Price Elasticity of Demand

Elasticity is the percentage change in quantity divided by the percentage change in price, and the whole argument is about which percentages. The point formula divides both by the starting values, so raising 10 to 12 and cutting 12 to 10 give different elasticities for the same pair of points — which is uncomfortable, since it is the same segment of the same curve. The midpoint (arc) formula divides by the average of the two values instead and is symmetric, which is why it is the default here. The same arithmetic answers cross elasticity, where the sign separates substitutes from complements, and income elasticity, where it separates normal goods from inferior ones.

An elasticity past 1 in magnitude means a price rise loses revenue and a cut gains it; below 1 the reverse. That is the textbook part, and the page shows it. What matters more in practice is contribution: with a unit cost, a price cut that lifts revenue can still lose money, because the extra volume is sold on a thinner margin. So the page also gives the break-even volume change — the percentage swing that leaves contribution exactly flat — which is the number worth arguing about in a pricing meeting. With constant elasticity above 1 the Lerner relation adds the markup a profit-maximiser would hold: 1 ÷ |E| of the price.

Two points, one moment. Elasticity is not a property of a product; it is a property of a point on a demand curve at a moment in time, and it changes along the curve and with competitors, season, income, inventory and everything else that moved while the price did. A single before-and-after pair cannot separate the price effect from any of that, so treat the number as a reading rather than a law, and use a controlled test before repricing a book on it. The Lerner markup rests on the elasticity staying constant and the cost being the true marginal one — both heroic assumptions from two observations. Nothing leaves the browser; the same four anonymous usage counts as the rest of the site apply.