor by which an initial change in investment expenditure produces a magnified change in total national income:

• Direct Relationship: Multiplier ($k$) is directly proportional to $MPC$. Higher $MPC$ yields a larger multiplier!
• Extreme Values:
  • If $MPC = 1 \implies k = \frac{1}{0} = \infty$ (Infinite expansion).
  • If $MPC = 0 \implies k = \frac{1}{1} = 1$ (Output expands only by initial $\Delta I$).
  • Range: $1 \le k \le \infty$.

A. Deficient Demand & The Deflationary Gap:

When Aggregate Demand is less than Aggregate Supply at full employment level ($AD < AS_{FE}$).

• Deflationary Gap: The vertical shortfall of aggregate demand below the full employment level of aggregate demand. Causes unintended inventories, wage-price deflation, and persistent involuntary unemployment (recession).
• Remedies:
  • Fiscal Policy (Expansionary): Increase government spending ($G \uparrow$) and slash taxes ($T \downarrow$).
  • Monetary Policy (Expansionary): Slash Repo Rate, cut CRR and SLR, and buy securities via OMO.

B. Excess Demand & The Inflationary Gap:

When Aggregate Demand exceeds the maximum physical productive capacity of the economy at full employment ($AD > AS_{FE}$).

• Inflationary Gap: The vertical excess of aggregate demand over full employment aggregate demand. Real physical output cannot expand beyond full employment; hence, excess demand causes pure demand-pull price inflation!
• Remedies:
  • Fiscal Policy (Contractionary): Cut government spending ($G \downarrow$) and hike taxes ($T \uparrow$).
  • Monetary Policy (Contractionary): Hike Repo Rate, increase CRR/SLR, and sell securities via OMO.