1.2.3 Price, Income & Cross Elasticities of Demand

Edexcel A-Level Economics (9EC0) | Theme 1.2.3

Specification Coverage: Edexcel unit 1.2.3 - Price, Income and Cross Elasticities of Demand. Students should be able to understand and calculate price elasticity of demand (PED), income elasticity of demand (YED), and cross elasticity of demand (XED). They should also be able to interpret the significance of these elasticities for firms and governments, with real-world examples.

Price Elasticity of Demand (PED)

Definition: PED measures the responsiveness of quantity demanded to a change in the good's own price.

\[ \text{PED} = \frac{\%\Delta Q_D}{\%\Delta P} \]
Diagram showing different PED values from perfectly inelastic to perfectly elastic
Figure 1: Price Elasticity of Demand ranges. Shows how the slope of the demand curve varies from vertical (perfectly inelastic, PED=0) to horizontal (perfectly elastic, PED=∞).
PED Value Classification Explanation & Example
\[ \text{PED} = 0 \] Perfectly inelastic Quantity demanded does not respond to price changes (theoretical, e.g., essential medicine).
\[ 0 < \text{PED} < 1 \] Relatively inelastic Quantity demanded changes by a smaller percentage than the price change (e.g., necessities, addictive goods).
\[ \text{PED} = 1 \] Unitary elasticity Quantity demanded changes by the exact same percentage as the price.
\[ \text{PED} > 1 \] Relatively elastic Quantity demanded changes by a larger percentage than the price change (e.g., luxuries, goods with many substitutes).
\[ \text{PED} = \infty \] Perfectly elastic Any price increase causes quantity demanded to fall to zero (theoretical).

Key Determinants of PED:

  • Number & Closeness of Substitutes: More/better substitutes mean higher (more elastic) PED.
  • Necessity vs. Luxury: Necessities tend to be price inelastic; luxuries tend to be elastic.
  • Proportion of Income: Goods that take a large portion of income tend to be more price elastic.
  • Time Period: Demand becomes more elastic over the long run as consumers find alternatives.

Income Elasticity of Demand (YED)

Definition: YED measures the responsiveness of quantity demanded to a change in consumer income.

\[ \text{YED} = \frac{\%\Delta Q_D}{\%\Delta Y} \]
YED Value Classification Explanation & Example
\[ \text{YED} > 1 \] Income elastic luxury Demand increases more than proportionally to income (e.g., holidays, designer goods).
\[ 0 < \text{YED} < 1 \] Income inelastic necessity Demand increases but less than proportionally to income (e.g., food, basic clothing).
\[ \text{YED} = 0 \] Income independent Demand does not change with income (rare, theoretical).
\[ \text{YED} < 0 \] Inferior Good Demand decreases as income rises (e.g., budget brands, bus travel).

Cross Elasticity of Demand (XED)

Definition: XED measures the responsiveness of quantity demanded for Good A to a change in the price of Good B.

\[ \text{XED} = \frac{\%\Delta Q_{D_A}}{\%\Delta P_B} \]
XED Value Relationship Explanation & Example
\[ \text{XED} > 0 \] Substitutes A rise in the price of Good B increases demand for Good A (e.g., Coke and Pepsi). A higher positive value indicates stronger substitutability.
\[ \text{XED} < 0 \] Complements A rise in the price of Good B decreases demand for Good A (e.g., printers and ink). A lower negative value (e.g., -2.5) indicates stronger complementarity.
\[ \text{XED} = 0 \] Unrelated goods No relationship between the two products.

Significance of Elasticities

For Firms:

PED & Revenue: To maximise revenue, a firm should raise price if demand is inelastic (PED < 1) and lower price if demand is elastic (PED > 1).

YED: Helps plan for the economic cycle. Produce/sell more luxuries in booms and more inferior goods in recessions.

XED: Informs pricing and competitive strategy. Understanding complements and substitutes is vital.

For Governments:

PED & Taxation: Placing an indirect tax on goods with inelastic demand (e.g., cigarettes) raises significant tax revenue with a relatively small fall in quantity. Taxing elastic goods can severely reduce sales and employment.

PED & Subsidies: Subsidising goods with elastic demand (e.g., green tech) can cause a large increase in consumption.

Key Exam Tips

  1. Calculations: Be confident calculating % changes and each elasticity. Show your working.
    \[ \%\Delta = \frac{\text{New} - \text{Old}}{(\text{New} + \text{Old})/2} \times 100 \]
  2. Interpretation: The sign (positive/negative) of YED and XED is as important as the number. For PED, the number's size is key.
  3. Application: Always link the numerical result to its real-world meaning (e.g., PED = -0.4 means demand is inelastic, so a tax will be largely passed to the consumer").
  4. Evaluation: Elasticity is not static—it can change over time or if the price change is very large.