Elasticity

Own-price elasticity of demand is the percentage change in quantity demanded divided by the percentage change in the good's own price, holding other determinants constant. Income elasticity replaces the price term with the percentage change in consumer income, and cross-price elasticity replaces it with the percentage change in the price of a related good.

Two computational conventions matter. The point (or arc) version measured from discrete data divides the change in quantity by the change in price and multiplies by the ratio of price to quantity at a reference point, which means the answer depends on which point is chosen. The midpoint convention removes that ambiguity by expressing each percentage change relative to the average of the starting and ending values. For a linear demand function of the form quantity equals a constant minus a coefficient times price, elasticity equals the negative of that coefficient multiplied by price divided by quantity.

For own-price elasticity the sign is negative by the law of demand, so classification rests on absolute value. Magnitude above one is elastic, below one inelastic, and exactly one unit elastic. The extremes are instructive: perfectly inelastic demand traces a vertical line, perfectly elastic demand a horizontal one, and neither behaves like a normal downward-sloping curve.

Income elasticity is read by sign first. Positive means a normal good, negative an inferior good, and positive values above one identify goods whose consumption grows faster than income, the pattern behind discretionary and luxury categories. Cross-price elasticity is also sign-driven: positive indicates substitutes, because a rise in the other good's price pushes buyers toward this one, while negative indicates complements, since the two are consumed together. Values close to zero suggest the goods are effectively unrelated.

The revenue link is the most practically used implication. When demand is elastic, a price increase reduces total revenue because the quantity response dominates; when demand is inelastic, a price increase raises revenue. At unit elasticity revenue is at its maximum with respect to price. On a straight-line demand curve the slope is constant but elasticity is not: demand is elastic at high prices and low quantities, unit elastic at the midpoint, and inelastic toward the quantity intercept.

What makes demand elastic is largely the availability of close substitutes. Reinforcing factors include the share of the budget the good absorbs, whether it is treated as a necessity or a discretionary purchase, how narrowly the product category is defined, and the time allowed for adjustment. Demand is typically more elastic over long horizons because consumers can change habits, contracts and equipment.

Candidates should be able to compute any of the three elasticities from a table of prices, quantities and incomes, state the classification, and translate it into a revenue or expenditure conclusion. A second common application is tax incidence and the burden of subsidies: the side of the market that is relatively more inelastic absorbs the larger share of a per-unit tax, because it has less capacity to withdraw from the transaction. Elasticity of supply is defined symmetrically and behaves the same way.

Beyond the exam, elasticity estimates drive pricing strategy, regulated utility rate cases, excise tax design, and the decomposition of demand shifts into substitution and income effects. Analysts also use income elasticity to sort sectors into cyclical and defensive groups when forecasting revenue through an economic cycle.