calculation of: average and marginal propensities to save (aps and mps)

1. Foundations of Economic Thinking

1.1 Scarcity, Choice & Opportunity Cost

• Scarcity: Limited resources vs unlimited wants – the fundamental economic problem.
• Choice: Because of scarcity, individuals, firms and governments must decide which goods/services to produce and consume.
• Opportunity Cost: The value of the next best alternative fore‑gone when a choice is made.

1.2 The Three Basic Economic Questions

1. What to produce?
2. How to produce?
3. For whom to produce?

1.3 Factors of Production & Their Rewards

Factor	Reward
Land (natural resources)	Rent
Labour	Wages
Capital (machinery, buildings)	Interest
Entrepreneurship	Profit

1.4 Production‑Possibility Curve (PPC)

• Shows maximum output combinations of two goods when resources are fully and efficiently employed.
• Key features: concave shape (increasing opportunity cost), points on the curve = efficient, inside = under‑utilised, outside = unattainable.
• Shifts:
  • Outward shift: Technological progress or increase in factor supplies.
  • Inward shift: Natural disaster, war, or loss of resources.

1.5 Classification of Goods

Type	Characteristics
Private goods	Rival & excludable (e.g., a sandwich).
Public goods	Non‑rival & non‑excludable (e.g., street lighting).
Merit goods	Undervalued by consumers; government may subsidise (e.g., education).
De‑merit goods	Over‑consumed; government may tax or restrict (e.g., cigarettes).

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2. The Price System: Demand, Supply & Elasticities

2.1 Demand

• Law of demand: Quantity demanded falls when price rises, ceteris paribus.
• Demand curve – downward sloping.
• Determinants (shifters): income, tastes, prices of related goods, expectations, number of buyers.

2.2 Supply

• Law of supply: Quantity supplied rises when price rises, ceteris paribus.
• Supply curve – upward sloping.
• Determinants (shifters): input prices, technology, expectations, number of sellers, taxes/subsidies.

2.3 Market Equilibrium

Equilibrium occurs where Q_D = Q_S. At this price there is no tendency for change.

2.4 Elasticities

Elasticity	Formula	Interpretation
Price elasticity of demand (PED)	\(\displaystyle \frac{\%\Delta Q_D}{\%\Delta P}\)	|PED| > 1: elastic; |PED| < 1: inelastic; |PED| = 1: unit‑elastic.
Price elasticity of supply (PES)	\(\displaystyle \frac{\%\Delta Q_S}{\%\Delta P}\)	Similar interpretation to PED.
Income elasticity of demand (YED)	\(\displaystyle \frac{\%\Delta Q_D}{\%\Delta Y}\)	Positive → normal good; negative → inferior good.
Cross‑price elasticity of demand (XED)	\(\displaystyle \frac{\%\Delta Q_{D1}}{\%\Delta P_{2}}\)	Positive → substitutes; negative → complements.

2.5 Consumer & Producer Surplus

• Consumer surplus: Area between demand curve and market price up to the quantity bought.
• Producer surplus: Area between supply curve and market price up to the quantity sold.
• Both are measures of welfare; policy changes (taxes, subsidies) shift these areas.

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3. Government Intervention in Markets (Micro‑level)

3.1 Taxes

• Imposed on buyers, sellers or both – creates a wedge between price paid (P_b) and price received (P_s).
• Incidence depends on relative elasticities: the more inelastic side bears a larger share of the tax burden.
• Result: dead‑weight loss (loss of total surplus).

3.2 Subsidies

• Payments to producers or consumers – shift the relevant curve outward.
• Creates a wedge opposite to a tax; can increase total surplus but costs government revenue.

3.3 Price Controls

• Maximum price (price ceiling): Set below equilibrium → shortage.
• Minimum price (price floor): Set above equilibrium → surplus.
• Often lead to black‑market activity or rationing.

3.4 Public Goods & Merit/De‑merit Goods

• Public goods are provided by the state because the market would under‑supply them.
• Merit goods are subsidised; de‑merit goods are taxed or restricted.

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4. Macroeconomic Framework

4.1 Macroeconomic Objectives

Goal	Typical Indicator
Economic growth	Real GDP growth rate
Low unemployment	Unemployment rate (U‑rate)
Price stability	Inflation rate (CPI)
External balance	Current‑account balance
Equitable distribution of income	Gini coefficient, poverty rates

4.2 The Circular Flow of Income (Expanded)

• Households supply factors of production and receive factor incomes (wages, rent, interest, profit).
• Firms produce goods/services, pay factor incomes, and receive revenue from sales.
• Government collects taxes, makes transfers, and spends on goods & services.
• Foreign sector imports (spending on foreign goods) and exports (foreign spending on domestic goods).

Key Identities (Closed vs Open Economy)

Closed economy (no government, no foreign trade):
\(\displaystyle Y = C + I + G\) (where \(G = 0\)).

Open economy (including government):
\(\displaystyle Y = C + I + G + (X - M)\).

