ECON10181 Macroeconomic Analysis 1 | Ultimate Revision Guide

Course Overview

Master the fundamentals of macroeconomic analysis from measurement to the complete IS-LM-PC model.

Exam Format (90 minutes)

Section	Content	Marks	Time
A	5 Multiple Choice Questions	20	~15 min
B	2 Long Questions (Q6: IS-LM, Q7: IS-LM-PC)	50	~50 min
C	1 Essay (choose 1 of 2)	30	~25 min

Materials Allowed: One A4 sheet, hand-written (not photocopied), with your own notes + Non-programmable calculator

Textbook: BAG Chapters 2-9 are examinable (excluding Chapter 6.2 onwards)

The Big Picture

Macroeconomics studies aggregate economic activity—the interaction of people, firms, and governments at the economy-wide level.

Core Focus

Macroeconomics centres on three key variables: Output (GDP), Unemployment, and Inflation.

Course Progression

Measurement (L1) — GDP, price levels, inflation
Goods Market (L2) — Keynesian cross, demand determines output
Financial Markets (L3) — Money demand/supply, interest rates
IS-LM Model (L4) — Combining goods and financial markets
Labour Market (L5) — Wage-setting, price-setting, natural unemployment
Phillips Curve (L6) — Inflation-unemployment relationship
IS-LM-PC Model (L7) — Short-run to medium-run dynamics
Inflation (L8) — Fisher equation, nominal vs real

Quick Navigation

LECTURE 01

Measurement & GDP

Three approaches to GDP, deflators, CPI, chain-type indexes

LECTURE 02

Goods Market

Consumption function, multipliers, paradox of saving, hand-to-mouth consumers

LECTURE 03

Financial Markets

Money demand, bond demand, banking system, modern vs traditional LM

LECTURE 04

IS-LM Model

Deriving IS & LM curves, policy analysis, crowding out

LECTURE 05

Labour Market

WS-PS model, natural unemployment rate, real wage determination

LECTURE 06

Phillips Curve

Inflation-unemployment tradeoff, expectations, Okun's Law

LECTURE 07

IS-LM-PC Model

Complete macro model, shock analysis, medium-run equilibrium

LECTURE 08

Inflation & Interest Rates

Fisher equation, ZLB, Quantity Theory of Money

Lecture 1 • BAG Ch. 2

Measurement of Macroeconomic Variables

Understanding how we measure economic activity through GDP, price indices, and growth rates.

What is GDP?

Definition

Gross Domestic Product (GDP): The market value of all FINAL goods and services produced within a country in a given period of time.

Key Terms

Market value: Uses market prices to aggregate different goods
Final goods: Goods sold to end users (not intermediate goods)
Within a country: Geographical boundary (vs GNP which uses nationality)
Given period: Usually quarterly or annually

Three Approaches to GDP

Expenditure Approach

Y = C + I + G + (X − IM)

C = Consumption (households) I = Investment (firms) G = Government spending X = Exports IM = Imports (X − IM) = Net exports

Production Approach

Value Added = Revenue − Cost of Intermediate Inputs

Sum of value added at each stage of production

Income Approach

GDP = Labour Income + Capital Income

Key Insight

All three approaches must give the same answer! This is an accounting identity.

Nominal vs Real GDP

Nominal GDP

Nominal GDP = Σ (Current Pricei × Current Quantityi)

Values goods at current market prices. Affected by both price and quantity changes.

Real GDP

Real GDP = Σ (Base Year Pricei × Current Quantityi)

Values goods at constant (base year) prices. Only affected by quantity changes.

Tutorial 1 - GDP Calculations

Given data for Laptops, Fish & Chips, Cars (2011 vs 2019):

2011 Nominal GDP = 150(£500) + 200(£5) + 20(£2,800) = £132,000
2019 Nominal GDP = 300(£450) + 180(£5) + 25(£3,700) = £228,400
Nominal GDP growth = (228,400 − 132,000) / 132,000 = 73.03%

2019 Real GDP (2011 prices) = 300(£500) + 180(£5) + 25(£2,800) = £220,900
Real GDP growth = (220,900 − 132,000) / 132,000 = 67.35%

Price Indices

GDP Deflator

GDP Deflator = Nominal GDPReal GDP × 100

Paasche index (uses current period quantities as weights) Covers ALL domestically produced goods EXCLUDES imports Weights change every period

