7.8.5—PED and firm revenue

Price elasticity of demand measures the percentage change in quantity demanded divided by the percentage change in price. If demand is elastic, a price cut raises total revenue; if demand is inelastic, a price cut lowers total revenue; unit elasticity leaves revenue unchanged at the margin.

Total revenue is price times quantity. The relationship is local and depends on where the firm is on its demand curve, so do not infer it from the sign alone.

If a 10% price cut increases quantity by 20%, demand is elastic and revenue changes approximately from P×Q to 0.9P×1.2Q=1.08PQ, an 8% rise.

The negative sign in PED indicates the inverse relationship; elasticity classification uses the absolute value, and “inelastic” does not mean quantity never changes.