Economics · Ch 3 — Demand

Elasticity of Demand — Price, Income and Cross Elasticity

The Law of Demand only tells us the DIRECTION in which quantity demanded moves when price changes. Elasticity of demand measures the DEGREE — how responsive quantity demanded is to a change in price, income, or the price of a related good. This is one of the most numerically tested topics in Gujarat Std 11 Commerce Economics, so every formula below must be usable directly in computation, not just recalled in words.

1. Price elasticity of demand ( $E_p$ or $E_d$ ) measures responsiveness of quantity demanded to a change in the good's OWN price:

E_p = \frac{\%\ \text{change in quantity demanded}}{\%\ \text{change in price}} = \frac{\Delta Q / Q}{\Delta P / P} = \frac{\Delta Q}{\Delta P} \times \frac{P}{Q}

Because price and quantity move in opposite directions, $E_p$ is mathematically negative, but by convention it is reported as an absolute (numerical) value.

Value of $E_p$	Type	Meaning
$E_p = 0$	Perfectly inelastic	Quantity demanded does not change at all with price (a life-saving drug with no substitute)
$E_p < 1$	Relatively inelastic	% change in quantity demanded is SMALLER than % change in price (necessities)
$E_p = 1$	Unitary elastic	% change in quantity demanded EQUALS % change in price
$E_p > 1$	Relatively elastic	% change in quantity demanded is LARGER than % change in price (luxuries, goods with many substitutes)
$E_p = \infty$	Perfectly elastic	An infinitesimal price change causes an infinite change in quantity demanded (a theoretical extreme)

Total outlay (total expenditure) method — a quicker, non-computational way to judge elasticity taught alongside the percentage method: outlay = price × quantity.

If price falls and total outlay RISES → demand is elastic.
If price falls and total outlay stays the SAME → demand is unitary elastic.
If price falls and total outlay FALLS → demand is inelastic.

2. Income elasticity of demand ( $E_y$ ) measures responsiveness of quantity demanded to a change in the CONSUMER'S INCOME, price held constant:

E_y = \frac{\%\ \text{change in quantity demanded}}{\%\ \text{change in income}} = \frac{\Delta Q / Q}{\Delta Y / Y}

Positive $E_y$ → normal good (demand rises as income rises); $E_y > 1$ marks a luxury, $0 < E_y < 1$ marks a necessity.
Negative $E_y$ → inferior good (demand FALLS as income rises past a point).

3. Cross elasticity of demand ( $E_{xy}$ ) measures responsiveness of quantity demanded of good X to a change in the PRICE of a RELATED good Y:

E_{xy} = \frac{\%\ \text{change in quantity demanded of X}}{\%\ \text{change in price of Y}} = \frac{\Delta Q_x / Q_x}{\Delta P_y / P_y}

Positive $E_{xy}$ → X and Y are substitutes (tea and coffee: coffee's price rises → tea's demand rises). …

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