ECON10181 Macroeconomic Analysis 1 | Ultimate Revision Guide

Course Overview

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

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

LECTURE 02

Goods Market

Consumption function, equilibrium, multiplier

LECTURE 03

Financial Markets

Money demand, supply, interest rates

LECTURE 04

IS-LM Model

Deriving IS & LM curves, policy analysis

LECTURE 05

Labour Market

WS-PS model, natural unemployment rate

LECTURE 06

Phillips Curve

Inflation-unemployment tradeoff, expectations

LECTURE 07

IS-LM-PC Model

Complete model, short to medium run

LECTURE 08

Inflation & Interest

Fisher equation, real rates, liquidity trap

Lecture 1 • BAG Ch. 2

Introduction to Macroeconomics & Measurement

Understanding how we measure aggregate economic activity through GDP, price levels, and inflation.

Gross Domestic Product (GDP)

Definition

GDP is the value of all final goods and services produced in an economy during a given period of time.

Expenditure Approach

GDP by Expenditure

Y = C + I + G + (X − IM)

Y = GDP (total output) C = Consumption (household spending) I = Investment (business capital + housing) G = Government purchases X = Exports IM = Imports

Nominal vs Real GDP

Nominal GDP

Nominal GDP = Σ (Current Pricei × Quantityi)

Sum of all goods valued at current year prices

Real GDP

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

Sum of all goods valued at base year prices (removes price effects)

GDP Deflator

GDP Deflator = Nominal GDPReal GDP × 100

Paasche index: Uses current quantities as weights Covers all domestic production, excludes imports

Consumer Price Index (CPI)

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

Laspeyres index: Uses fixed base-year basket as weights Covers consumer goods only, includes imports

GDP Growth Rate

gY = Yt − Yt−1Yt−1 × 100%

g_Y = growth rate of GDP Y_t = GDP in current period Y_t−1 = GDP in previous period

Inflation Rate

π = Pt − Pt−1Pt−1 × 100%

π = inflation rate P_t = price level (CPI or Deflator) in current period P_t−1 = price level in previous period

GDP Per Capita

GDP per capita = GDPPopulation

Measures average output/income per person

Chain-Type Index (Important for Essays)

Chain-Type Index Construction

1

Calculate growth rates using two consecutive years as base

2

Average the two growth rates: g_avg = (g_{2011 base} + g_{2019 base}) / 2

3

Set index = 1 in reference year, solve for other years using: Index_t × (1 + g_avg) = Index_t+1

4

Multiply index by reference year's Nominal GDP to get Real GDP in chained prices

Advantage: Updates weights annually, avoids substitution bias Key insight: Chain-weighted GDP ≈ average of Paasche and Laspeyres measures

📝 Exam Focus: Measurement

Common Question Types (Tutorial 1, Past Papers)

GDP Calculations: Given quantities and prices for multiple goods across years, calculate nominal GDP, real GDP, and growth rates
GDP Deflator vs CPI: Compute both measures and explain why they differ (Paasche vs Laspeyres weights)
Chain-Type Indexes (2023-24 Section C): Explain why chain-weighted indexes are more accurate than fixed-weight indexes
GDP Limitations (2022-23 Section C): Essay on what GDP doesn't measure (sustainability, environment, informal economy)

Step-by-Step Methodology

1

Nominal GDP: Sum of (current price × current quantity) for all goods

2

Real GDP: Sum of (base year price × current quantity) for all goods

3

Growth rate: (Y_t − Y_t−1) / Y_t−1 × 100%

4

GDP Deflator: (Nominal GDP / Real GDP) × 100

5

CPI: Cost of fixed basket at current prices / Cost at base year prices × 100

2023-24 Section C: Chain-Type Indexes

Fixed-weight indexes use base year prices → substitution bias over time. Chain-type indexes update weights annually → better captures actual consumption patterns. Key example: computer prices fell dramatically since 1985.