Consumer Price Index (CPI)

CPI = Cost of basket at current pricesCost of basket at base prices × 100

Laspeyres index (uses base period quantities as weights) Covers consumer goods only INCLUDES imports Fixed weights (substitution bias)

Tutorial 1 - CPI Calculation

Consumer basket: 1 laptop, 10 fish & chips, 0.2 car

2011 cost = 1(£500) + 10(£5) + 0.2(£2,800) = £1,110
2019 cost = 1(£450) + 10(£5) + 0.2(£3,700) = £1,240
CPI₂₀₁₉ = (1,240 / 1,110) × 100 = 111.7
CPI inflation = (111.7 − 100) / 100 = 11.71%

Warning

CPI inflation (11.71%) differs from GDP deflator inflation (3.40%) due to: different weights, import inclusion, coverage of goods.

Chain-Type Index (4-Step Construction)

1

Calculate real GDP growth using year t prices

2

Calculate real GDP growth using year t+1 prices

3

Average the two growth rates

4

Set index = 1 in reference year, multiply by nominal GDP

Tutorial 1 - Chain Index Construction

Growth with 2011 prices: 67.35%
Growth with 2019 prices: 60.28%
Average growth = (67.35 + 60.28) / 2 = 63.81%
2011 index = 1 / 1.6381 = 0.6104 (setting 2019 = 1)
2011 Real GDP (chained 2019) = £228,400 × 0.6104 = £139,426

2023-24 Section C: Chain-Type Indexes

Chain-type indexes more accurate because they update weights continuously, avoiding distortion from using outdated base year prices. Key example: computer prices fell dramatically since 1985.

GDP Limitations

GDP does NOT account for:

Home production and unpaid work
Informal/underground economy
Environmental degradation and resource depletion
Quality of life, leisure, and well-being
Income distribution and inequality
Sustainability of growth

Tutorial 1 Q3

Working extra hour earning £12, buying £10 takeout → measured GDP increases by £22, but overstates true output because home-cooked meal (not in GDP) is replaced.

2022-23 Stiglitz Quote

"GDP tells you nothing about sustainability." Be ready to discuss environmental costs and debt-financed growth.

Lecture 2 • BAG Ch. 3

The Goods Market

Understanding how demand determines output in the short run through the Keynesian cross model.

The Consumption Function

Consumption Function

C = c0 + c1(Y − T)

c₀ = autonomous consumption (>0): consumption when income = 0 c₁ = MPC (marginal propensity to consume), 0 < c₁ < 1 Y − T = Y_D = disposable income

Key Insight

MPC < 1 means people save part of additional income. This is crucial for multiplier analysis.

Equilibrium Output Derivation

Aggregate Demand (Closed Economy)

Z ≡ C + I + G

Equilibrium Condition

Production equals demand: Y = Z

1

Start: Y = Z = C + I + G

2

Substitute C: Y = c₀ + c₁(Y − T) + Ī + Ḡ

3

Expand: Y = c₀ + c₁Y − c₁T + Ī + Ḡ

4

Collect Y: Y − c₁Y = c₀ − c₁T + Ī + Ḡ

5

Factor: Y(1 − c₁) = c₀ − c₁T + Ī + Ḡ

Equilibrium Output

Y = 11 − c1 × (c0 − c1T + I + G)

1/(1−c₁) = multiplier (c₀ − c₁T + Ī + Ḡ) = autonomous spending

Tutorial 2 Q1 - Complete Keynesian Cross

Given: C = 240 + 0.8Y_D, I = 200, G = 600, T = 400

Z = 240 + 0.8(Y − 400) + 200 + 600 = 720 + 0.8Y
Y = Z → Y = 720 + 0.8Y → 0.2Y = 720 → Y = 3600
Y_D = 3600 − 400 = 3200
C = 240 + 0.8(3200) = 2800
Multiplier = 1/(1−0.8) = 5

All Multiplier Variants

Model	Multiplier Formula	Notes
Basic	`1 / (1 − c₁)`	c₁ = MPC
Tax Multiplier	`−c₁ / (1 − c₁)`	Negative; smaller magnitude
With Income Tax	`1 / (1 − c₁(1−t₁))`	t₁ = marginal tax rate
With Endogenous I	`1 / (1 − c₁ − b₁)`	Requires c₁ + b₁ < 1
Combined	`1 / (1 − c₁ − b₁ + c₁t₁)`	Most general form

Tutorial 2 Q2 - Income-Dependent Taxes

Income-dependent taxes reduce the multiplier → AUTOMATIC STABILIZER. Output responds less to autonomous spending shocks.

