variation in price elasticity of demand along the length of a straight-line demand curve

Price Elasticity of Demand (PED)

Price elasticity measures how much the quantity demanded of a good changes when its price changes.

Formula: \$Ed = \dfrac{\% \Delta Qd}{\% \Delta P}\$

🔍 Interpretation:

• \$|E_d| > 1\$ → elastic (quantity changes a lot)
• \$|E_d| = 1\$ → unit‑elastic (quantity changes proportionally)
• \$|E_d| < 1\$ → inelastic (quantity changes little)

📌 Example: If the price of pizza rises from \$10 to \$12 (20% increase) and the quantity demanded falls from 100 to 80 pizzas (20% decrease), then \$E_d = \frac{-20\%}{20\%} = -1\$ → unit‑elastic.

Variation of PED along a Straight‑Line Demand Curve

For a straight‑line demand curve \$Q = a - bP\$, the elasticity is not constant. It changes because the percentage changes in price and quantity differ at different points.

Notice how \$E_d\$ becomes more negative (more elastic) as we move up the demand curve.

💰 Income Elasticity of Demand (YED)

Income elasticity tells us how quantity demanded changes when consumers' income changes.

Formula: \$E{Y} = \dfrac{\% \Delta Qd}{\% \Delta I}\$

🔍 Interpretation:

• \$E_{Y} > 1\$ → luxury good (demand rises more than income)
• \$0 < E_{Y} < 1\$ → necessity (demand rises but less than income)
• \$E_{Y} < 0\$ → inferior good (demand falls as income rises)

📌 Example: If income rises by 10% and the quantity of organic milk demanded increases by 15%, \$E_{Y} = \frac{15\%}{10\%} = 1.5\$ → luxury good.

🔄 Cross Elasticity of Demand (XED)

Cross elasticity measures how the demand for one good responds to a price change in another good.

Formula: \$E{XY} = \dfrac{\% \Delta Q{X}}{\% \Delta P_{Y}}\$

🔍 Interpretation:

• \$E_{XY} > 0\$ → substitute (demand for X rises when Y’s price rises)
• \$E_{XY} < 0\$ → complement (demand for X falls when Y’s price rises)
• \$E_{XY} \approx 0\$ → goods are unrelated.

📌 Example: If the price of coffee increases by 5% and the quantity of tea demanded increases by 2%, \$E_{XY} = \frac{2\%}{5\%} = 0.4\$ → tea is a substitute for coffee.

📝 Exam Tips

• Always show the sign of elasticity (negative for PED).
• Remember that elasticity is a ratio of percentages, not absolute changes.
• When calculating along a straight‑line demand curve, pick two points and compute the percentage changes.
• Use the interpretation table to quickly classify goods.
• Practice with real‑world examples (e.g., smartphones, coffee, organic food) to cement concepts.

📚 Summary

Elasticity tells us how sensitive demand is to changes in price, income, or the price of related goods. It helps businesses set prices, governments plan taxes, and economists predict market behaviour.

Key take‑away: Elasticity is not constant along a demand curve; it depends on the point you’re looking at.