Key Distinctions for Essays

GDP Deflator: Paasche (current quantities), domestic output only, excludes imports
CPI: Laspeyres (fixed basket), consumer goods only, includes imports
GDP misses: Home production, informal economy, environmental costs, sustainability

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)

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

Aggregate Demand & Equilibrium

Aggregate Demand (Closed Economy)

Z ≡ C + I + G

Z = aggregate demand for goods C = consumption I = investment G = government spending

Equilibrium Condition

Production equals demand: Y = Z

Equilibrium Output (Derivation)

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

Y = 11 − c1 × (c0 − c1T + I + G)

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

Saving-Investment Identity

Private Saving

S ≡ Y − T − C

S = private (household) saving Y − T = disposable income C = consumption

Public Saving

Public Saving = T − G

If T > G: budget surplus (positive public saving) If T < G: budget deficit (negative public saving)

S-I Identity (Closed Economy)

S + (T − G) = I

Total saving = Investment Private saving + Public saving = Investment

The Multiplier

Basic Multiplier

Multiplier = 11 − c1

c₁ = MPC (marginal propensity to consume) If c₁ = 0.8, multiplier = 1/(1−0.8) = 5

Tax Multiplier

ΔYΔT = −c11 − c1

Negative because ↑T → ↓Y_D → ↓C → ↓Y |Tax multiplier| < Spending multiplier (because of c₁ < 1)

With Income Tax: T = t₀ + t₁Y

Multiplier = 11 − c1 + c1t1 = 11 − c1(1 − t1)

t₀ = lump-sum tax component t₁ = marginal tax rate (0 < t₁ < 1) Higher t₁ → smaller multiplier → automatic stabilizer

With Endogenous Investment: I = b₀ + b₁Y

Multiplier = 11 − c1 − b1

b₁ = sensitivity of investment to output Requires c₁ + b₁ < 1 for positive multiplier Higher b₁ → larger multiplier

Combined: Income Tax + Endogenous Investment

Multiplier = 11 − c1 − b1 + c1t1

This is the most general form from Tutorial 2 & past exams

Numerical Example (Tutorial 2 Style)

Ex

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

1

Z = C + I + G = 240 + 0.8(Y−400) + 200 + 600 = 720 + 0.8Y

2

Set Y = Z: Y = 720 + 0.8Y

3

0.2Y = 720 → Y = 3600

4

Verify: C = 240 + 0.8(3200) = 2800, Z = 2800 + 200 + 600 = 3600 ✓

📝 Exam Focus: Goods Market

Common Question Types (Tutorial 2, Past Papers)

Equilibrium Output Derivation: Start from Z = C + I + G, apply Y = Z, solve for Y
Multiplier Calculations: Basic multiplier, with income tax (t₁), with endogenous investment (b₁)
Automatic Stabilizers (Tutorial 2 Q2): How T = t₀ + t₁Y affects the multiplier and stability
Policy Analysis: Effect of ΔG or ΔT on equilibrium output

Step-by-Step: Solving for Equilibrium

1

Write demand: Z = c₀ + c₁(Y − T) + Ī + Ḡ

2

Apply equilibrium: Y = Z

3

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

4

Collect Y terms: Y − c₁Y = c₀ − c₁T + Ī + Ḡ

5

Solve: Y = [1/(1−c₁)] × (c₀ − c₁T + Ī + Ḡ)

Know Your Multipliers

Basic: 1/(1−c₁) — larger c₁ = larger multiplier
With income tax: 1/(1−c₁+c₁t₁) — t₁ reduces multiplier (automatic stabilizer)
With I(Y): 1/(1−c₁−b₁) — b₁ increases multiplier
Tax multiplier: −c₁/(1−c₁) — smaller than spending multiplier!

Paradox of Saving (Essay Topic)

If all consumers try to save more (↓c₀), equilibrium Y falls but total saving S = I is unchanged (with fixed I). Individual rationality ≠ collective outcome. This illustrates why macro ≠ simple aggregation of micro.

