Elasticity measures how strongly one variable responds to another, and it is one of the most important tools in applied microeconomics. Price elasticity of demand (PED) is defined as the percentage change in quantity demanded divided by the percentage change in price: \( \text{PED} = \%\Delta Q_d / \%\Delta P \). When PED exceeds one, demand is elastic and consumers are highly responsive to price; when PED is less than one, demand is inelastic and consumers are relatively unresponsive. The special case PED equals one is called unit elastic, where quantity and price change by the same percentage. At the extremes, perfectly inelastic demand (PED = 0) gives a vertical demand curve (quantity is fixed regardless of price), while perfectly elastic demand (PED = \(\infty\)) gives a horizontal demand curve (any price increase drives quantity to zero).
Several factors shape elasticity. Demand tends to be more elastic when close substitutes are available, when the good is a luxury rather than a necessity, when it represents a large share of the consumer's budget, and when consumers have more time to adjust. To calculate elasticity consistently regardless of the direction of change, economists often use the midpoint method, which averages the initial and final values in both numerator and denominator. Elasticity also directly affects total revenue \( TR = P \times Q \). When demand is elastic, a price decrease raises total revenue; when demand is inelastic, a price decrease reduces total revenue.
Beyond own-price elasticity, two related measures are important. Cross-price elasticity of demand (XED) is the percentage change in quantity demanded of good A divided by the percentage change in the price of good B. A positive XED indicates substitute goods, while a negative XED indicates complementary goods. Income elasticity of demand (YED) is the percentage change in quantity demanded divided by the percentage change in income. A positive YED characterizes normal goods (and YED greater than one indicates a luxury), while a negative YED identifies inferior goods, for which demand falls as income rises. A particularly unusual case is the Giffen good, an inferior good in which the income effect from a price increase is so strong that quantity demanded actually rises.