factors affecting: cross elasticity of demand

Cambridge A‑Level Economics 9708 – Complete Syllabus Notes


1. Core Economic Concepts (AS‑Level)

1.1 Scarcity, Choice & Opportunity Cost

  • Resources are limited → societies must decide how to allocate them.
  • Every choice involves a trade‑off; the next best alternative forgone is the opportunity cost.

1.2 Economic Methodology

  • Positive statements – describe how the economy works (testable).
    Example: “A rise in the price of petrol reduces the quantity demanded of diesel cars.”
  • Normative statements – prescribe what ought to be (value‑laden).
    Example: “The government should subsidise electric vehicles.”
  • Use of ceteris paribus (all other things equal) to isolate cause‑effect relationships.

1.3 Factors of Production & Economic Systems

  • Land, labour, capital, entrepreneurship.
  • Economic systems: market, command, mixed – each allocates resources differently.

1.4 Production Possibility Curve (PPC)

  • Shows maximum output combinations of two goods when resources are fully employed.
  • Shape (concave) reflects increasing opportunity cost.
  • Shifts:
    • Outward – economic growth (more resources/technology).
    • Inward – recession, natural disaster.

2. Micro‑economics Fundamentals (AS‑Level)

2.1 Demand & Supply

  • Demand: quantity of a good consumers are willing & able to buy at each price, ceteris paribus.
    • Law of demand – inverse relationship between price and quantity demanded.
    • Determinants: price of the good, income, prices of related goods, tastes, expectations, number of buyers.
  • Supply: quantity producers are willing & able to sell at each price.
    • Law of supply – direct relationship between price and quantity supplied.
    • Determinants: price of the good, input costs, technology, expectations, number of sellers.
  • Market equilibrium – where the demand and supply curves intersect (E).
    Movement vs. shift: a change in the price of the good causes a movement along the curve; a change in any determinant causes a shift.

2.2 Consumer & Producer Surplus

  • Consumer surplus (CS) – the difference between what consumers are willing to pay and what they actually pay.
  • Producer surplus (PS) – the difference between the price received and the minimum price producers are willing to accept.
  • Both are measures of economic welfare; a policy that creates a dead‑weight loss reduces total surplus.

2.3 Government Intervention in Markets (Micro)

  1. Taxes – shift supply (or demand) left; incidence depends on relative elasticities; creates dead‑weight loss.
  2. Subsidies – shift supply (or demand) right; increase welfare but cost the exchequer.
  3. Price controls
    • Maximum price (price ceiling) – may create a shortage.
    • Minimum price (price floor) – may create a surplus.
  4. Public‑good provision – government supplies non‑rival, non‑excludable goods (e.g., street lighting).
  5. Merit & de‑merit goods – government intervenes to correct market failure (e.g., education, tobacco).
  6. Regulation – standards, licensing, safety requirements.

3. Elasticities of Demand (Core AS & A‑Level Content)

3.1 What is an Elasticity?

Elasticities measure the responsiveness of one variable to a percentage change in another variable. They are dimensionless and allow comparison across different markets.

3.2 Price Elasticity of Demand (PED)

Definition & Formula
\[ \varepsilon_{p}= \frac{\%\Delta Q_{d}}{\%\Delta P} \]
Numerical Example (mid‑point method)
InitialNew
Price, \(P_{1}=£10\)Price, \(P_{2}=£12\)
Quantity, \(Q_{1}=500\)Quantity, \(Q_{2}=450\)
\[ \%\Delta P=\frac{P_{2}-P_{1}}{(P_{1}+P_{2})/2}\times100 =\frac{12-10}{11}\times100\approx18.2\% \] \[ \%\Delta Q_{d}= \frac{Q_{2}-Q_{1}}{(Q_{1}+Q_{2})/2}\times100 =\frac{450-500}{475}\times100\approx-10.5\% \] \[ \varepsilon_{p}= \frac{-10.5\%}{18.2\%}\approx-0.58 \] Interpretation: \(|\varepsilon_{p}|<1\) → demand is **inelastic**; a 1 % rise in price reduces quantity demanded by less than 1 %.
Value Ranges & Total‑Revenue (TR) Test
Range of \(\varepsilon_{p}\)LabelTR when price rises
\(\varepsilon_{p}<-1\)ElasticTR falls
\(\varepsilon_{p}=-1\)Unit‑elasticTR unchanged
\(-1<\varepsilon_{p}<0\)InelasticTR rises
\(\varepsilon_{p}=0\)Perfectly inelasticTR rises with any price increase
\(\varepsilon_{p}=-\infty\)Perfectly elasticTR falls to zero with any price increase
Determinants of PED (Cambridge Syllabus)
  • Availability of close substitutes.
  • Proportion of income spent on the good.
  • Nature of the good – luxury vs. necessity.
  • Definition of the market – narrow vs. broad.
  • Time horizon – long‑run > short‑run elasticity.
Elasticity Along a Straight‑Line Demand Curve
  • Upper (high‑price) segment – elastic (\(|\varepsilon_{p}|>1\)).
  • Mid‑point – unit‑elastic (\(|\varepsilon_{p}|=1\)).
  • Lower (low‑price) segment – inelastic (\(|\varepsilon_{p}|<1\)).
Short‑run vs. Long‑run PED
  • Short run – limited ability to find substitutes or change habits → lower elasticity.
  • Long run – consumers can adjust, technology can evolve → higher elasticity.