4.3 Aggregate Demand (AD) & Aggregate Supply (AS)

• AD curve: Downward sloping – higher price level reduces real spending (wealth effect, interest‑rate effect, exchange‑rate effect).
• SRAS curve: Upward sloping – prices rise faster than wages in the short run.
• LRAS curve: Vertical at potential output (Y_P) – reflects full‑employment output.

Shifts in AD

Cause	Direction of Shift
Increase in government spending (G)	Right
Decrease in taxes (increase disposable income)	Right
Fall in interest rates (boost investment)	Right
Fall in net exports (X‑M)	Left

Shifts in SRAS

Cause	Direction of Shift
Higher input prices (e.g., oil shock)	Left
Improved technology	Right
Increase in expected future prices	Left

4.4 Measuring National Income

• GDP (Nominal): Market value of final goods & services produced within a country in a year at current prices.
• Real GDP: Adjusted for inflation (using a base‑year price index).
• GNI: GDP + net primary income from abroad.
• NNI: GNI – depreciation.

4.5 Unemployment

Type	Definition
Frictional	Short‑term job search between jobs.
Structural	Mismatch between workers’ skills and job requirements.
Cyclical	Result of insufficient aggregate demand.
Seasonal	Related to regular seasonal fluctuations.

4.6 Inflation

• Measured by the Consumer Price Index (CPI) or the Retail Price Index (RPI).
• Causes:
  • Demand‑pull: AD shifts right faster than SRAS.
  • Cost‑push: SRAS shifts left due to higher production costs.
  • Built‑in: Adaptive expectations (wage‑price spiral).

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5. Propensities to Save and Consume

5.1 Definitions

Concept	Formula	Interpretation
Average Propensity to Consume (APC)	\(\displaystyle APC = \frac{C}{Y}\)	Share of total income spent on consumption.
Average Propensity to Save (APS)	\(\displaystyle APS = \frac{S}{Y}\)	Share of total income saved.
Marginal Propensity to Consume (MPC)	\(\displaystyle MPC = \frac{\Delta C}{\Delta Y}\)	Extra consumption from an extra £1 of income.
Marginal Propensity to Save (MPS)	\(\displaystyle MPS = \frac{\Delta S}{\Delta Y}\)	Extra saving from an extra £1 of income.

Because every pound is either spent or saved:

\[ APC + APS = 1 \qquad\text{and}\qquad MPC + MPS = 1 \]

5.2 Numerical Example (Closed Economy)

Period	Income \(Y\) (£)	Consumption \(C\) (£)	Savings \(S\) (£)
1	1 000	800	200
2	1 200	960	240

Average Propensities

• Period 1: \(\displaystyle APS_1 = \frac{200}{1\,000}=0.20\;(20\%)\)
• Period 2: \(\displaystyle APS_2 = \frac{240}{1\,200}=0.20\;(20\%)\)

Marginal Propensities (between the two periods)

\[ \Delta Y = 200,\qquad \Delta S = 40 \] \[ MPS = \frac{\Delta S}{\Delta Y}= \frac{40}{200}=0.20\;(20\%) \] \[ MPC = 1-MPS = 0.80\;(80\%) \]

5.3 Interpretation

A constant APS/MPS of 0.20 implies that for every extra £1 of income, households save 20p and spend 80p. The constancy simplifies multiplier analysis but may not hold over large income ranges.

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6. The Keynesian Multiplier

6.1 Derivation

In a simple closed economy without government:

\[ Y = C + I \]

With the consumption function \(C = a + MPC \times Y\) (where \(a\) is autonomous consumption), substituting gives:

\[ Y = a + MPC \times Y + I \] \[ Y - MPC \times Y = a + I \] \[ Y(1-MPC) = a + I \] \[ \boxed{Y = \frac{1}{1-MPC}\,(a+I)}\qquad\text{or}\qquad k = \frac{1}{MPS} \]

6.2 Multiplier Value (example)

Using the previous example where \(MPS = 0.20\): \[ k = \frac{1}{0.20}=5 \]

Thus a £1 increase in autonomous expenditure (e.g., government spending) raises equilibrium income by £5, assuming propensities remain unchanged.

6.3 Assumptions & Limitations

• Propensities (MPC, MPS) are constant over the income range considered.
• Prices, interest rates, and exchange rates are held constant (ceteris paribus).
• Closed‑economy simplification – no imports/exports, no taxes.
• Short‑run focus: no capacity constraints or changes in productivity.

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7. Fiscal, Monetary & Supply‑Side Policy

7.1 Fiscal Policy

• Expansionary: Increase G or reduce T → AD shifts right; multiplier amplifies impact.
• Contractionary: Decrease G or increase T → AD shifts left.
• Budget‑deficit multiplier: \(\displaystyle k_{deficit}= \frac{1}{MPS - MPC_{tax}}\) (where \(MPC_{tax}\) is the marginal propensity to consume out of disposable income after tax).

