Aggregate Expenditure Model & Multiplier Effect (Week 5)

Aggregate Expenditure (AE) Model – Short-Run Overview

• Focus: relationship between total (planned) spending and real GDP in the short run, holding the overall price level constant.
• AE components:
  • Consumption ($C$)
  • Planned (intended) Investment ($I_P$)
  • Government Purchases ($G$)
  • Net Exports ($NX = X - M$)
• Core equilibrium idea:
  • Demand side (planned AE) intersects supply side (actual production $Y$).
  • If $AE = Y$ → macroeconomic equilibrium.

Planned vs. Actual Investment – Inventory Metaphor

• Restaurant example:
  • Plans to serve 10 portions (planned investment in inventory).
  • Actual customers may differ ⇒ actual investment (change in inventories) diverges from plan.
• Macro link:
  • AE > Y → inventories fall → firms raise production → GDP & employment rise.
  • AE < Y → inventories rise → firms cut production → GDP & employment fall.

Consumption (C) – Determinants & Function

• Long-run upward trend (real, 2012 dollars) since 1980s.
• Key determinants
  1. Current Disposable Income ($Y_D = Y + TR - T$)
  2. Household Wealth ($\text{Wealth}=\text{Assets}-\text{Liabilities}$)
  • Positive relationship with $C$.
  1. Expected Future Income
  • E.g., students spend based on higher anticipated post-graduation earnings.
  1. Price Level (CPI)
  • Higher prices ↓ real wealth ↓ $C$; lower prices ↑ real wealth ↑ $C$.
  1. Real Interest Rate ($r<em>{real}=r</em>{nom}-\pi$)
  • $r_{real} \uparrow$ → saving ↑, borrowing ↓, $C$ ↓.
  • $r_{real} \downarrow$ → saving ↓, borrowing ↑, $C$ ↑.

Consumption Function

• Linear form: $C = \bar C + c\,Y_D$
  • $\bar C$ = autonomous (necessity) consumption (exists even with zero income).
  • $c$ (= MPC, 0<c<1) = marginal propensity to consume.
• Example calculation:
  • $\Delta C = 39.7 \text{ billion},\; \Delta Y_D = 51.9 \text{ billion}$
  • $MPC = \frac{\Delta C}{\Delta Y_D} = 0.76$ ⇒ each extra $1$ of income → $0.76$ spent, $0.24$ saved.

MPC & MPS Relationship (national level)

• Income identity (ignoring NX): $Y = C + S + T$.
• Changes: $\Delta Y = \Delta C + \Delta S + \Delta T$.
• For balanced-budget assumption ( $\Delta T = 0$ ):
  $1 = MPC + MPS$ where $MPS = \frac{\Delta S}{\Delta Y}$.
• Table illustration: $MPC = 0.6$, $MPS = 0.4$ satisfy identity.

Planned Investment ($I_P$) – Drivers

• Expected future profitability (optimism ↑ ⇒ $I_P$ ↑).
• Real interest rate (higher cost of borrowing ↓ $I_P$).
• Corporate taxes (higher taxes ↓ $I<em>P$; tax cuts ↑ $I</em>P$ — policy link e.g., Trump era).
• Cash flow (internal funds = revenues − expenses; more cash → easier self-finance).

Government Purchases (G)

• Real government spending (2012 dollars) has trended upward.
• Often financed via borrowing (public or foreign savers).

Net Exports (NX)

• NX>0 → exports exceed imports (trade surplus).
• NX<0 → imports exceed exports (trade deficit). Post-2010 Canada shows persistent negatives in example graph.

45-Degree Diagram & Macroeconomic Equilibrium

• Axes:
  • Vertical: Real AE.
  • Horizontal: Real GDP ($Y$).
• 45° line: all points where $AE=Y$.
• AE schedule: $AE = C + I_P + G + NX$ (upward-sloping, intercept = autonomous spending).
• Regions:
  • Above 45° → AE>Y → expansionary pressure (inventories ↓, GDP ↑, unemployment ↓).
  • Below 45° → AE<Y → recessionary pressure (inventories ↑, GDP ↓, unemployment ↑).
• Intersection → potential GDP ($Y^*$) with only natural unemployment (structural + frictional).

Multiplier Effect

Concept

• Change in autonomous expenditure (
  $\Delta A$ in $\bar C,\; \bar I,\; G,\; NX$) causes more than proportional change in equilibrium GDP.
• Simple multiplier (no taxes/trade):
  $k = \frac{1}{1-MPC}$

Algebraic Derivation

• Aggregate expenditure:
  $AE = \bar{AE} + cY$ (where $\bar{AE}=\bar C+\bar I+G+NX$).
• Equilibrium: $Y=\bar{AE}+cY \Rightarrow Y = \frac{\bar{AE}}{1-c}$.
• Therefore $\Delta Y = k \; \Delta \bar{AE}$.