3.3 Income Elasticity of Demand (YED)

Definition & Formula
\[ \varepsilon_{y}= \frac{\%\Delta Q_{d}}{\%\Delta Y} \]
Interpretation
  • \(\varepsilon_{y}>0\) – normal good.
    • \(\varepsilon_{y}>1\) – luxury (elastic).
    • 0 < \(\varepsilon_{y}\)< 1 – necessity (inelastic).
  • \(\varepsilon_{y}<0\) – inferior good (demand falls as income rises).
Factors Influencing YED
  • Nature of the good (luxury vs. necessity).
  • Availability of close substitutes (more substitutes → higher YED).
  • Consumer preferences and cultural factors.
  • Time horizon – long‑run YED is usually larger as tastes evolve.

3.4 Cross Elasticity of Demand (XED)

Definition & Formula
\[ \varepsilon_{xy}= \frac{\%\Delta Q_{d}^{x}}{\%\Delta P^{y}} \] Measures the percentage change in the quantity demanded of good **x** when the price of good **y** changes.
Sign & Economic Relationship
  • \(\varepsilon_{xy}>0\) – **substitutes** (e.g., tea ↔ coffee).
  • \(\varepsilon_{xy}<0\) – **complements** (e.g., cars ↔ petrol).
  • \(\varepsilon_{xy}=0\) – **independent** goods.
Key Determinants of the Magnitude of XED
FactorEffect on \(|\varepsilon_{xy}|\)Explanation
Degree of closeness (substitutes/complements) Higher Strong functional overlap or joint use magnifies the response.
Availability of alternatives More alternatives → Higher Consumers can switch more easily when the price of one good changes.
Time period Long run → Higher Adjustment processes (search, habit change) need time.
Share of expenditure on the goods Higher share → Higher Price change affects a larger part of the consumer’s budget.
Consumer preferences & brand loyalty Strong loyalty → Lower Consumers resist switching even if relative prices change.
Market definition Narrow definition → Higher Goods are more directly comparable, so cross‑price effects are larger.
Nature of the relationship (fixed‑ratio vs. discretionary) Fixed‑ratio complements (e.g., printers & ink) → High negative XED.
Discretionary complements (e.g., movies & popcorn) → Lower negative XED.
Degree of joint consumption determines the size of the response.
Diagram – Shift of Demand for Good X

When the price of good Y rises:

  • Substitutes – demand for X shifts right (increase).
  • Complements – demand for X shifts left (decrease).

Insert a hand‑drawn or software diagram showing the original demand curve D₁, the shifted curve D₂, and the resulting change in equilibrium price and quantity.


4. Macroeconomics Foundations (AS‑Level)

4.1 Measuring National Income

  • GDP (Nominal) – market value of all final goods & services produced within a country in a given period.
  • Alternative measures: GNI (adds net primary income from abroad), NNI (adds net factor income from abroad, subtracts depreciation).
  • Three approaches:
    • Production (value added) approach.
    • Income approach.
    • Expenditure approach: \(GDP = C + I + G + (X-M)\).
  • Common measurement problems: informal sector, underground economy, double counting, price changes.