Tutorial 2 Q3 - Endogenous Investment

If b₁ > 0, multiplier INCREASES because: ↑Y → ↑I → ↑Z → ↑Y → ... (positive feedback loop).

2024-25 MCQ Q5

When taxes ↑ by ΔT, ZZ line shifts down by c₁ΔT (initial effect), then total output change = [c₁/(1−c₁)] × ΔT (multiplier effect).

Saving-Investment Identity

Private Saving

S ≡ Y − T − C

S-I Identity

S + (T − G) = I

S = private saving T − G = public saving (surplus if +, deficit if −)

Tutorial 2 Q1d - S-I Verification

S = Y − T − C = 3600 − 400 − 2800 = 400
Public saving = T − G = 400 − 600 = −200 (budget deficit)
Total saving = 400 + (−200) = 200 = I ✓

Paradox of Saving

If all consumers try to save more (↓c₀):

Individual intention: ↑Saving
Collective result: ↓Consumption → ↓Y → S remains unchanged (S = I)

2024-25 Section C

"Efforts to increase private saving can paradoxically reduce aggregate demand, leaving saving unchanged." Key: In Keynesian model, Y adjusts to make S=I always hold.

Transfer Payments (2023-24 Exam Topic)

Net Taxes

T = ttax − tpay

t_tax = taxes paid t_pay = transfers received

2023-24 Q6 - Transfer to Households

If government increases transfers by γ (not tax-financed):
New Y_D = Y − t_tax + t_pay + γ
IS shifts RIGHT → Output increases

If funded by taxing high-income (MPC_high < MPC_low) and transferred to low-income:
Net effect: Output INCREASES because low-income have higher MPC.

Hand-to-Mouth Consumers (2024-25 Topic)

Definition

Hand-to-mouth consumers: Consumers who spend ALL disposable income: C_h = (Y − T)

Aggregate Consumption with Hand-to-Mouth

C = α[c0 + c1(Y−T)] + (1−α)(Y−T)

α = fraction of unconstrained consumers (save part of income) (1−α) = fraction of hand-to-mouth consumers (spend everything)

New Multiplier

Multiplier = 11 − αc1 − (1−α)

Key Insight

More hand-to-mouth consumers (lower α) → LARGER multiplier → Fiscal policy MORE effective, Monetary policy LESS effective.

Lecture 3 • BAG Ch. 4

Financial Markets

Money demand, supply, and how interest rates are determined.

Money Demand

General Form

Md = $Y × L(i)

L(i) is decreasing in i (opportunity cost of holding money)

Linear Form

Md = $Y × (a − bi) or Md = d1Y − d2i

↑Y → ↑M^d (more transactions needed) ↑i → ↓M^d (higher opportunity cost, switch to bonds)

Bond Demand & Wealth Constraint

Wealth Allocation

Wealth = Md + Bd

B^d = Wealth − M^d

Tutorial 3 Q1 - Bond Demand Derivation

Given: Wealth = £50,000, Y = £60,000, M^d = $Y(0.35 − i)

M^d = 60,000(0.35 − i) = 21,000 − 60,000i
B^d = 50,000 − (21,000 − 60,000i) = 29,000 + 60,000i

If i increases by 10pp: ΔB^d = 60,000 × 0.10 = £6,000 increase

2024-25 MCQ Q1 - Bond Demand Calculation

Given: Wealth = £5,000, Y = £15,000, M^d = Y(0.3 − i)

M^d = 15,000(0.3 − i) = 4,500 − 15,000i
B^d = 5,000 − (4,500 − 15,000i) = 500 + 15,000i
Answer: (C). Note: ↑i → ↑B^d (bonds more attractive)

Key Insight

Higher interest rates → bonds more attractive → B^d increases. Higher income → need more money → M^d increases, B^d decreases (given fixed wealth).