7.2 Monetary Policy

• Tools: Open‑market operations, policy interest rate, reserve requirements.
• Transmission mechanisms:
  • Interest‑rate channel – lower rates raise investment and consumption.
  • Liquidity‑preference (Keynes) – changes in money supply affect interest rates.
  • Loanable‑funds (classical) – supply‑demand for loanable funds determines the real interest rate.
• Monetary multiplier: \(\displaystyle m = \frac{1}{RR}\) where \(RR\) is the reserve ratio.

7.3 Supply‑Side (Structural) Policy

• Improving productivity: investment in education, training, R&D.
• Reducing market failures: deregulation, competition policy.
• Incentives for investment: tax reliefs, subsidies for capital formation.
• Effect on LRAS: shifts right, increasing potential output without causing inflation.

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8. Open‑Economy Extensions

8.1 International Trade

• Comparative advantage: Countries specialise in goods with lower opportunity cost.
• Terms of trade = \(\displaystyle \frac{P_{exports}}{P_{imports}}\).
• Protectionist measures (tariffs, quotas) raise domestic prices, reduce imports, and generate government revenue but create dead‑weight loss.

8.2 Balance of Payments (BoP)

Current‑account components	Effect on BoP
Exports (X)	Credit (inflow)
Imports (M)	Debit (outflow)
Net income from abroad	Credit/Debit depending on direction
Net transfers	Credits (receipts) or debits (payments)

8.3 Exchange‑Rate Determination (Floating)

• Demand for a currency = demand for domestic goods + foreign investment inflows.
• Supply = domestic investors buying foreign assets + import payments.
• Depreciation makes exports cheaper and imports more expensive → AD shifts right (net‑export boost).

8.4 Open‑Economy Multiplier

\[ k_{open} = \frac{1}{MPS + m} \] where \(m\) is the marginal propensity to import (MPM). A higher MPM reduces the multiplier because part of extra income leaks abroad.

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9. Key Points to Remember

1. APC = C/Y; APS = S/Y; MPC = ΔC/ΔY; MPS = ΔS/ΔY. All are expressed as decimals or percentages.
2. APC + APS = 1 and MPC + MPS = 1 – knowing one gives the other.
3. The expenditure multiplier \(k = 1/MPS\) (closed economy) or \(k = 1/(MPS + MPM)\) (open economy).
4. Higher APS/MPS reduces immediate consumption demand, shifting AD left; lower APS/MPS has the opposite effect.
5. Fiscal policy works through the multiplier; monetary policy works mainly via the interest‑rate channel.
6. Supply‑side measures shift LRAS right, raising potential output without creating inflationary pressure.
7. All calculations assume ceteris paribus and that propensities are constant over the relevant income range.

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10. Syllabus Checklist – Cambridge IGCSE/A‑Level 9708 (AS + A‑Level)

Syllabus Code	Topic	Covered?
1.1‑1.6	Basic economic ideas, factors of production, PPC, classification of goods	✓
2.1‑2.5	Demand & supply, elasticity, market equilibrium, consumer & producer surplus	✓
3.1‑3.4	Government micro‑intervention (taxes, subsidies, price controls, public/merit/de‑merit goods)	✓
4.1‑4.6	Macroeconomic objectives, circular flow (four‑sector), AD/AS, growth, unemployment, inflation	✓
5.1‑5.4	Propensities, multiplier, fiscal policy, monetary policy, supply‑side policy	✓
6.1‑6.5	International trade, protectionism, balance of payments, exchange rates, open‑economy multiplier	✓
7‑11 (A‑Level extensions)	Utility, market structures, labour market, growth & development, exchange‑rate regimes	To be developed in later modules.

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11. Practice Questions

1. In a closed economy, income rises from £800 to £1 000. Consumption rises from £560 to £720.

   • Calculate APS and MPS for the change.
   • What is the value of the expenditure multiplier?

2. The government introduces a tax cut that reduces taxes by £50 million. If the MPC is 0.75, estimate the impact on equilibrium national income using the multiplier concept.

3. Explain two real‑world factors that could cause the APS to fall as income rises. Relate your answer to the ceteris paribus assumption.

4. Country A has a marginal propensity to import (MPM) of 0.25 and a marginal propensity to save (MPS) of 0.15. Compute the open‑economy multiplier.

5. Draw and label a diagram showing the effect of a £10 billion increase in government spending on AD, price level and output in the short run. Indicate the multiplier effect.

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12. Further Reading & Resources

• Cambridge International AS & A Level Economics (9708) – Chapter 4 (Circular Flow), Chapter 5 (Aggregate Demand & Supply), Chapter 6 (Policy Instruments).
• BBC Bitesize – “Keynesian Multiplier” video (5 min).
• Interactive circular‑flow and AD/AS simulations (Cambridge’s online learning hub).
• Past paper questions on APS, MPS, multiplier and open‑economy extensions (June 2024, Paper 2, Q12‑Q14).
• Investopedia & Khan Academy – concise tutorials on elasticity, fiscal & monetary policy.