Lecture 3 • BAG Ch. 4

Financial Markets I: Money

Understanding money demand, money supply, and how the interest rate is determined.

Money Demand

Money Demand Function (General)

Md = $Y × L(i)

M^d = nominal money demand $Y = nominal income (P × Y) L(i) = liquidity preference (decreasing in i) ↑Y → ↑M^d (more transactions) ↑i → ↓M^d (hold bonds instead)

Linear Form (Tutorial 3 Style)

Md = $Y × (a − b × i)

Example: M^d = $Y × (0.35 − i) Or: M^d = d₁Y − d₂i (in real terms)

Money Market Equilibrium

MP = Y × L(i)

M̄/P = real money supply (exogenous if CB sets M) Equilibrium: real money supply = real money demand

Wealth Constraint & Bond Market

Wealth Allocation

Wealth = Md + Bd

M^d = money demand B^d = bond demand Total wealth is split between money and bonds

Walras' Law

If money market clears, bond market clears automatically:
Excess supply of bonds = Excess demand for money

Banking System & Money Multiplier

Money Multiplier

Money Supply = H × 1θ

H = monetary base (central bank money) θ = reserve ratio (reserves/deposits) 1/θ = money multiplier

Numerical Example (Tutorial 3 Q3)

Ex

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

1

Money multiplier = 1/0.1 = 10

2

Total money supply = £100bn × 10 = £1000bn

3

For equilibrium: £1000bn = £5tr × (0.8 − 4i)

4

Solve: 0.2 = 0.8 − 4i → i = 15%

📝 Exam Focus: Financial Markets

Common Question Types (Tutorial 3)

Money Demand Function: Given M^d = $Y × L(i), solve for equilibrium interest rate
Money vs Bonds (Tutorial 3 Q1): Wealth = M^d + B^d. Show excess supply of bonds = excess demand for money
Open Market Operations: CB buys bonds → ↑M → ↓i (and vice versa)
Money Multiplier (Tutorial 3 Q3): If reserve ratio = θ, money multiplier = 1/θ

Step-by-Step Methodology

1

Set M^s/P = M^d/P (money market equilibrium)

2

Substitute money demand: M̄/P = $Y × L(i)

3

Solve for i

Tutorial 3 Q3: Banking System

With reserve ratio θ = 0.1, monetary base H = £100bn:
Overall money supply = H × (1/θ) = £100bn × 10 = £1000bn

Modern vs Traditional LM

Modern: CB sets i directly, M adjusts → horizontal LM (i = ī)
Traditional: CB sets M, i adjusts → upward-sloping LM

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 (business confidence) b₁ = sensitivity to output (↑Y → ↑I, accelerator effect) b₂ = sensitivity to interest rate (↑i → ↓I, cost of borrowing)

IS Curve Derivation

IS Derivation (Goods Market Equilibrium)

1

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

2

Equilibrium: Y = Z

3

Y = c₀ + c₁Y − c₁T + b₀ + b₁Y − b₂i + Ḡ

4

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

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

This is the IS relation: Y as function of i (downward sloping)

IS Curve (i as function of Y)

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

Intercept: (c₀ − c₁T + b₀ + Ḡ)/b₂ Slope: −(1 − c₁ − b₁)/b₂ (negative → downward sloping)

LM Curve

Traditional LM (CB sets M)

MP = d1Y − d2i

Solve for i: i = (d₁Y − M̄/P) / d₂ Upward sloping: ↑Y → ↑M^d → ↑i to restore equilibrium

Modern LM (CB sets i)

i = i

Horizontal line: CB sets interest rate, M adjusts endogenously This is the approach used in IS-LM-PC model

IS Curve Slope Analysis

IS Slope (di/dY)

Slope = − 1 − c1 − b1 + c1t1b2

Crowding Out

↑G → IS shifts right → ↑Y and ↑i → ↓I (crowded out)
Net effect on Y positive but less than simple multiplier predicts.

