the multiplier process: definition of the multiplier

1. The Circular Flow of Income

1.1 Key Economic Agents

• Households – own and supply the four factors of production (land, labour, capital, entrepreneurship) and receive income (wages, rent, interest, profit).
• Firms – combine the factors to produce goods and services; pay factor‑income to households.
• Government – collects taxes and makes spending injections (public services, welfare, infrastructure).
• Financial sector – mobilises household savings and channels them into investment.
• Foreign sector – imports and exports create additional leakages and injections.

1.2 Leakages and Injections (Open Economy)

Leakages (L)	Injections (J)
Savings (S)	Investment (I)
Taxes (T)	Government spending (G)
Imports (M)	Exports (X)

1.3 Diagrammatic Representation

Suggested diagram: A circular‑flow chart showing households, firms, government, financial sector and foreign sector. Arrows should indicate the three leakages (S, T, M) and the three injections (I, G, X). This visualises the condition L = J that must hold for equilibrium.

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2. The Multiplier Process

2.1 Definition

The multiplier measures the proportionate change in equilibrium national income (Y) that results from an autonomous change in expenditure (A) – for example a change in government spending, investment or exports.

k = ΔY / ΔA

2.2 Key Concepts

• Equilibrium – total spending (aggregate demand) equals total output (aggregate supply).
• Autonomous expenditure – spending that does not depend on current income (e.g., G, I, X).
• MPC (marginal propensity to consume) – the fraction of each additional pound of disposable income that is spent.
• MPS (marginal propensity to save) – 1 – MPC.
• Time – the multiplier works through successive rounds of re‑spending.

2.3 Deriving the Multiplier

2.3.1 Closed Economy (no government, no foreign sector)

Equilibrium condition:

Y = C + I

Consumption function:

C = C₀ + cY  (c = MPC, 0 < c < 1)

Substituting and rearranging:

Y = C₀ + cY + I

Y(1 ‑ c) = C₀ + I

Y = (C₀ + I) / (1 ‑ c)

Holding autonomous consumption (C₀) constant, a change in autonomous investment (ΔI) gives

ΔY = ΔI / (1 ‑ c)

Hence the simple expenditure multiplier

k = 1 / (1 ‑ c) = 1 / MPS

2.3.2 Open Economy with Government

Aggregate demand (AD) now includes taxes and net exports:

Y = C + I + G + (X ‑ M)

Assumptions:

• Disposable income: Y_d = Y (1 ‑ t)  (t = marginal tax rate)
• Consumption: C = C₀ + cY_d = C₀ + c(1 ‑ t)Y
• Imports: M = mY  (m = marginal propensity to import)

Substituting into AD:

Y = C₀ + c(1 ‑ t)Y + I + G + X ‑ mY

Collecting Y‑terms:

Y [1 ‑ c(1 ‑ t) + m] = C₀ + I + G + X

Open‑economy multiplier:

k = 1 / [1 ‑ c(1 ‑ t) + m]

Both the tax rate (t) and the import propensity (m) act as leakages, reducing the multiplier relative to the closed‑economy case.

2.4 Interpretation

• Higher MPC (or lower MPS) → larger multiplier because a greater share of each extra pound is re‑spent.
• Higher tax rates or import propensities increase leakages → smaller multiplier.
• The process works through successive rounds of spending; each round is smaller than the previous until the incremental impact becomes negligible.

2.5 Worked Example (Open Economy)

Government increases spending by £100 million. The economy has:

• MPC = 0.75 → MPS = 0.25
• Marginal tax rate t = 0.20
• Marginal propensity to import m = 0.10

Multiplier:

k = 1 / [1 ‑ 0.75(1 ‑ 0.20) + 0.10]  = 1 / [1 ‑ 0.75 × 0.80 + 0.10]  = 1 / [1 ‑ 0.60 + 0.10]  = 1 / 0.50 = 2.0

Change in equilibrium income:

ΔY = k × ΔG = 2.0 × £100 m = £200 million

2.6 Evaluation – Factors that Influence the Size of the Multiplier

Factor	Effect on Multiplier	Typical Exam‑style Evaluation Point
Marginal propensity to consume (MPC)	Higher MPC → larger multiplier	In a recession households may increase saving, lowering MPC and the multiplier.
Marginal tax rate (t)	Higher t → more leakage → smaller multiplier	Progressive tax systems can dampen the impact of fiscal stimulus.
Marginal propensity to import (m)	Higher m → more leakage abroad → smaller multiplier	Small open economies often have low multipliers because much of the extra spending leaks as imports.
Capacity utilisation (idle resources vs. full‑capacity)	Idle resources → multiplier close to theoretical value; full‑capacity → crowding‑out reduces multiplier	In a boom, increased demand may push up prices rather than output.
Financial market conditions	Tight credit → induced consumption muted → smaller multiplier	During a credit crunch, fiscal stimulus may be less effective.

