Macroeconomics Lesson 6 – Aggregate Expenditure Model

Focus: Very‐short-run macro model where all individual prices are assumed fixed.
Consequence of fixed prices
- Overall price level stays constant.
- $\text{Aggregate Demand (AD)}$ therefore directly determines real GDP (output).
Synonyms
- "Keynesian Cross" diagram = 45° line diagram.
- Same analytical core adopted in IS–LM, AS–AD introductions.
Guiding questions addressed in the lesson
- What determines expenditure plans when the price level is fixed?
- How is real GDP determined under fixed prices?
- Definition, size, and intuition of the expenditure multiplier.
- Logical bridge between Aggregate Expenditure (micro-foundation) and Aggregate Demand (macro curve).

Total spending identity (National‐income accounting):
- $Y = C + I + G + X - M$
- $Y$ : Real GDP (also aggregate income)
- $C$ : Consumption expenditure
- $I$ : Investment (gross private domestic)
- $G$ : Government expenditure on goods & services
- $X$ : Exports
- $M$ : Imports
Two-way causality under fixed prices (ceteris paribus)
- Rising $Y$ ➔ higher planned $C$ and $M$ ➔ higher total AE.
- Higher AE ➔ firms raise production ➔ higher $Y$ .
Key endogenous vs. exogenous components
- Endogenous (induced) with respect to $Y$ : $C,\;M$ .
- Exogenous (autonomous): $I,\;G,\;X$ (also autonomous pieces of $C$ and $M$ ).

Disposable income (after taxes): $YD = Y - T$
- $T$ = Net taxes = Taxes − Transfer payments.
Household budget identity: $YD = C + S$
Behavioural relationships (holding interest rate, wealth, expectations, etc. constant)
- Consumption function: Planned $C$ as a function of $YD$ .
- Saving function: Planned $S$ as a function of $YD$ .
Graphical interpretation (Figure 6.1)
- 45° line where $C = YD$ (zero saving).
- Above 45°: C > YD (dissaving; borrowing/wealth draw-down).
- Below 45°: C < YD (positive saving).

Definitions
- $MPC = \dfrac{\Delta C}{\Delta YD}$
- $MPS = \dfrac{\Delta S}{\Delta YD}$
Empirical classroom example (Figure 6.2)
- $\Delta YD = \$2\ \text{trn}$ ➔ $\Delta C = \$1.5\ \text{trn}$ ➔ $MPC = 0.75$ .
- Same $\Delta YD$ ➔ $\Delta S = \$0.5\ \text{trn}$ ➔ $MPS = 0.25$ .
Accounting identity proof
- Starting from $C + S = YD$ take small changes: $\Delta C + \Delta S = \Delta YD$ .
- Divide by $\Delta YD$ ⇒ $MPC + MPS = 1$ .

Short-run assumption: U.S. imports primarily driven by domestic real GDP.
Definition: $\text{Marginal Propensity to Import (MPM)} = \dfrac{\Delta M}{\Delta Y}$ .
- Illustration: $\Delta Y = \$1\ \text{trn}$ raises $M$ by $\$0.25\ \text{trn}$ ⇒ $MPM = 0.25$ .

Planned AE formula under fixed prices
- $AE = C + I + G + X - M$ (all "planned" values; imports subtracted).
Components by nature
- Induced expenditure: $C - M$ portions that vary with $Y$ .
- Autonomous expenditure: $I + G + X$ (plus autonomous slices of $C, M$ ) – does not vary with $Y$ .
AE schedule
- Tabular listing of planned AE for each potential $Y$ .
AE curve
- Graph plotting AE (vertical axis) vs. $Y$ (horizontal axis), typically upward sloping with slope < 1.
- Slope equals $MPC - MPM$ when only $C$ and $M$ are induced and no taxes.

Accounting fact: Actual expenditure ≡ Actual $Y$ for any point in time.
Equilibrium condition: $AE_{planned} = Y$ .
- Graphically: AE curve intersects 45° line.
Inventory link (Figure 6.4)
- If AE_{planned} > Y ➔ unplanned inventory depletion ➔ firms increase output ➔ $Y$ rises.
- If Y > AE_{planned} ➔ unplanned inventory accumulation ➔ firms cut output ➔ $Y$ falls.
- Convergence continues until inventories are stable (equilibrium).

