factors affecting: cross elasticity of demand

📚 Price Elasticity, Income Elasticity & Cross Elasticity of Demand

1️⃣ What is Elasticity?

Elasticity measures how much one variable changes in response to a change in another variable. Think of it like a rubber band: the more you stretch it, the more it changes.

2️⃣ Price Elasticity of Demand (PED)

Shows how much the quantity demanded of a good changes when its price changes.

Formula: \$E_{p} = \dfrac{\% \Delta Q}{\% \Delta P}\$

• Elastic (\$|E_{p}| > 1\$) – big change in quantity.
• Inelastic (\$|E_{p}| < 1\$) – small change in quantity.
• Unitary (\$|E_{p}| = 1\$) – proportional change.

3️⃣ Income Elasticity of Demand (YED)

Shows how quantity demanded changes when consumer income changes.

Formula: \$E_{Y} = \dfrac{\% \Delta Q}{\% \Delta I}\$

• Normal goods (\$E_{Y} > 0\$) – demand rises with income.
• Inferior goods (\$E_{Y} < 0\$) – demand falls as income rises.
• Luxury goods (\$E_{Y} > 1\$) – demand rises more than income.

4️⃣ Cross Elasticity of Demand (XED)

Shows how the quantity demanded of one good changes when the price of another good changes.

Formula: \$E{xy} = \dfrac{\% \Delta Qx}{\% \Delta P_y}\$

• Substitutes (\$E_{xy} > 0\$) – price rise of good y → demand for good x rises.
• Complements (\$E_{xy} < 0\$) – price rise of good y → demand for good x falls.
• Independent (\$E_{xy} = 0\$) – no effect.

5️⃣ Factors Affecting Cross Elasticity

6️⃣ Example: Coffee & Tea

Suppose the price of coffee rises by 10%. If the quantity demanded of tea increases by 5%, the cross‑elasticity is:

\$E_{tea,coffee} = \dfrac{5\%}{10\%} = 0.5\$

This positive value indicates coffee and tea are substitutes, but the elasticity is less than 1, so the relationship is relatively inelastic.

7️⃣ Table: Cross Elasticity for Common Goods

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