Numerical Example (Tutorial 4 Style)

Ex

Given: C = 500 + 0.2Y_D, I = 200 + 0.25Y − 1000i, G = 300, T = 200

1

IS: Y = 500 + 0.2(Y−200) + 200 + 0.25Y − 1000i + 300

2

Y = 960 + 0.45Y − 1000i → 0.55Y = 960 − 1000i

3

IS equation: Y = 1745.45 − 1818.18i

Ex

Given: (M/P)^d = 2Y − 8000i, M/P = 1500

1

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

2

Substitute into IS: Y = 1745.45 − 1818.18 × (Y−750)/4000

3

Equilibrium: Y ≈ 1436.5, i ≈ 17%

📝 Exam Focus: IS-LM Model

Common Question Types (Tutorial 4, 2022-23 Q6, 2023-24 Q6)

IS Derivation: Start from Z = C + I + G, apply Y = Z, solve for Y as function of i
IS Slope Analysis (Past Exam Favourite!): How does t₁ or b₂ affect IS slope? (↑t₁ → steeper IS; ↑b₂ → flatter IS)
Policy Analysis: Effect of ↑G or ↓T on Y and i, with graphs
Income Tax Extension (2022-23 Q6): T = t₀ + t₁Y gives multiplier 1/(1−c₁−b₁+c₁t₁)
Transfer Payments (2023-24 Q6): How transfers vs taxes affect equilibrium differently

Step-by-Step: Deriving IS Curve

Standard Method (7 Marks in Exam)

Write Z = C(Y−T) + I(Y,i) + G
Substitute specific functions (e.g., C = c₀ + c₁(Y−T), I = b₀ + b₁Y − b₂i)
Apply equilibrium: Y = Z
Collect Y terms on LHS, solve for Y
Result: Y = [1/(1−c₁−b₁)] × (Autonomous spending − b₂i)

IS Slope Formula (Exam Favourite)

IS Slope (di/dY) = − 1 − c1 − b1 + c1t1b2

↑t₁ → steeper IS → monetary policy less effective ↑b₂ → flatter IS → monetary policy more effective

2022-23 MCQ Pattern

"If BoE holds interest rate constant in response to ↑G, money supply will increase, and impact on income will be larger than if M held constant." (Answer: A)

Lecture 5 • BAG Ch. 7

The Labour Market

Understanding wage setting, price setting, and the natural rate of unemployment.

Wage & Price Setting

Wage Setting (WS) - General Form

W = Pe × F(u, z)

W = nominal wage P^e = expected price level F(u,z) = wage-setting function u = unemployment rate (↑u → ↓W) z = catch-all (benefits, min wage, union power)

WS - Linear Form (Used in Exams)

W = Pe(1 − αu + z)

α = wage sensitivity to unemployment (wage flexibility) Higher α → wages respond more to unemployment

WS as Real Wage (assuming P^e = P)

WP = 1 − αu + z

This is the WS curve: downward sloping in (u, W/P) space

Price Setting (PS)

P = (1 + m)W

P = price level m = markup (firms' market power) Firms set price as markup over wage cost

Real Wage from PS

WP = 11 + m

This is the PS curve: horizontal line in (u, W/P) space Higher markup m → lower real wage that firms are willing to pay Key insight: Real wage determined by PS alone!

P^e = expected price level F(u,z) = wage-setting function u = unemployment rate (↑u → ↓W) z = catch-all (benefits, min wage, etc.) (↑z → ↑W)

Price Setting (PS)

P = (1 + m)W

P = price level m = markup (firms' market power) W = nominal wage Firms set price as markup over wage cost

Real Wage from PS

WP = 11 + m

W/P = real wage m = markup Higher markup → lower real wage firms willing to pay

Natural Unemployment

Natural Unemployment Rate

un = m + zα

u_n = natural rate of unemployment m = markup (↑m → ↑u_n) z = labour market rigidities (↑z → ↑u_n) α = wage sensitivity to unemployment

