significance of relative percentage changes, the size and sign of the coefficient of: price elasticity of demand

📊 Price Elasticity of Demand

What is it? 📈 It measures how much the quantity demanded of a good changes when its price changes.

Formula: \$E_p = \dfrac{\%\ \text{change in quantity demanded}}{\%\ \text{change in price}\$

Think of it like a rubber band: the more elastic (stretchy) the band, the bigger the change in length for a small tug.

💡 Significance of Relative Percentage Changes

Because we use percentages, we can compare goods of different sizes or prices. A 10% drop in price leading to a 20% rise in quantity demanded means the demand is elastic (coefficient < -1).

🔢 Size and Sign of the Coefficient

  1. Elastic demand (|\$E_p\$| > 1): Quantity changes more than price. Example: Smartphones – a price drop leads to a big jump in sales.

  2. Unitary elastic (|\$E_p\$| = 1): Quantity changes proportionally to price.

  3. Inelastic demand (|\$E_p\$| < 1): Quantity changes less than price. Example: Salt – price changes little affect how much people buy.

  4. Negative sign because quantity demanded falls when price rises.

📈 Example: Calculating Elasticity

Price falls from £10 to £8 (20% drop). Quantity demanded rises from 100 to 140 units (40% rise).

Elasticity: \$E_p = \dfrac{40\%}{-20\%} = -2\$ → Elastic demand.

📝 Examination Tips

  • Show the formula clearly and plug in the numbers.

  • State the sign and interpret the result (elastic, unitary, inelastic).

  • Use a real‑world example to demonstrate understanding.

💰 Income Elasticity of Demand

What is it? It measures how quantity demanded changes when consumer income changes.

Formula: \$E_I = \dfrac{\%\ \text{change in quantity demanded}}{\%\ \text{change in income}\$

Analogy: Think of income as a “budget” – the more you have, the more you can spend on different goods.

📊 Interpretation

  • Positive \$E_I\$ – normal goods. The higher the income, the more you buy.

  • Negative \$E_I\$ – inferior goods. As income rises, you buy less.

  • Large positive \$E_I\$ (>1) – luxury goods.

  • Small positive \$E_I\$ (0–1) – necessity goods.

📈 Example: Income Elasticity

Income rises from £20,000 to £25,000 (25% increase). Demand for organic food rises from 200 to 260 units (30% increase).

Elasticity: \$E_I = \dfrac{30\%}{25\%} = 1.2\$ → Luxury good.

📝 Examination Tips

  • Identify whether the good is normal or inferior.

  • Explain the sign of \$E_I\$ and its economic meaning.

  • Use a clear example and calculate the coefficient.

🔗 Cross Elasticity of Demand

What is it? It measures how the quantity demanded of one good responds to a price change in another good.

Formula: \$E_{xy} = \dfrac{\%\ \text{change in quantity demanded of } x}{\%\ \text{change in price of } y\$

Analogy: Think of two friends – if one friend’s mood changes, the other’s reaction can be positive, negative, or neutral.

📊 Interpretation

  • Positive \$E_{xy}\$ – substitutes (e.g., tea and coffee).

  • Negative \$E_{xy}\$ – complements (e.g., printers and ink cartridges).

  • Zero \$E_{xy}\$ – unrelated goods.

📈 Example: Cross Elasticity

Price of coffee rises from £1.50 to £1.80 (20% increase). Demand for tea falls from 300 to 240 units (20% decrease).

Elasticity: \$E_{tea,coffee} = \dfrac{-20\%}{20\%} = -1\$ → Complementary goods.

📝 Examination Tips

  • State whether goods are substitutes or complements.

  • Show the calculation and interpret the sign.

  • Use a real example to illustrate the relationship.

📚 Summary Table of Elasticities

Elasticity TypeFormulaInterpretation
Price Elasticity\$Ep = \dfrac{\%\Delta Qd}{\%\Delta P}\$Elastic (>1), Unitary (=1), Inelastic (<1)
Income Elasticity\$EI = \dfrac{\%\Delta Qd}{\%\Delta I}\$Normal (+), Inferior (-), Luxury (>1)
Cross Elasticity\$E{xy} = \dfrac{\%\Delta Q{x}}{\%\Delta P_{y}}\$Substitutes (+), Complements (-), Unrelated (0)

🎯 Final Exam Checklist

  1. Define the elasticity and write the correct formula.

  2. Show all steps of the calculation with percentages.

  3. State the sign and interpret the result (elastic, unitary, inelastic).

  4. Explain the economic significance (e.g., consumer behaviour, revenue implications).

  5. Use a clear, real‑world example to demonstrate understanding.