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3. Core AS & A‑Level Topics (Cambridge 9708)

3.1 AS 1 – Basic Economic Ideas

• Scarcity & Choice – limited resources, unlimited wants; trade‑offs and opportunity cost.
• Opportunity Cost – the next best alternative foregone; illustrated with a production‑possibility curve (PPC).
• Methodology – positive vs. normative statements; ceteris paribus; use of models and diagrams.
• Factors of Production – land, labour, capital, entrepreneurship (human vs. physical capital).
• Classification of Goods – private, public, common‑pool, club, merit, demerit, and free goods.

3.2 AS 2 – Markets & Elasticities

Concept	Definition / Formula	Key Diagram
Price Elasticity of Demand (PED)	%(ΔQd) / %(ΔP) = (P/Q) × (dQ/dP)	Demand curve with two points showing slope
Price Elasticity of Supply (PES)	%(ΔQs) / %(ΔP)	Supply curve
Income Elasticity of Demand (YED)	%(ΔQd) / %(ΔY)	Normal vs. inferior goods
Cross‑price Elasticity (XED)	%(ΔQd of good A) / %(ΔP of good B)	Substitutes & complements

Worked example (PED): If price of coffee falls from £3 to £2.70 and quantity demanded rises from 100 kg to 115 kg, PED = [(15/100) ÷ (0.30/3)] ≈ 1.5 (elastic).

3.3 AS 3 – Government Intervention (Micro)

Instrument	Purpose	Incidence Diagram	Typical Impact	Evaluation
Tax on a good	Raise revenue / correct negative externalities	Supply curve shifts up by tax amount; burden shared according to elasticities	Price to consumers ↑, price received by producers ↓; dead‑weight loss	Regressive effect if demand is inelastic; may reduce market efficiency.
Subsidy	Encourage production/consumption of a merit good	Supply (or demand) curve shifts down (or up) by subsidy amount	Consumer price ↓, producer price ↑; potential fiscal cost	Risk of over‑consumption; budgetary pressure.
Price ceiling	Make a good affordable (e.g., rent control)	Maximum price set below equilibrium	Shortage, queuing, black market	May lead to under‑investment and reduced quality.
Price floor	Support producers (e.g., minimum wage)	Minimum price set above equilibrium	Surplus, unemployment or waste	Fiscal cost if government purchases surplus.
Regulation (e.g., emission standards)	Correct externalities	Shift of supply curve (higher marginal cost)	Higher price, lower output; internalises external cost	Compliance costs; possible market distortion.

3.4 AS 4 – Macro‑economics Fundamentals

3.4.1 National‑Income Accounting

• GDP (expenditure approach) = C + I + G + (X ‑ M)
• GNI = GDP + Net factor income from abroad.
• NNI = GNI ‑ Depreciation.
• Distinguish between nominal and real values (use of price index).

3.4.2 Aggregate Demand & Aggregate Supply (AD/AS)

AD curve – downward‑sloping; shows total demand for output at different price levels.

Short‑run AS (SRAS) – upward‑sloping; reflects sticky wages and prices.

Long‑run AS (LRAS) – vertical at potential output (full‑employment level).

Key shifts:

• AD rightward: increase in C, I, G or (X‑M); causes higher output and, depending on capacity, higher price level.
• SRAS rightward: fall in input costs, technological progress; raises output, lowers price level.
• LRAS rightward: growth in factors of production; raises potential output.

3.4.3 Macroeconomic Objectives

• Economic growth – increase in real GDP per capita.
• Unemployment – frictional, structural, cyclical; measured by the unemployment rate.
• Inflation – demand‑pull vs. cost‑push; measured by CPI or RPI.
• Balance of payments – current‑account surplus/deficit; capital account flows.

