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{real}=r{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 ↓ IP; tax cuts ↑ IP — 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.
  • 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{real} raises both C and IP, 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{real}=r{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.