Aggregate demand and its components
Aggregate demand (AD) = total planned (ex-ante) spending on final goods and services in an economy during a period.
AD = C + I + G + (X − M)
- C: household consumption expenditure.
- I: planned investment by firms (machines, buildings, stocks). In the short run we take it as autonomous (fixed, not depending on income).
- G: government spending on goods and services.
- X − M: net exports.
In the two-sector model (households and firms): AD = C + I. Aggregate supply (AS) = value of output = income, so AS = C + S.
Consumption function, APC and MPC
Consumption function: C = c̄ + bY
- c̄ = autonomous consumption: spending even when income is zero (from past savings or borrowing).
- b = MPC (marginal propensity to consume) = ΔC ÷ ΔY. 0 ≤ MPC ≤ 1.
APC (average propensity to consume) = C ÷ Y. At low income APC > 1 (people dissave), at the break-even point APC = 1, and it falls as income rises.
| Y | C = 40 + 0.8Y | APC | S | APS |
|---|---|---|---|---|
| 0 | 40 | – | −40 | – |
| 200 | 200 | 1.00 | 0 | 0 |
| 400 | 360 | 0.90 | 40 | 0.10 |
| 500 | 440 | 0.88 | 60 | 0.12 |
Saving function, APS and MPS
Y = C + S, so S = Y − C = −c̄ + (1 − b)Y.
- APS = S ÷ Y. Can be negative at low income.
- MPS = ΔS ÷ ΔY = 1 − MPC.
Two key facts: APC + APS = 1 and MPC + MPS = 1, because every rupee of income is either spent or saved.
Short-run equilibrium output
In the short run prices are fixed and there are idle resources, so output adjusts to demand.
AD = AS approach
Equilibrium where planned spending = output: c̄ + bY + I = Y, so Y* = (c̄ + I) ÷ (1 − b). With c̄ = 40, I = 60, b = 0.8: Y* = 100 ÷ 0.2 = 500.
If AD > AS (Y below 500): firms' stocks fall below plan → they raise output. If AD < AS (Y above 500): unsold stocks pile up → output falls. So the economy moves to 500.
Saving = investment approach
Equilibrium also where planned saving = planned investment: −40 + 0.2Y = 60 → Y = 500. Saving is a leakage, investment an injection.
Note: equilibrium output need not be full-employment output; that is the next lesson.
Investment multiplier
The investment multiplier (k) = ΔY ÷ ΔI: how many times income rises when investment rises.
k = 1 ÷ (1 − MPC) = 1 ÷ MPS
Why it works (rounds)
| Round | ΔY (income) | ΔC (spent, MPC 0.8) |
|---|---|---|
| 1 | 100 | 80 |
| 2 | 80 | 64 |
| 3 | 64 | 51.2 |
| … | … | … |
| Total | 500 | 400 |
ΔY = 100 × 5 = 500. The process stops because in each round a part (MPS) leaks into saving.
Range: if MPC = 0, k = 1 (minimum). If MPC = 1, k is infinite. Higher MPC → larger k.
It also works in reverse: a fall in investment lowers income by k times.
Key formulas and definitions
- AD = C + I + G + (X − M); two-sector AD = C + I
- C = c̄ + bY, where b = MPC = ΔC/ΔY
- APC = C/Y; APS = S/Y; APC + APS = 1
- MPS = ΔS/ΔY; MPC + MPS = 1
- Equilibrium: Y = C + I, or S = I; Y* = (c̄ + I)/(1 − b)
- k = ΔY/ΔI = 1/(1 − MPC) = 1/MPS
Worked examples
1. Income rises from ₹1000 to ₹1200 and consumption from ₹900 to ₹1050. Find MPC and MPS.
MPC = 150 ÷ 200 = 0.75. MPS = 1 − 0.75 = 0.25.
2. At income ₹800 consumption is ₹680. Find APC and APS.
APC = 680 ÷ 800 = 0.85. APS = 1 − 0.85 = 0.15 (saving 120 ÷ 800).
3. MPC = 0.9. Find the investment multiplier.
k = 1 ÷ (1 − 0.9) = 1 ÷ 0.1 = 10.
4. MPS = 0.25 and investment rises by ₹200 crore. Find the rise in income.
k = 1 ÷ 0.25 = 4. ΔY = 4 × 200 = ₹800 crore.
5. C = 50 + 0.75Y and I = 100. Find equilibrium income, and consumption and saving at equilibrium.
Y = 50 + 0.75Y + 100 → 0.25Y = 150 → Y = 600. C = 50 + 450 = 500. S = 600 − 500 = 100 = I. ✓
6. Income rose by ₹1000 crore when investment rose by ₹250 crore. Find MPC.
k = 1000 ÷ 250 = 4 = 1 ÷ (1 − MPC) → 1 − MPC = 0.25 → MPC = 0.75.
7. S = −30 + 0.2Y, I = 50. Find equilibrium income.
S = I: −30 + 0.2Y = 50 → 0.2Y = 80 → Y = 400.
Common mistakes
- Writing multiplier = 1/MPC. It is 1/(1 − MPC) = 1/MPS.
- Thinking APS cannot be negative. At very low income people dissave, so APS < 0 and APC > 1.
- Believing MPC can be more than 1 in the Keynesian model. It lies between 0 and 1.
- Assuming equilibrium output is always full-employment output. It can be below it.