Price elasticity of demand is a precise way to quantify how strongly buyers react to price changes. This page focuses on computing it correctly, choosing percentage-change methods, and avoiding the common mistake of confusing elasticity with slope.

Core concept: responsiveness in percentage terms

Because PED is based on percent changes, it can be compared across goods with different units (e.g., movie tickets vs. gasoline).

What “slope is not elasticity” means

A demand curve’s slope is $\Delta P / \Delta Q$ (or $dP/dQ$), and it depends on the units used for price and quantity.

A straight-line demand curve is divided into regions where demand is elastic, unit elastic, and inelastic. The figure helps show why slope can be constant while elasticity changes: elasticity depends on percentage changes (which vary with the starting $P$ and $Q$), not just the line’s steepness. Source

Elasticity instead uses percent changes, so it is unitless and varies along a linear demand curve even when slope is constant.

Computing PED: the required components

To calculate PED between two points, you need:

• Two prices ($P_1$, $P_2$)

• The corresponding quantities demanded ($Q_1$, $Q_2$)

• A consistent method for percent change (simple base vs. midpoint)

Be clear about the direction of change:

• If price rises, quantity demanded typically falls, making the raw ratio negative.

• In AP Micro, PED is commonly reported in absolute value (as a positive number) unless a question explicitly asks for the sign.

Formulas (simple percent change and midpoint)

Use the midpoint method (also called arc elasticity) when calculating elasticity between two discrete points, because it avoids getting different answers depending on whether you treat the move as $1 \rightarrow 2$ or $2 \rightarrow 1$.

Choosing the right method on AP-style tasks

When midpoint is preferred

Use midpoint percent change when:

• You are given two prices and two quantities

• You are asked for elasticity “between” two points

• The prompt does not specify a base value for percent changes

When simple percent change may appear

Simple percent change (using the initial value as the base) may be used if:

• The problem explicitly says “from the initial price of…” and “from the initial quantity of…”

• The question expects a directional (start-to-end) framing

Common calculation and interpretation pitfalls

• Forgetting to use percent change: Using $\Delta Q/\Delta P$ gives slope, not elasticity.

• Mixing bases: If you use midpoint for $$, you must also use midpoint for $$.

• Sign confusion: The raw PED is usually negative; if the question asks whether demand is “more” or “less” responsive, report $|E_d|$.

• Rounding too early: Round PED at the end to avoid compounding error.

• Using the wrong $Q$: Quantity demanded comes from the demand curve point at that price (not total market size unless specified).