Elasticities (PED, PES, YED, XED)

Price elasticity of demand (PED)

PED measures the responsiveness of quantity demanded to a change in price:

$$PED = \frac{\%\ \Delta\ \text{quantity demanded}}{\%\ \Delta\ \text{price}}$$

PED is negative (the law of demand) but is usually quoted as a magnitude.

Elastic (|PED| > 1): quantity changes proportionately more than price.
Inelastic (|PED| < 1): quantity changes proportionately less than price.
Unitary (|PED| = 1): proportionate changes are equal.
Perfectly inelastic (0) — vertical; perfectly elastic (∞) — horizontal.

Determinants: number and closeness of substitutes (more → more elastic), proportion of income spent, whether the good is a necessity or luxury, whether it is addictive/habitual, and time (demand is more elastic in the long run).

PED and total revenue (TR = P × Q): if demand is elastic, a price cut raises TR; if inelastic, a price rise raises TR. TR is maximised where PED = 1.