Numerical Illustration

• Initial $\bar I = 75$, $\bar C = 30$, $c=0.8$ ⇒ $\bar{AE}=105$.
  $Y_1=\frac{105}{0.2}=525$.
• Increase $\bar I$ by $5$ ⇒ $\bar{AE}=110$ ⇒ $Y_2=\frac{110}{0.2}=550$.
• Result: $\Delta Y = 25$ even though $\Delta I = 5$.
• Multiplier: $k= \frac{25}{5}=5 = \frac{1}{1-0.8}$.

Intuitive Spending Chain (geometric series)

• First round: firm buys computer $5$.
• Second: computer shop spends $0.8\times5 = 4$.
• Third: parts maker spends $0.8\times4=3.2$.
• Sum: $5[1+0.8+0.8^2+\ldots]=\frac{5}{1-0.8}=25$.

Factors Affecting Multiplier

• Higher $MPC$ ⇒ larger $k$ (denominator $1-MPC$ smaller).
• Leakages (taxes, imports) in reality reduce $k$ below simple model.

Aggregate Demand (AD) Curve & Price Level Link

• Transition from 45° diagram (fixed price) to AD (varying price).
• Axes:
  • Vertical: Price Level ($P$).
  • Horizontal: Real GDP ($Y$).
• AD is downward-sloping because:
  1. Wealth Effect: $P \uparrow$ → real wealth ↓ → $C$ ↓ → $Y$ ↓.
  2. International-Trade Effect: $P \uparrow$ → domestic goods relatively dear → exports ↓, imports ↑, $NX$ ↓ → $Y$ ↓.
• Shift mechanism: any rise in autonomous spending (e.g., $I_P$ boost) shifts AE up → higher $Y$ at given $P$ → entire AD curve shifts right.

Comprehensive Numerical Example (with G & NX)

• Given:
  • $C = 100 + 0.8Y$
  • $I_P = 125$
  • $G = 125$
  • $NX = -30$
• Equilibrium:
  $Y = C + I_P + G + NX = 100+0.8Y +125 +125 -30$
  $0.2Y = 320 \Rightarrow Y = 1600$.
• Multiplier $k = 5$ (because $MPC=0.8$).
• Policy change: $\Delta G = +20$ ⇒ $\Delta Y = k\,\Delta G = 5 \times 20 = 100$ ⇒ new $Y=1700$.

Policy & Real-World Relevance

• Stimulus Packages: Government raises $G$ during recessions; via multiplier, GDP expands more than the initial outlay.
• Corporate Tax Cuts: Intended to boost $I_P$; can shift AE & AD right but may raise inequality (ethical debate: "tax cuts for the rich").
• Interest-Rate Policy: Central bank lowering $r<em>{real}$ raises both $C$ and $I</em>P$, amplifying GDP through multiplier.
• Trade Balance Concerns: Persistent NX<0 subtracts from AE; export promotion or import substitution strategies counteract.

Key Equations & Formulas (Quick Reference)

• Aggregate Expenditure: $AE = C + I_P + G + NX$
• Disposable Income: $Y_D = Y + TR - T$
• Consumption Function: $C = \bar C + cY_D$
• MPC: $MPC = \frac{\Delta C}{\Delta Y_D}$
• MPS: $MPS = 1 - MPC$
• Equilibrium GDP (simple model): $Y = \frac{\bar{AE}}{1-MPC}$
• Simple Expenditure Multiplier: $k = \frac{1}{1-MPC}$
• Real Interest Rate: $r<em>{real}=r</em>{nom}-\pi$
• Net Exports: $NX = X - M$

Ethical & Practical Implications Discussed

• Government debt financing vs. future tax burden.
• Equity concerns of corporate tax cuts (who benefits?).
• Use of stimulus spending to mitigate cyclical unemployment.

Study Tips & Connections to Previous Material

• Relate price-level effects back to Week-3 CPI discussion (real vs. nominal comparisons).
• Compare individual demand curve vs. economy-wide AD curve (same inverse $P$-$Y$ relationship but different scale & drivers).
• Understand the difference between autonomous vs. induced (income-dependent) spending—core to multiplier logic.
• Practice drawing 45° diagram → shift AE → map movement to AD graph.