definition of price elasticity, income elasticity and cross elasticity of demand (PED, YED, XED)

Definition: PED measures how much the quantity demanded of a good changes when its price changes.

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

Analogy: Think of a water balloon. If you squeeze it (price goes up), the balloon shrinks (quantity demanded falls). The more it shrinks, the more elastic it is.

Example: If the price of pizza rises from \$10 to \$12 (20% increase) and the quantity sold falls from 100 to 80 pizzas (20% decrease), then \$PED = \dfrac{-20\%}{20\%} = -1\$.

Interpretation:

• \$|PED| > 1\$: Elastic – quantity demanded changes a lot.
• \$|PED| < 1\$: Inelastic – quantity demanded changes little.
• \$|PED| = 1\$: Unit‑elastic – quantity changes proportionally.

Definition: YED shows how quantity demanded changes when consumers’ income changes.

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

Analogy: Imagine a student who gets a part‑time job. If their pocket money increases, they might buy more ice‑cream. The more they buy, the higher the YED.

Example: If a student’s income rises from \$200 to \$240 (20% increase) and they buy 30 to 45 ice‑creams (50% increase), then \$YED = \dfrac{50\%}{20\%} = 2.5\$.

Interpretation:

• \$YED > 0\$: Normal good – demand rises with income.
• \$YED > 1\$: Luxury good – demand rises more than income.
• \$0 < YED < 1\$: Necessity – demand rises but less than income.
• \$YED < 0\$: Inferior good – demand falls as income rises.

Definition: XED measures how the quantity demanded of one good responds to a price change in another good.

Formula: \$XED = \dfrac{\%\ \text{change in quantity demanded of Good A}}{\%\ \text{change in price of Good B}}\$

Analogy: Picture two friends who always share a pizza. If one friend’s pizza price goes up, the other might order more of the cheaper pizza instead.

Example: If the price of coffee rises from \$3 to \$3.60 (20% increase) and the quantity of tea sold rises from 200 to 260 cups (30% increase), then \$XED = \dfrac{30\%}{20\%} = 1.5\$.

Interpretation:

• \$XED > 0\$: Substitute goods – demand for A rises when B’s price rises.
• \$XED < 0\$: Complementary goods – demand for A falls when B’s price rises.
• \$XED = 0\$: No relationship – goods are unrelated.

1️⃣ Show the formula first. Write the elasticity expression before plugging in numbers.

2️⃣ Keep the sign. Remember that demand curves slope downwards, so price changes usually give a negative sign for PED.

3️⃣ Interpret the magnitude. After calculating, state whether the good is elastic, inelastic, normal, luxury, etc.

4️⃣ Use examples. If time allows, give a quick real‑world example to illustrate your answer.

5️⃣ Check units. Percent changes must be in the same units (e.g., % price, % quantity).