Price Elasticity of Demand

Two computational conventions appear at Level I. The arc, or midpoint, method divides the change in quantity by the average of the starting and ending quantities, then divides the change in price by the average of the two prices, and takes the ratio of those two figures. Using averages as the base means the same elasticity results whether price rises or falls between the two points, removing the direction bias that plagues simple percentage changes.

Point elasticity instead multiplies the slope term, the derivative of quantity with respect to price, by the ratio of price to quantity at the specific point examined. For a demand function written as quantity equals a constant minus a coefficient times price, the coefficient is that slope term. Because the price-to-quantity ratio changes at every point on the curve, elasticity is a local measure, not a property of the curve as a whole.

On a straight-line demand curve the slope is fixed, yet elasticity travels the full range. Near the vertical intercept, price is high and quantity is close to zero, so the price-to-quantity ratio is enormous and demand is highly elastic. Moving down the curve, price falls and quantity rises, shrinking that ratio until elasticity reaches negative one at the midpoint. Below the midpoint demand is inelastic, approaching zero elasticity at the horizontal intercept where price is negligible.

Only a specific curved demand function, one in which quantity equals a constant times price raised to a fixed negative exponent, delivers constant elasticity, and that exponent is the elasticity. Recognising the difference between slope and elasticity is the single most reliable way to avoid errors on demand-curve questions.

Three factors dominate. The closeness and availability of substitutes matters most: a single brand of soft drink faces elastic demand while soft drinks as a category do not, because consumers can switch brands far more easily than they can abandon the category. The share of income the good absorbs matters next; expenditure on salt or postage is trivial enough that price changes barely register, whereas housing or vehicles command attention.

Time is the third and most frequently tested. Elasticity rises with the horizon because substitution requires adjustment, such as replacing appliances, relocating, or renegotiating contracts. Short-run demand for energy, pharmaceuticals under patent, and addictive goods is typically inelastic; long-run demand for the same goods is materially more responsive. Necessities skew inelastic, discretionary and luxury purchases skew elastic.

The revenue link is the concept's commercial payoff. When demand is elastic, quantity responds proportionally more than price, so cutting price raises total revenue and raising price lowers it. When demand is inelastic the relationship reverses, and at unit elasticity total revenue is at its maximum, meaning marginal revenue equals zero. This is why a profit-maximising firm with market power never operates on the inelastic segment of its demand curve: it could raise price, sell less, and increase revenue while cutting cost.

The same logic underpins optimal markup, which widens as demand becomes less elastic, and it explains why tax burdens fall mainly on the side of the market that is less responsive. In equity analysis, low own-price elasticity is the quantitative expression of pricing power and defensive earnings.