Definition: Factor by which a change in autonomous expenditure (∆A) is magnified into a larger change in equilibrium $Y$ (∆Y).
- $Multiplier = \dfrac{\Delta Y}{\Delta A}$ .
Algebraic derivation with AE-curve slope ((z))
- $Multiplier = \dfrac{1}{1 - z}$ where $z = \dfrac{dAE}{dY}$ .
Special cases
- No taxes, no imports: $z = MPC$ ⇒ $Multiplier = \dfrac{1}{1 - MPC} = \dfrac{1}{MPS}$ .
- With taxes/imports, $z = MPC\,(1 - t) - MPM$ ((t) = marginal tax rate), so multiplier shrinks.
Numerical illustrations (Figures 6.5 & 6.6)
- Slope $z = 0.75$ (no taxes/imports) ⇒ $Multiplier = 4$ .
- Adding taxes & imports ⇒ slope $z = 0.5$ ⇒ $Multiplier = 2$ .
Intuition
- Initial autonomous rise (e.g., investment) boosts $Y$ .
- Higher income induces more consumption, further elevating $Y$ .
- Successive rounds continue but diminish geometrically (determined by MPC).

Figure 6.7 reveals sequential rounds: Round 0 = ∆A, Round 1 = MPC·∆A, Round 2 = MPC²·∆A, …
Link to business‐cycle turning points
- Peaks & troughs often triggered by changes in autonomous components (investment, exports, fiscal shifts).
- ↑ Autonomous Expenditure ➔ unplanned inventory falls ➔ expansion.
- ↓ Autonomous Expenditure ➔ unplanned inventory rises ➔ recession.
Graphical business cycle (Figure 5.1)
- Trend growth vs. short-run fluctuations (expansion A → peak; peak B → recession → trough).

Real-world firms rarely keep prices frozen indefinitely.
- Persistent inventory gaps prompt both quantity and price adjustments.
Moving beyond Lesson 6
- AS-AD model (Lesson 7) incorporates price level flexibility: simultaneous determination of $Y$ and price level.
- AE model provides the horizontal slice (fixed‐price case) underlying the downward-sloping AD curve.

AE curve: Relationship between planned spending and $Y$ at a given price level.
AD curve: Relationship between price level (P) and equilibrium $Y$ when AE interacts with price-dependent mechanisms (wealth effect, interest‐rate effect, exchange-rate effect).
Derivation mechanism (Figures 6.8a & 6.8b)
1. Start with AE₀ at price level 110 and equilibrium $Y = \$13\ \text{trn}$ (Point B on AD).
2. Increase price level to 130 ➔ wealth ↓ & substitution effects ➔ AE curve shifts down to AE₁.
- New equilibrium $Y = \$12\ \text{trn}$ (Point A) – movement up along AD.
1. Decrease price level to 90 ➔ AE shifts up to AE₂; equilibrium $Y = \$14\ \text{trn}$ (Point C) – movement down along AD.
Key insight: Each possible price level maps to a distinct AE curve; connecting equilibrium points traces the AD curve.

Fiscal stimulus (∆G or tax cuts raising autonomous $C$ ) exerts multiplied impact, magnitude depending on MPC, tax/import leakages.
Automatic stabilisers (income taxes, import leakages) dampen multiplier ➔ smoother business cycles.
AE analysis underlies short-run Keynesian policy prescriptions; AS-AD required for price-level & inflation considerations.

National income identity: $Y = C + I + G + X - M$
Disposable income: $YD = Y - T$
Household allocation: $YD = C + S$
Marginal propensities: $MPC = \dfrac{\Delta C}{\Delta YD},\; MPS = \dfrac{\Delta S}{\Delta YD},\; MPC + MPS = 1$
Marginal propensity to import: $MPM = \dfrac{\Delta M}{\Delta Y}$
Equilibrium condition (Keynesian Cross): $AE_{planned}(Y) = Y$
Multiplier (general): $k = \dfrac{1}{1 - z}$ where $z$ is AE-slope.
No‐tax / no‐import case: $k = \dfrac{1}{1 - MPC} = \dfrac{1}{MPS}$ .

Lesson 7 will combine AE insights with Aggregate Supply to build the full AS-AD framework, explaining simultaneous movements in output and the price level.