4.2 Circular Flow of Income

Two‑sector (households ↔ firms) and three‑sector (adds government) models illustrate flows of:

  • Real resources (labour, capital, land) from households to firms.
  • Monetary payments (wages, rent, profit) from firms to households.
  • Government taxes, transfers and spending in the three‑sector model.

Insert a simple circular‑flow diagram with arrows for resources, money, and government interaction.

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

Components of AD
  • Consumption (C), Investment (I), Government spending (G), Net exports (X‑M).
AD Curve
  • Downward sloping – real‑GDP falls as the price level rises (wealth effect, interest‑rate effect, exchange‑rate effect).
AS Curves
  • Short‑run AS (SRAS) – upward sloping because some input prices are sticky.
  • Long‑run AS (LRAS) – vertical at the economy’s potential output (full‑employment output).
Shifts in AD and AS
CurveShift DirectionTypical Causes
AD rightIncreaseHigher consumer confidence, tax cuts, expansionary fiscal policy, expansionary monetary policy, rise in foreign demand.
AD leftDecreaseHigher taxes, reduced consumer confidence, contractionary fiscal/monetary policy, fall in foreign demand.
SRAS rightIncreaseLower input prices, productivity gains, technological improvement, favourable expectations.
SRAS leftDecreaseHigher wages, oil price shocks, adverse supply shocks, expectations of higher future costs.
LRAS rightIncreaseEconomic growth – more capital, labour, better technology.
LRAS leftDecreaseDecrease in resources (e.g., natural disaster), long‑run decline in productivity.

4.4 Economic Growth, Unemployment & Inflation

Economic Growth
  • Increase in potential output (LRAS shift right).
  • Measured by the growth rate of real GDP.
  • Sources: capital accumulation, labour force growth, technological progress, improvements in productivity.
Unemployment
  • Frictional – short‑term job search.
  • Structural – mismatch of skills/locations.
  • Classical (real‑wage) – wages above equilibrium.
  • Demand‑deficient (cyclical) – insufficient aggregate demand.
Inflation
  • General rise in the price level, measured by the Consumer Price Index (CPI) or Retail Price Index (RPI).
  • Types:
    • Demand‑pull – AD curve shifts right faster than SRAS.
    • Cost‑push – SRAS shifts left (e.g., oil shock).
    • Built‑in – wage‑price spiral.

5. Government Macro‑policy (A‑Level)

5.1 Fiscal Policy

  • Expansionary – increase G or cut taxes → AD right → higher output & price level (possible inflation).
  • Contractionary – decrease G or raise taxes → AD left → lower output & price level.
  • Considerations: multiplier effect, crowding‑out, timing (recognition, implementation, impact lags).

5.2 Monetary Policy (Central Bank)

  • Instruments: open‑market operations, policy interest rate, reserve requirements.
  • Expansionary → lower interest rates → increase investment & consumption → AD right.
  • Contractionary → higher rates → AD left.
  • Liquidity trap, credibility of the central bank, and exchange‑rate effects are evaluation points.

5.3 Supply‑Side (Structural) Policies

  • Improving productivity: investment in education, training, R&D, infrastructure.
  • Labour‑market reforms: deregulation, reducing minimum‑wage rigidity.
  • Tax incentives for investment, deregulation of markets.
  • Evaluation – time lag, distributional effects, risk of increasing inequality.

6. International Trade & Finance (AS‑Level)

6.1 Reasons for Trade

  • Comparative advantage – countries specialise in goods with lower opportunity cost.
  • Economies of scale, variety, and access to natural resources.

6.2 Protectionist Instruments & Arguments

  • Tariffs, quotas, import licences, subsidies, voluntary export restraints.
  • Arguments for protection: infant industry, national security, protecting jobs, correcting market failure.
  • Arguments against: higher consumer prices, retaliation, dead‑weight loss, inefficiency.

6.3 Balance of Payments (BOP)

  • Current account (trade in goods & services, income, transfers) + Capital account (financial flows) = 0 (by definition).
  • Surplus → net lender; deficit → net borrower.
  • Policy responses: exchange‑rate adjustments, fiscal/monetary measures.

6.4 Exchange Rates

  • Floating vs. fixed regimes.
  • Determinants in a floating system: relative inflation, interest rates, expectations, terms of trade.
  • Impact on AD:
    • Depreciation → exports cheaper, imports more expensive → AD right.
    • Appreciation → opposite effect.