3.5 AS 5 – Macro‑policy

3.5.1 Fiscal Policy

• Expansionary: increase G or cut T → AD rightward; multiplier determines size of output change.
• Contractionary: decrease G or raise T → AD leftward.
• Automatic stabilisers (e.g., progressive tax, unemployment benefits) operate without discretionary action.
• Evaluation points – crowding‑out, time lags, impact on public debt, distributional effects.

3.5.2 Monetary Policy

• Tools: open‑market operations, policy interest rate, reserve requirements.
• Expansionary: lower interest rates → increase I and C (especially housing); shift AD rightward.
• Contractionary: raise rates → reduce I and C; shift AD leftward.
• Liquidity trap, credibility of central bank, exchange‑rate effects as evaluation points.

3.5.3 Supply‑side Policies

• Improving productivity: investment in R&D, training, deregulation.
• Incentives for work: tax cuts, welfare‑to‑work programmes.
• Evaluation – time lag, distributional impact, possible increase in inequality.

3.6 AS 6 – International Trade & Finance

• Balance of Payments (BoP) – current account (trade, services, income, transfers) + capital/financial account = 0.
• Exchange Rate Regimes – fixed, floating, managed float; impact on exports/imports.
• Trade Protection – tariffs, quotas, subsidies, voluntary export restraints; diagrams of supply‑side shifts.
• Trade Blocs – customs union, common market, economic union; effects on member and non‑member welfare.

3.7 A‑Level Topics (selected)

3.7.1 Utility & Consumer Behaviour

• Utility theory – total vs. marginal utility; law of diminishing marginal utility.
• Indifference curves – properties, marginal rate of substitution (MRS).
• Budget constraint – slope = –(price of X / price of Y); consumer equilibrium where MRS = price ratio.

3.7.2 Market Structures & Failure

• Perfect competition – price taker, long‑run zero economic profit.
• Monopoly – price maker, dead‑weight loss; price discrimination.
• Oligopoly – kinked‑demand model, collusion, game theory (prisoner’s dilemma).
• Information asymmetry – adverse selection, moral hazard.

3.7.3 Labour Markets

• Derivation of wage rate – labour demand (MPL) = labour supply (reservation wage).
• Types of unemployment – frictional, structural, cyclical.
• Trade unions, minimum wage, discrimination – impact on equilibrium wage and employment.

3.7.4 Development Economics

• Measures of development – HDI, GNI per capita, poverty rates.
• Barriers to growth – low savings, poor institutions, debt overhang.
• Role of aid, FDI, technology transfer; multiplier effects of large‑scale investment.

3.7.5 Globalisation & Economic Integration

• Drivers – trade, capital flows, technology, multinational enterprises.
• Benefits – economies of scale, competition, consumer choice.
• Costs – inequality, loss of policy autonomy, environmental concerns.

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4. Assessment Objective (AO) Checklist for the Multiplier Topic

AO	What to demonstrate
AO1 – Knowledge & Understanding	Define multiplier, MPC, MPS, marginal tax rate, marginal propensity to import; state the closed‑ and open‑economy formulae; explain the circular‑flow equilibrium condition L = J.
AO2 – Application	Calculate the multiplier for given values of c, t and m; compute the resulting change in equilibrium income after a fiscal injection; use the circular‑flow diagram to illustrate leakages and injections.
AO3 – Analysis & Evaluation	Analyse how changes in MPC, tax policy, openness, or capacity utilisation affect the multiplier; evaluate the reliability of multiplier estimates in real‑world policy making (e.g., time‑lag, crowding‑out, data uncertainty).

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5. Quick Revision Summary

1. The multiplier shows how an autonomous change in expenditure leads to a larger total change in national income.
2. Closed‑economy multiplier: k = 1 / (1 ‑ MPC) = 1 / MPS.
3. Open‑economy multiplier with government: k = 1 / [1 ‑ c(1 ‑ t) + m].
4. Higher MPC → larger multiplier; higher tax rate or import propensity → smaller multiplier.
5. Multiplier analysis underpins fiscal‑policy evaluation, especially in AS 5 and AS 6.
6. Remember to link the multiplier to the circular‑flow model (leakages = injections) and to the broader macro‑policy framework.