The Goods Market

Components of Aggregate Demand

coreExam · medium

Aggregate demand Z = C + I + G + NX decomposes into four components. Consumption C depends on disposable income: C = c₀ + c₁(Y − T), where c₀ is autonomous and c₁ is the marginal propensity to consume. Investment I depends on output and interest rate. Government spending G and taxes T are policy. Net exports NX depend on foreign variables. Each component has its own multiplier effect.

Derivation

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The Four Components

Z = C + I + G + NX

| Component | Depends on | Main driver | |-----------|------------|-------------| | $C$ | $(Y - T)$ , wealth, confidence | Disposable income | | $I$ | $Y$ , $r$ , $\Pi^e$ | Sales and borrowing cost | | $G$ | Policy | Government choice | | $NX$ | $Y$ , $Y^*$ , $\varepsilon$ | Domestic + foreign output, real exchange rate |

The Consumption Function

C = c_0 + c_1(Y - T), \quad 0 < c_1 < 1

$c_0$ : autonomous consumption — wealth, confidence, habit. Shifts $Z$ up/down.
$c_1$ : marginal propensity to consume. Slope of the $Z$ curve.

The reason $c_1 < 1$ is that households save part of income. This is what creates the Keynesian multiplier: $1/(1 - c_1) > 1$ , not infinite.

The Three Multipliers

| Shock | Multiplier | |-------|------------| | $\Delta G$ | $1/(1 - c_1)$ | | $\Delta T$ | $-c_1/(1 - c_1)$ | | $\Delta G = \Delta T$ | $1$ (balanced budget) |

Equilibrium

Set $Y = Z$ and solve:

Y^* = \frac{c_0 - c_1 T + I + G + NX}{1 - c_1}

An increase in any autonomous term feeds back through the multiplier $1/(1-c_1)$ .

Worked Example

c₀ = 100, c₁ = 0.6, I = 150, G = 200, T = 200. Closed economy (NX = 0).

Y* = (c₀ − c₁T + I + G)/(1 − c₁) = (100 − 120 + 150 + 200)/0.4 = 330/0.4 = 825.
C = 100 + 0.6·(825 − 200) = 100 + 375 = 475.
Check: Y = C + I + G = 475 + 150 + 200 = 825. ✓
Now ΔT = +50 (tax rise): Y* = (100 − 150 + 150 + 200)/0.4 = 300/0.4 = 750. ΔY = −75.

Initial Y = 825, C = 475. After ΔT = +50: Y falls to 750. Tax multiplier −c₁/(1−c₁) = −1.5; ΔY = −1.5 × 50 = −75.

Common Mistakes

—Using c₁ (MPC) as the multiplier — it's 1/(1−c₁), not c₁.
—Forgetting that tax changes affect Y through disposable income: ΔT changes C, not Y directly.
—Missing the balanced-budget multiplier: equal ΔG = ΔT has multiplier 1 (not 0).
—Ignoring autonomous shifts (c₀, I): these also trigger the multiplier.

Exam Cues

→Multipliers: spending 1/(1−c₁), tax −c₁/(1−c₁), balanced budget 1.
→Z curve has slope c₁, 45° line: Y = Z gives equilibrium.
→Consumption function: C = c₀ + c₁(Y−T). Know both autonomous and marginal parts.
→Shifts vs movements: ΔG, Δc₀, ΔI shift Z; changes in Y move along Z.