Money Market Equilibrium

Equilibrium

MP = Y × L(i)

Real money supply = Real money demand

Tutorial 3 Q2 - Equilibrium Interest Rate

Given: M^d = 4000 − 16000i, M^s = 2720

4000 − 16000i = 2720
16000i = 1280 → i = 8%

If M^s reduced to 2400: i = (4000−2400)/16000 = 10%
To set i = 4%: M^s = 4000 − 16000(0.04) = 3360

Banking System & Money Multiplier

Money Multiplier

Money Supply = H × 1θ

H = monetary base (high-powered money) θ = reserve ratio 1/θ = money multiplier

Tutorial 3 Q3 - Banking System

Given: θ = 0.1, H = £100bn, Y = £5tr, M^d = $Y(0.8 − 4i)

Money multiplier = 1/0.1 = 10
Money supply = £100bn × 10 = £1,000bn
Demand for reserves: H^d = θ × M^d = 0.1 × 5000(0.8 − 4i)
Equilibrium: 100 = 500(0.8 − 4i) → 100 = 400 − 2000i → i = 15%

Modern vs Traditional LM

Approach	CB Sets	What Adjusts	LM Curve
Modern	Interest rate i	M adjusts endogenously	Horizontal (i = ī)
Traditional	Money supply M	i adjusts	Upward-sloping

2024-25 MCQ Q4

With traditional LM (CB sets M), if money demand ↑ at every (Y,i) → LM shifts LEFT → ↓Y and ↑i.

Lecture 4 • BAG Ch. 5

The IS-LM Model

Combining goods and financial markets to analyze fiscal and monetary policy.

Investment Function

Investment

I = b0 + b1Y − b2i

b₀ = autonomous investment b₁ = accelerator effect (sensitivity to output) b₂ = interest rate sensitivity

IS Curve Derivation (7-Mark Exam Format)

1

Write aggregate demand: Z = C + I + G = c₀ + c₁(Y−T) + b₀ + b₁Y − b₂i + Ḡ

2

Apply equilibrium condition: Y = Z

3

Expand and collect Y terms: Y = c₀ + c₁Y − c₁T + b₀ + b₁Y − b₂i + Ḡ

4

Solve for Y: Y(1 − c₁ − b₁) = c₀ − c₁T + b₀ + Ḡ − b₂i

IS Relation (Y as function of i)

Y = 11 − c1 − b1 (c0 − c1T + b0 + G − b2i)

IS Curve (i as function of Y)

i = c0 − c1T + b0 + Gb2 − 1 − c1 − b1b2Y

Tutorial 4 Q1 - Full IS-LM Solution

Given: C = 500+0.2Y_D, I = 200+0.25Y−1000i, G=300, T=200, M/P=1500, (M/P)^d=2Y−8000i

IS Derivation:
Y = 500 + 0.2(Y−200) + 200 + 0.25Y − 1000i + 300
0.55Y = 960 − 1000i
IS: Y = 1745.45 − 1818.18i

LM Derivation:
1500 = 2Y − 8000i
LM: i = (Y − 750)/4000

Equilibrium: Y ≈ 1436.5, i = 17%

IS Slope Analysis

IS Slope (di/dY)

Slope = − 1 − c1 − b1 + c1t1b2

Parameter Change	Effect on IS Slope	Policy Implication
↑t₁ (income tax rate)	IS becomes STEEPER	Monetary policy LESS effective
↑b₂ (investment i-sensitivity)	IS becomes FLATTER	Monetary policy MORE effective
↑c₁ (MPC)	IS becomes FLATTER	Multiplier larger
↑b₁ (investment Y-sensitivity)	IS becomes FLATTER	Multiplier larger

2022-23 Q6

"How does IS slope depend on t₁?" Higher t₁ → steeper IS because automatic stabilizers dampen multiplier, making Y less responsive to i.

Crowding Out

Mechanism

When G increases with traditional (upward-sloping) LM:
1. IS shifts right → ↑Y and ↑i
2. Higher i reduces private investment
3. Net ↑Y positive but SMALLER than simple multiplier suggests

Tutorial 4 Q1g - Fiscal Expansion with Fixed i

If CB maintains i = 5% when G increases from 300 to 600:

New IS: Y = 2290.91 − 1818.18i
At i = 5%: Y = 2200 (up from 1654.5)

Full multiplier effect because NO crowding out (i constant).
CB must increase M to maintain i = 5%.

2022-23 MCQ Q4

If BoE holds i constant when G↑, M will INCREASE and impact on Y will be LARGER than if M held constant.