Natural Output

Yn = L(1 − un)

Y_n = natural level of output L = labour force u_n = natural unemployment rate L(1−u_n) = employment level

📝 Exam Focus: Labour Market

Common Question Types (Tutorial 5, 2023-24 MCQ)

W/P from PS (MCQ Favourite): "If markup m = 11%, what is real wage?" Answer: W/P = 1/(1+0.11) = 0.90
Natural Unemployment: Given WS and PS, find u_n = (m+z)/α
Effect of Policy Changes: How do ↓minimum wage, ↑markup, ↑union power affect u_n?
Bargaining Power (2023-24 MCQ): If worker bargaining power ↑, real wage stays constant (determined by PS!), but nominal W and P both rise

Key Methodology

Finding Natural Unemployment

Write WS: W/P = F(u,z) = 1 − αu + z
Write PS: W/P = 1/(1+m)
Set WS = PS: 1 − αu + z = 1/(1+m)
Solve for u_n

Critical Insight

Real wage is determined by PS, not WS! WS affects nominal wage, but firms pass costs to prices. Result: W/P = 1/(1+m) regardless of worker bargaining power. Changes in z or worker power only affect u_n, not W/P.

Lecture 6 • BAG Ch. 8

The Phillips Curve

Understanding the relationship between inflation and unemployment.

Phillips Curve

General Form

π = πe + (m + z) − αu

π = actual inflation π^e = expected inflation m = markup z = labour market factors α = sensitivity of inflation to unemployment u = unemployment rate

With Natural Rate

π − πe = −α(u − un)

π − π^e = inflation surprise u − u_n = unemployment gap When u < u_n: inflation rises above expectations When u > u_n: inflation falls below expectations

Expectations Formation

πe = (1 − θ)π + θπt−1

π^e = expected inflation θ = weight on past inflation (0 ≤ θ ≤ 1) π̄ = central bank's inflation target π_t−1 = last period's inflation θ = 0: fully anchored | θ = 1: fully adaptive

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

Wage Indexation (Tutorial 6 Q2)

PC with Wage Indexation

πt = [λπt + (1−λ)πet] + φ − αut

λ = fraction of workers with indexed contracts Indexed workers: wages adjust automatically with actual π Non-indexed workers: wages based on expected π^e

Solving for π (when λ = 0.5)

1

π_t = 0.5π_t + 0.5π^e_t + φ − αu_t

2

0.5π_t = 0.5π^e_t + φ − αu_t

3

π_t = π^e_t + 2(φ − αu_t)

Key effect: Indexation amplifies the effect of u on π Higher λ → inflation responds more to unemployment gap

Okun's Law

ut − ut−1 = −β(gY − gY)

u_t − u_t−1 = change in unemployment β = Okun coefficient (≈ 0.4) g_Y = actual GDP growth rate ḡ_Y = normal GDP growth rate (≈ 3%) If GDP grows 1% above normal, u falls by 0.4pp

📝 Exam Focus: Phillips Curve

Common Question Types (Tutorial 6, Past MCQs)

Multi-Period Inflation (2022-23 MCQ, 2023-24 MCQ): Given PC and π^e = θπ_t−1, calculate π for t, t+1, t+2...
Anchored vs Adaptive (θ=0 vs θ=1): Compare inflation paths under different expectation assumptions
Wage Indexation (Tutorial 6 Q2): How indexation steepens the PC and accelerates inflation
Supply Shocks (Tutorial 6 Q3): Oil price shocks → ↑m → ↑u_n
Okun's Law (2022-23 MCQ): Calculate Δu given output growth

Step-by-Step: Multi-Period Inflation

1

Find u_n from PC: Set π = π^e, solve u_n = φ/α (from π = π^e + φ − αu)

2

Period t: π_t = π^e_t + φ − αu_t (substitute given u_t and π^e_t)

3

Period t+1: If θ=1, π^e_t+1 = π_t; if θ=0, π^e_t+1 = π̄

4

Repeat for subsequent periods

Exam Pattern (MCQ)

