[Introductory Macroeconomics] Chapter 4: Determination of Income and Employment

Determination of Income and Employment

Keynes argued that in the short run, the level of national income and employment is determined by aggregate demand (AD). This is the fundamental departure from classical theory.

Aggregate Demand (AD)

Aggregate Demand is the total spending on goods and services in the economy at a given price level. In a two-sector economy:
AD = C + I
where C = consumption expenditure and I = investment expenditure.

Consumption Function

Key formulas

C = C₀ + c · Y

C₀ = autonomous consumption (even if Y = 0, people consume by drawing on savings)

c = Marginal Propensity to Consume (MPC) — fraction of additional income spent on consumption

Y = National Income

Savings Function

S = Y - C = -C₀ + (1 - c) · Y = -C₀ + s · Y
where s = Marginal Propensity to Save (MPS) = 1 - MPC

Note: MPC + MPS = 1

Investment

In the Keynesian model, investment (I) is treated as autonomous (exogenous) — it depends on expectations and is independent of current income. So I = I₀.

Equilibrium Income

Equilibrium occurs where:
AD = AS (Aggregate Supply = National Income = Y)
C + I = Y
OR equivalently (savings-investment approach):
S = I

Solving: C₀ + c · Y + I = Y
=> Y - c · Y = C₀ + I
=> Y (1 - c) = C₀ + I
=> Y · = (C₀ + I) / (1 - c) = (C₀ + I) / s

Investment Multiplier (k)

The multiplier shows by how much national income changes for a unit change in autonomous expenditure (investment).
k = 1 / (1 - MPC) = 1 / MPS

If MPC = 0.8, k = 1 / 0.2 = 5. A Rs. 100 crore increase in investment raises national income by Rs. 500 crore.

Inflationary and Deflationary Gaps

Inflationary Gap: When AD at full employment level exceeds the full-employment output. Excess demand causes prices to rise (inflation).
Deflationary Gap: When AD at full employment level is less than full-employment output. Deficient demand leads to output below potential and unemployment.

Both gaps are measured at the full-employment level of income:
Gap = |AD at full employment - Full employment output|

Example 1

Finding equilibrium income
Given: C = 100 + 0.8Y, I = 200. AD = 100 + 0.8Y + 200 = 300 + 0.8Y. At equilibrium AD = Y. So Y = 300 + 0.8Y => Y - 0.8Y = 300 => 0.2Y = 300 => Y · = Rs. 1,500.

Example 2

The multiplier in action
Investment increases by Rs. 50 crore. MPC = 0.75. Multiplier k = 1 / (1 - 0.75) = 4. Change in income = 4 x 50 = Rs. 200 crore. A Rs. 50 crore injection raises total income by Rs. 200 crore through successive rounds of spending.

Example 3

Why the multiplier works
A firm invests Rs. 100 crore in building a factory. Workers receive Rs. 100 crore in wages. They spend Rs. 80 crore (MPC = 0.8) on goods. Those producers earn Rs. 80 crore and spend Rs. 64 crore. And so on. Total spending = 100 + 80 + 64 + ... = 100 / (1 - 0.8) = Rs. 500 crore.

Example 4

Savings-Investment equilibrium
S = -100 + 0.2Y (savings function where MPS = 0.2). I = 200. At equilibrium S = I: -100 + 0.2Y = 200 => 0.2Y = 300 => Y · = Rs. 1,500. Same answer as Example 1, confirming both approaches are equivalent.

Example 5

Deflationary gap
Full employment output = Rs. 2,000 crore. AD at Rs. 2,000 crore level = 300 + 0.8 x 2,000 = 300 + 1,600 = Rs. 1,900 crore. Deflationary gap = 2,000 - 1,900 = Rs. 100 crore. The economy is operating below potential.

Example 6

Inflationary gap
Full employment output = Rs. 1,000 crore. AD = 300 + 0.8 x 1,000 = 1,100 crore. Inflationary gap = 1,100 - 1,000 = Rs. 100 crore. Excess demand causes inflation.

Example 7

MPC, MPS and their relationship
If a family earns an extra Rs. 1,000 and spends Rs. 700 on consumption: MPC = 700 / 1,000 = 0.7. MPS = 300 / 1,000 = 0.3. MPC + MPS = 1. Multiplier = 1 / 0.3 = 3.33. Every Rs. 1,000 increase in investment will raise income by Rs. 3,333.

Common mistakes

MPC is always between 0 and 1; an MPC greater than 1 is not economically meaningful.
The equilibrium income may be below full employment — this is Keynes' key insight (underemployment equilibrium).
The multiplier works in both directions: a fall in investment will reduce income by multiplier x fall.
Do not confuse "deflationary gap" with "deflation" — a deflationary gap causes unemployment, not necessarily falling prices in the Keynesian model.

Summary

In the Keynesian model, income and employment are determined by aggregate demand. Equilibrium is where AD = Y, or equivalently S = I. The multiplier (k = 1/MPS) amplifies the effect of investment on income. When actual equilibrium is below full employment, a deflationary gap exists; above, an inflationary gap. Government policy must close these gaps.