Policy Stabilization Choice

Tutorial 4 Q3

Shocks from GOODS market (IS shifts): Hold M constant better (i changes offset shock)
Shocks from MONEY market (LM shifts): Hold i constant better (CB accommodates money demand)

Lecture 5 • BAG Ch. 7

The Labour Market

Wage-setting, price-setting, and the natural rate of unemployment.

Wage-Setting (WS) Relation

General Form

W = Pe × F(u, z)

P^e = expected price level u = unemployment rate z = catch-all variable

As Real Wage (assuming P^e = P)

WP = 1 − αu + z

DOWNWARD sloping in (u, W/P) space ↑u → ↓W/P (workers have less bargaining power) ↑z → ↑W/P (unemployment benefits, union power push wages up)

Price-Setting (PS) Relation

Price Setting

P = (1 + m)W

m = markup (firms' market power over workers)

Real Wage from PS

WP = 11 + m

HORIZONTAL line in (u, W/P) space Higher markup → lower real wage

Critical Insight

Real wage is determined by PS alone, NOT WS! Changes in worker bargaining power (z) only affect unemployment, NOT the real wage.

2023-24 MCQ Q2 - Real Wage Calculation

Given: Markup m = 11% = 0.11

W/P = 1/(1 + 0.11) = 1/1.11 = 0.90
Answer: (C) 0.90

2023-24 MCQ Q3 - Worker Bargaining Power

If worker bargaining power ↑ throughout economy:
• WS shifts UP (workers demand higher wages at each u)
• But PS unchanged: W/P = 1/(1+m) still determines real wage
• Result: Higher nominal W and P, SAME real wage, HIGHER u_n
Answer: (E) Real wage remains constant

2024-25 MCQ Q2 - Decrease in Markup

If markup m decreases:
• PS shifts UP (W/P = 1/(1+m) increases)
• WS unchanged
• Result: Higher real wage, LOWER natural unemployment
Answer: (B) PS shifts upward, increasing real wage

Natural Rate of Unemployment

Setting WS = PS:

Natural Unemployment Rate

un = m + zα

↑m (markup) → ↑u_n ↑z (labour rigidities) → ↑u_n ↑α (wage flexibility) → ↓u_n

Natural Output

Yn = L(1 − un)

Tutorial 6 Q3 - Natural Unemployment Calculation

Given: m = 0.03, z = 0.03

For α = 1: u_n = (0.03 + 0.03)/1 = 6%
For α = 2: u_n = (0.03 + 0.03)/2 = 3%

Higher α (wage flexibility) → lower u_n

Tutorial 6 Q3c - Oil Price Shock

If markup doubles (m: 0.03 → 0.06):

For α = 1: u_n = (0.06 + 0.03)/1 = 9% (↑3pp)
For α = 2: u_n = (0.06 + 0.03)/2 = 4.5% (↑1.5pp)

Higher wage flexibility weakens adverse supply shock effects.

Lecture 6 • BAG Ch. 8

The Phillips Curve

Understanding the relationship between inflation and unemployment.

Phillips Curve

General Form

π = πe + (m + z) − αu

With Natural Rate

π − πe = −α(u − un)

When u < u_n: inflation RISES above expectations When u > u_n: inflation FALLS below expectations When u = u_n: inflation equals expectations (medium-run)

Expectations Formation

General Expectations

πe = (1 − θ)π + θπt−1

θ = 0 (Fully Anchored): π^e = π̄ — Expectations fixed at target θ = 1 (Fully Adaptive): π^e = π_t−1 — Expectations based on last period

Accelerationist PC (θ = 1)

Δπ = −α(u − un)

Δπ = change in inflation (π_t − π_t−1) No permanent tradeoff: only u = u_n is sustainable

Key Insight

With adaptive expectations, there is NO permanent tradeoff between inflation and unemployment. Keeping u < u_n causes inflation to ACCELERATE continuously.