2022-23 & 2023-24: Given π_t = π^e_t + 0.15 − 2u_t and u_n = 5%, if u held at 3% forever:
• With θ=0: π constant at π̄ + α×(u_n−u) = high but stable
• With θ=1: π accelerates by αε each period (no permanent tradeoff)

Key Relationship

u < u_n → π rises | u > u_n → π falls | u = u_n → π stable (medium run)

Lecture 7 • BAG Ch. 9

The IS-LM-PC Model

The complete macroeconomic model from short run to medium run.

The Complete Model

IS-LM-PC System

IS: Y = C(Y−T) + I(Y, r) + G

LM: r = r

PC: π − πe = −α(u − un)

Y = output r = real interest rate (not nominal i!) r̄ = policy rate set by central bank π = inflation u = unemployment Note: Investment depends on real rate r, not nominal i

Medium-Run Equilibrium

Y = Yn (output at natural level), π = π (inflation at target), πe = π (expectations correct)

📝 Exam Focus: IS-LM-PC Model

Common Question Types (Tutorial 7, 2022-23 Q7, 2023-24 Q7)

IS-LM-PC Diagram (25 marks): Draw initial equilibrium, show shock effect, CB response
Shock Analysis: Consumer confidence ↓ or ↑, fiscal policy, credit expansion
Policy Response: How must CB change r to return Y to Y_n?
GDP Composition: How do C, I change in medium run after permanent shock?
Expectations (θ=0 vs θ=1): How does inflation behave if CB doesn't respond?

Step-by-Step: IS-LM-PC Shock Analysis (25-Mark Questions)

1

Initial state: Draw Y = Y_n, r = r_n, π = π̄

2

Identify shock: What shifts? IS (demand shocks) or PC (supply shocks)?

3

Short-run effect: IS shifts → new Y, read π from PC

4

CB response: ↓r if Y < Y_n (boost demand); ↑r if Y > Y_n (cool demand)

5

Medium-run: Y → Y_n, but composition of GDP changes (C vs I tradeoff)

2022-23 Q7: Consumer Confidence ↓

IS shifts left → Y ↓ → π < π̄ → CB cuts r → I ↑ → Y returns to Y_n
Medium-run composition: C lower, I higher, r lower than before

2023-24 Q7: Consumer Credit Expansion (↓Saving)

IS shifts right → Y ↑ → π > π̄ → CB raises r → I ↓ → Y returns to Y_n
Medium-run composition: C higher, I lower, r higher than before

Lecture 8 • BAG Ch. 6.1

Inflation, Interest Rates & the Liquidity Trap

Understanding the Fisher equation and monetary policy limitations.

Fisher Equation

Exact Form

(1 + r) = 1 + i1 + πe

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

Derivation (Tutorial 8 Q1)

1

Borrow P_t today → buy 1 unit of good

2

Repay (1+i)P_t next year

3

In goods: repay (1+i)P_t / P^e_t+1 units

4

This equals (1+r), so: (1+r) = (1+i)/(1+π^e)

Approximate Form

r ≈ i − πe

Valid when i and π^e are small (cross-term negligible) Example: if i = 5% and π^e = 2%, then r ≈ 3%

Ex Ante vs Ex Post

Ex ante: r = i − πe Ex post: r = i − π

Ex ante = expected real rate at time of decision Ex post = realized real rate (actual inflation known) Investment decisions based on ex ante rate

Zero Lower Bound (ZLB)

rmin = −πe

ZLB: Nominal rate i cannot go below 0 When i = 0: r = 0 − π^e = −π^e If π^e = 0: r_min = 0 (no negative real rates!) If π^e = 4%: r_min = −4% (more CB room)

Quantity Theory

Quantity Equation

M × V = P × Y

M = money supply V = velocity of money (how fast money circulates) P = price level Y = real output P × Y = nominal GDP