7. Advanced Micro – Consumer Behaviour & Market Structures (A‑Level)

7.1 Utility Theory

  • Total utility – overall satisfaction from consumption.
  • Marginal utility (MU) – additional satisfaction from one more unit.
  • Law of diminishing marginal utility → downward‑sloping demand.

7.2 Indifference Curves & Budget Constraint

  • Indifference curves represent combinations of two goods giving equal utility.
  • Higher curves → higher utility.
  • Marginal rate of substitution (MRS) = slope of indifference curve = \(-\frac{MU_x}{MU_y}\).
  • Consumer equilibrium where the highest attainable indifference curve is tangent to the budget line (MRS = price ratio).

7.3 Production & Cost Curves (Firm‑level)

  • Short‑run: fixed and variable inputs → Total, Average, and Marginal cost curves (U‑shaped MC, falling AC then rising).
  • Long‑run: all inputs variable → LRAC envelope, economies of scale, constant returns, diseconomies.

7.4 Market Structures

StructureKey CharacteristicsPrice‑setting behaviourTypical Efficiency
Perfect competitionMany small firms, homogeneous product, free entry/exit.Price taker – price = MC = MR.Allocative & productive efficiency (P = MC, minimum AC).
Monopolistic competitionMany firms, differentiated products, some entry barriers.Price > MC, but downward‑sloping demand.Excess capacity – not fully efficient.
OligopolyFew large firms, inter‑dependent, may produce homogeneous or differentiated goods.Strategic behaviour – kinked demand, collusion, price leadership.Potential for inefficiency; outcomes depend on conduct.
MonopolySingle seller, high barriers to entry, unique product.Price‑setter – MR = MC, price > MC.Usually allocatively inefficient (P > MC) and may have productive inefficiency.

7.5 Evaluation of Market Failure & Government Role

  • Externalities, public goods, information asymmetry, monopoly power.
  • Policy tools: taxes/subsidies (Pigouvian), regulation, provision of public goods, competition law.
  • AO3 focus – weigh efficiency gains against distributional impacts, administrative costs, and unintended consequences.

8. Revision Checklist (AO1‑AO3)

  1. Definitions & formulas – be able to write each elasticity formula from memory.
  2. Diagram skills – draw and label:
    • PED curve with elastic, unit‑elastic and inelastic sections.
    • Shift of demand for X when the price of Y changes (XED).
    • AD/AS equilibrium and the effects of fiscal/monetary policy.
    • Circular‑flow diagram and PPC shifts.
    • Indifference curve & budget line equilibrium.
  3. Application – use real‑world examples (e.g., coffee/tea, smartphones/data plans, petrol/electric cars) to illustrate each elasticity and policy effect.
  4. Analysis – explain why a given determinant raises or lowers an elasticity; discuss short‑run vs. long‑run differences.
  5. Evaluation (AO3) – for any policy (tax, subsidy, monetary easing, trade protection) assess:
    • Efficiency (dead‑weight loss, welfare changes).
    • Equity (distributional impact).
    • Practicality (administrative cost, time lag, political feasibility).

9. Quick Practice Questions

  1. Explain why the cross‑elasticity of demand between tea and coffee is expected to be positive, and state what this implies for the relationship between the two goods.
  2. A new, cheaper data‑plan is introduced. Predict how the XED between smartphones and data plans will change and why.
  3. Discuss how the time period (short run vs. long run) influences the cross‑elasticity between gasoline and electric cars.
  4. Calculate the price elasticity of demand for a product that sees a 12 % price rise and a 5 % fall in quantity demanded. Classify the elasticity and state the likely effect on total revenue.
  5. Identify three determinants of income elasticity of demand and explain how each affects whether a good is a necessity, a luxury, or an inferior good.
  6. Using the AD/AS model, analyse the likely macro‑economic impact of a 5 % increase in government spending financed by borrowing.
  7. Evaluate the effectiveness of a tariff on imported steel in protecting domestic employment, considering both short‑run and long‑run effects.

10. Suggested Further Reading & Resources

  • Cambridge International AS & A Level Economics (9708) – Student Book, Chapters 2‑9.
  • Past paper questions – focus on AO2 (application) and AO3 (evaluation) marks.
  • Online video tutorials (e.g., Tutor2U, EconplusDal) for diagram practice.
  • IMF & World Bank data sites – real‑world examples for macro‑policy questions.

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