Multi-Period Calculations (KEY EXAM SKILL)

1

Find natural rate: u_n from PC (set π = π^e, solve for u)

2

Calculate π for period t using given u

3

Update π^e for t+1 based on θ

4

Repeat for subsequent periods

Tutorial 6 Q1 - Anchored Expectations (θ = 0)

Given: π = π^e + 0.1 − 2u, π̄ = 2%, initially u = u_n

u_n = 0.1/2 = 5%

If u reduced to (u_n − ε) permanently with θ = 0:
π^e = π̄ = 2% (always anchored)
π = 2% + αε = constant (elevated but stable)

Tutorial 6 Q2 - Adaptive Expectations (θ = 1)

Given: π = π^e + 0.1 − 2u, π^e = π_t−1, π₀ = 0, u = 4% forever

u_n = 0.1/2 = 5%, so u < u_n

π_t = 0 + 0.1 − 2(0.04) = 0.02 = 2%
π_t+1 = 0.02 + 0.02 = 4%
π_t+2 = 0.04 + 0.02 = 6%
π_t+3 = 0.06 + 0.02 = 8%

Inflation rises by 2pp each period!

2023-24 MCQ Q4 - Exam Calculation

Given: π = π^e + 0.2 − 4u, π^e = π_t−1, π₋₁ = 0, u = 4% forever

π_t = 0 + 0.2 − 4(0.04) = 0.2 − 0.16 = 0.04 = 4%
π_t+1 = 0.04 + 0.04 = 8%
π_t+2 = 0.08 + 0.04 = 12%

Answer: (D) t+1: 8% and t+2: 12%

Wage Indexation

PC with Wage Indexation

πt = [λπt + (1−λ)πet] + φ − αut

λ = fraction of workers with indexed contracts

Tutorial 6 Q2c - With Indexation (λ = 0.5)

0.5π_t = 0.5π_t−1 + 0.02
π_t = π_t−1 + 0.04

Inflation now accelerates by 4pp (not 2pp) each period!

Key Insight

Wage indexation AMPLIFIES effect of unemployment on inflation. More indexed contracts → faster inflation acceleration when u < u_n.

Okun's Law

ut − ut−1 = −β(gY − gY)

β ≈ 0.4 (Okun coefficient) ḡ_Y ≈ 3% (normal GDP growth rate) If GDP grows 1pp above normal, u falls by 0.4pp

2022-23 MCQ Q1 - Okun's Law

Given: u_t − u_t−1 = −0.4(g_Y − 3%)

If g_Y = 6%: u_t − u_t−1 = −0.4(6%−3%) = −1.2pp
Unemployment decreases by 1.2 percentage points
Answer: (B)

Lecture 7 • BAG Ch. 9

The IS-LM-PC Model

Bringing together IS-LM and Phillips Curve for complete macroeconomic analysis.

Complete Model System

IS-LM-PC System

IS: Y = C(Y−T) + I(Y,r) + G

LM: r = r̄ (CB sets real rate)

PC: π − π^e = −α(u − u_n) or π − π̄ = ψ(Y − Y_n)

Warning

In IS-LM-PC, investment depends on REAL interest rate r, not nominal rate i!

Medium-Run Equilibrium

Y = Y_n (output at potential)
π = π̄ (inflation at target)
π^e = π (expectations correct)
r = r_n (natural/neutral real rate)

5-Step Shock Analysis (25-Mark Questions)

1

INITIAL STATE: Draw IS-LM and PC showing Y = Y_n, r = r_n, π = π̄

2

IDENTIFY SHOCK TYPE:
• IS/Demand shock: Changes in c₀, I, G, taxes, consumer confidence
• PC/Supply shock: Changes in m (markup), z, oil prices, productivity

3

SHORT-RUN EFFECT: Determine which curve shifts and direction. IS shifts → new Y → read π from PC (π ≠ π̄ in short run)

4

CB RESPONSE:
• If Y < Y_n: CB cuts r to boost demand
• If Y > Y_n: CB raises r to cool demand

5

MEDIUM-RUN: Y returns to Y_n, but composition changes

Demand Shock Examples

2022-23 Q7 - Consumer Confidence Decrease

Short Run: ↓Consumer confidence → ↓c₀ → IS LEFT → Y < Y_n → π < π̄
CB Response: CB cuts r to stimulate → ↑I
Medium Run: Y returns to Y_n. Composition: C lower, I higher, r lower

2023-24 Q7 - Credit Expansion (Less Saving)

Short Run: ↑Consumer credit → ↓saving → ↑C → IS RIGHT → Y > Y_n → π > π̄
CB Response: CB raises r → ↓I
Medium Run: Y returns to Y_n. Composition: C higher, I lower, r higher

Supply Shock Example

2024-25 Q7 - Positive Productivity Shock

Initial: Technology lowers costs → m falls → PS UP → u_n falls → Y_n INCREASES
Short Run: Old Y now BELOW new Y_n → π < π̄
CB Response: CB cuts r to boost demand
Medium Run: Y rises to new higher Y_n. Both C and I increase (r lower, Y higher)

Key Insight

Supply shocks differ from demand shocks: positive supply shock allows BOTH higher output AND lower inflation. Demand shocks create inflation-output tradeoffs.