Inflation (if g_V = 0)

π = gM − gY

π = inflation rate g_M = money supply growth rate g_Y = real GDP growth rate Long-run view: inflation = excess money growth

📝 Exam Focus: Inflation & Interest Rates

Common Question Types (Tutorial 8, Past MCQs, Section C)

Fisher Equation (2022-23 MCQ, 2023-24 MCQ): Calculate real rate given nominal rate and expected inflation
Investment Decision: Compare real return on investment to real interest rate
Zero Lower Bound (2022-23 Section C, 2023-24 MCQ): Why π̄ > 0 provides policy room
Deflation Trap (Tutorial 8 Q2): How fiscal contraction at ZLB → deflation spiral
Quantity Theory (Tutorial 8 Q3, 2023-24 Section C): Calculate inflation from g_M and g_Y

Step-by-Step: Fisher Equation Application

1

Use approximation: r ≈ i − π^e

2

If i = 12% and π^e = 12%, then r = 0% → Firm invests if project's real return > 0%

3

At ZLB (i = 0): r_min = −π^e. If π^e = 0, then r cannot go negative

2023-24 MCQ: Fisher Effect

"If BoE reduces π from 6% to 3% while keeping r = 2% constant, how does i change?"
Answer: i = r + π^e. If π^e falls by 3pp, i falls by 3pp (Answer: B)

2022-23 Section C: Liquidity Trap

Essay angle: With π̄ = 0 and i at ZLB, real rate r = 0 − 0 = 0 cannot be reduced further. With π̄ = 4% and anchored expectations, CB can push r to −4% by setting i ≈ 0. This is why most CBs target π > 0.

QTM vs Phillips Curve (2023-24 Section C)

Critical Distinction

QTM (long run): π = g_M − g_Y. Higher g_Y → lower π (supply-side view)
Phillips Curve (short/medium run): Y ↑ → u ↓ → π ↑ (demand-driven view)
Resolution: QTM is a long-run identity; PC describes short-run dynamics. Different time horizons!

Reference

Complete Formula Sheet

All essential formulas for your A4 cheat sheet.

Goods Market

C = c0 + c1(Y − T)

Multiplier = 11 − c1

With t₁: 11 − c1(1−t1)

With b₁: 11 − c1 − b1

c₀ = autonomous consumption c₁ = MPC t₁ = marginal tax rate b₁ = investment sensitivity to Y

Labour Market

WP = 11 + m

un = m + zα

Yn = L(1 − un)

W/P = real wage m = markup z = labour factors α = wage sensitivity L = labour force

Phillips Curve

π − πe = −α(u − un)

Δπ = −α(u − un)

π = actual inflation π^e = expected inflation u_n = natural unemployment Δπ = change in inflation

Fisher & Okun

r ≈ i − πe

ut − ut−1 = −β(gY − gY)

r = real rate i = nominal rate β ≈ 0.4 (Okun coefficient) ḡ_Y = normal growth (~3%)

Exam Preparation

Exam Strategy & Tips

Key insights from past papers and essential exam techniques.

Exam Structure (90 minutes)

Section	Content	Marks	Time
A	5 Multiple Choice	20	~15 min
B	2 Long Questions	50	~50 min
C	1 Essay (choose 1 of 2)	30	~25 min

Allowed: One-side A4 handwritten notes, non-programmable calculator

Key Formulas for MCQ

Quick Reference

• WP = 11+m — real wage from PS (W = wage, P = price, m = markup)
• un = m+zα — natural unemployment (z = labour factors, α = sensitivity)
• r ≈ i − πe — Fisher equation (r = real, i = nominal, π^e = expected inflation)
• Multiplier = 11 − c1 — (c₁ = MPC)

Common Mistakes to Avoid

❌ Using i for investment instead of r
❌ Confusing GDP deflator with CPI
❌ Wrong multiplier when model has t₁ or b₁
❌ Not showing Y returns to Y_n in medium run
❌ Missing labels on graphs