formulae for and calculation of price elasticity, income elasticity and cross elasticity of demand

📈 Price Elasticity of Demand (PED)

Price elasticity measures how much the quantity demanded of a good changes when its price changes. Think of it like a seesaw: if the price goes up, the demand might drop (seesaw tilts), and if the price goes down, demand might rise.

  1. Find the initial price P₁ and quantity Q₁.

  2. Find the new price P₂ and quantity Q₂.

  3. Plug into the formula below.

FormulaExplanation

\$Ed = \frac{(Q2 - Q1)}{(P2 - P1)} \times \frac{P1}{Q_1}\$

Change in quantity ÷ change in price, adjusted for the starting price and quantity.

If |Ed| > 1, demand is elastic (big reaction). If |Ed| < 1, demand is inelastic (small reaction). If |E_d| = 1, it’s unit‑elastic.

💰 Income Elasticity of Demand (YED)

Income elasticity tells us how demand changes when people’s income changes. Imagine you get a new allowance – do you buy more snacks or stick to the same?

  1. Record the initial income I₁ and quantity Q₁.

  2. Record the new income I₂ and quantity Q₂.

  3. Use the formula below.

FormulaExplanation

\$Ey = \frac{(Q2 - Q1)}{(I2 - I1)} \times \frac{I1}{Q_1}\$

Change in quantity ÷ change in income, adjusted for the starting income and quantity.

If Ey > 0, the good is a normal good (demand rises with income). If Ey < 0, it’s a inferior good (demand falls as income rises).

🛍️ Cross Elasticity of Demand (XED)

Cross elasticity measures how the demand for one product changes when the price of another product changes. Think of two friends: if one’s price goes up, the other might become more popular.

  1. Take the price of product A PA and quantity of product B QB.

  2. After a price change, record new price PA' and new quantity of B QB'.

  3. Insert into the formula below.

FormulaExplanation

\$E{xy} = \frac{(QB' - QB)}{(PA' - PA)} \times \frac{PA}{Q_B}\$

Change in quantity of B ÷ change in price of A, adjusted for the starting price of A and quantity of B.

If E{xy} > 0, the goods are substitutes (price rise of A boosts demand for B). If E{xy} < 0, they are complements (price rise of A reduces demand for B).