Expectations and Sustainability

Tutorial 7 Q2

With θ = 1, if CB doesn't respond to positive demand shock → inflation accelerates without bound.
With θ = 0 → inflation elevated but constant.
Neither sustainable if CB targets π̄.

Tutorial 7 Q1d-f

Fiscal expansion (↑G or ↓T) → IS right → CB must ↑r to maintain Y = Y_n → natural real rate r_n increases permanently.

Lecture 8 • BAG Ch. 6.1

Inflation & Interest Rates

The Fisher equation, zero lower bound, and Quantity Theory of Money.

Fisher Equation

Exact Form

(1 + r) = (1 + i)(1 + πe)

Approximate Form (Most Used)

r ≈ i − πe

r = ex ante (expected) real interest rate i = nominal interest rate π^e = expected inflation

2022-23 MCQ Q3 - Investment Decision

Given: π^e = i (expected inflation = nominal rate), i = 12%, real return on machines > 0

r = i − π^e = i − i = 0
Since real return > 0 and cost of borrowing (r) = 0: Firm WILL invest
Answer: (E)

2023-24 MCQ Q5 - Fisher Effect

BoE wants to reduce π from 6% to 3%, keeping r = 2% constant

Initially: i = r + π^e = 2% + 6% = 8%
After: i = r + π^e = 2% + 3% = 5%
Nominal rate falls by 3pp. Answer: (B)

Zero Lower Bound (ZLB)

Nominal interest rate cannot fall below zero (or people hold cash)

Minimum Real Rate

rmin = 0 − πe = −πe

If π^e = 0: r_min = 0 (cannot achieve negative real rates) If π^e = 4%: r_min = −4% (CB can push r negative)

Why Inflation Target > 0?

With π̄ > 0 and anchored expectations, CB can achieve negative real rates by setting i ≈ 0. Provides 'ammunition' to stimulate economy in downturns. Avoids liquidity trap where monetary policy is ineffective.

2022-23 Section C: Liquidity Trap

With π̄ = 0 and i at ZLB, r = 0 − 0 = 0 cannot be lowered. With π̄ = 4%, CB can push r to −4%. This is why most CBs target π > 0.

Tutorial 8 Q2c - Deflation Spiral

If fiscal contraction causes π < 0 with i = 0 and θ = 1:

π^e becomes negative → r = 0 − (negative) = positive
Higher r → lower Y → more deflation → even higher r...
DEFLATION SPIRAL - CB cannot lower r because i at ZLB!

2023-24 MCQ Q1

In liquidity trap, monetary policy ineffective. Only FISCAL policy can stimulate (tax cut or spending increase). Answer: (B)

Quantity Theory of Money

Equation of Exchange

M × V = P × Y

M = money supply V = velocity (assumed constant) P = price level Y = real output

Inflation (if V constant)

π = gM − gY

Inflation = Money growth minus Real GDP growth

Tutorial 8 Q3 - QTM Calculations

Given: g_Y = 2%, g_M = 8%, i = 9%, V constant

Nominal GDP growth = g_M = 8%
Inflation π = g_M − g_Y = 8% − 2% = 6%
Real rate r = i − π = 9% − 6% = 3%

QTM vs Phillips Curve (2023-24 Section C)

Perspective	View	Time Horizon
QTM (Long-Run)	π = g_M − g_Y. Higher g_Y → lower π	Supply-side, long-run
Phillips Curve (Short-Run)	Y ↑ → u ↓ → π ↑	Demand-driven, short-run

Resolution

Not contradictory - different time horizons!
• If Y↑ due to productivity (supply): inflation falls (QTM view)
• If Y↑ due to demand stimulus: inflation rises (PC view)

Reference

Complete Formula Sheet

All essential formulas for your A4 cheat sheet.

Master Formula Table

Concept	Formula
Consumption	`C = c₀ + c₁(Y − T)`
Basic Multiplier	`1 / (1 − c₁)`
Tax Multiplier	`−c₁ / (1 − c₁)`
With Income Tax	`1 / (1 − c₁ + c₁t₁)`
With Endogenous I	`1 / (1 − c₁ − b₁)` [requires c₁+b₁<1]
Combined	`1 / (1 − c₁ − b₁ + c₁t₁)`
S-I Identity	`S + (T − G) = I`
Money Demand	`Mᵈ = $Y × L(i) = d₁Y − d₂i`
Bond Demand	`Bᵈ = Wealth − Mᵈ`
Money Multiplier	`Money Supply = H × (1/θ)`
Investment	`I = b₀ + b₁Y − b₂i` (or b₂r in IS-LM-PC)
IS Slope	`di/dY = −(1 − c₁ − b₁ + c₁t₁) / b₂`
WS (Real Wage)	`W/P = 1 − αu + z`
PS (Real Wage)	`W/P = 1 / (1 + m)`
Natural Unemployment	`uₙ = (m + z) / α`
Natural Output	`Yₙ = L(1 − uₙ)`
Phillips Curve	`π − πᵉ = −α(u − uₙ)`
Expectations	`πᵉ = (1−θ)π̄ + θπₜ₋₁`
Accelerationist PC	`Δπ = −α(u − uₙ)` [when θ = 1]
Okun's Law	`uₜ − uₜ₋₁ = −β(gY − ḡY)` [β≈0.4, ḡY≈3%]
Fisher Equation	`r ≈ i − πᵉ`
ZLB Minimum Rate	`r_min = −πᵉ` (when i = 0)
Quantity Theory	`MV = PY → π = gM − gY` (if V constant)
GDP Deflator	`(Nominal GDP / Real GDP) × 100`
CPI	`(Cost basket current / Cost basket base) × 100`
Growth Rate	`g = (Yₜ − Yₜ₋₁) / Yₜ₋₁ × 100%`
Inflation Rate	`π = (Pₜ − Pₜ₋₁) / Pₜ₋₁ × 100%`

Exam Preparation

Exam Strategy & Tips

Key insights from past papers (2022-2025) and essential exam techniques.

Section A: MCQ Patterns by Year

Year	Topics Tested
2022-23	Okun's Law, Anchored PC (θ=0), Fisher investment decision, IS slope/t₁, ZLB
2023-24	Liquidity trap, Real wage from PS, Worker bargaining, Adaptive PC (θ=1), Fisher effect
2024-25	Bond demand, PS shift (markup), QTM, Money demand shift, Tax multiplier graph

Section B: Long Question Templates

Q6 (IS-LM) - 25 marks

(a) Derive equilibrium Y [7 marks] - Show all algebra steps
(b) Analyze component (slope, parameter effects) [6 marks]
(c) Graphical representation [6 marks] - Label everything!
(d) Policy analysis or comparison [6 marks]

Q7 (IS-LM-PC) - 25 marks

(a) Draw initial equilibrium [7 marks] - Both IS-LM and PC diagrams
(b) Short-run effect [6 marks] - Identify shock, curve shift
(c) CB response [6 marks] - Show adjustment path
(d) Medium-run composition [6 marks] - C, I, r changes

Section C: Essay Topics

QTM vs Phillips Curve - Different time horizons
Chain-type indexes - Continuous weight updates
Liquidity trap and π̄ > 0 - Monetary policy room
Paradox of saving - S=I identity, Y adjusts
GDP deflator vs CPI - Imports, weights, coverage
GDP limitations - Stiglitz sustainability quote

Common Mistakes to AVOID

Using i instead of r in IS-LM-PC model
Wrong multiplier formula - check for t₁ and b₁
Thinking WS affects real wage - PS determines W/P
Mixing θ=0 (constant π) with θ=1 (accelerating π)
Forgetting Y returns to Yₙ in medium run
Unlabeled graphs - axes, curves, equilibrium points
GDP deflator vs CPI confusion - imports, weights
Forgetting crowding out with traditional LM

Final Checklist

Derive IS curve from scratch (7-mark question)
Multi-period Phillips Curve calculations
IS-LM-PC 5-step shock analysis
Fisher equation applications
All multiplier variants memorized
Chain-type index 4-step construction
250-word essay outlines prepared
A4 formula sheet organized