Measuring Price Elasticity — Point Method and Arc Method

Point Method (Geometric Method). This method measures elasticity AT A SINGLE POINT on a straight-line demand curve, using only the geometry of the line — the distance from that point to where the line meets each axis.

For a straight-line demand curve $DD'$ meeting the price axis at $D$ and the quantity axis at $D'$, and a chosen point $M$ on the line: the elasticity at $M$ equals $\dfrac{MD'}{MD}$, the ratio of the LOWER segment (from $M$ down to $D'$) to the UPPER segment (from $M$ up to $D$). At the exact MIDPOINT of a straight-line demand curve, the two segments are equal, so $E_d = 1$ there. Above the midpoint (closer to $D$, the price-axis end), the lower segment is longer than the upper one, so $E_d > 1$; below the midpoint (closer to $D'$, the quantity-axis end), $E_d < 1$. At $D$ itself, $E_d = \infty$; at $D'$ itself, $E_d = 0$. This means price elasticity is DIFFERENT at every point along a single straight-line demand curve, even though its slope never changes — an important and easily-tested idea.

<!-- FIGURE-NEEDED: A single downward-sloping straight-line demand curve DD' with D on the price (Y) axis and D' on the quantity (X) axis. Mark the midpoint M with equal segments MD and MD', and mark a point closer to D (labelled elastic segment) and a point closer to D' (labelled inelastic segment), so students can see how E_d changes along the same straight line. -->

Arc Method. When price changes over a NOTICEABLE (non-infinitesimal) range — as in most real data — the Percentage Method's answer differs slightly depending on which of the two price-quantity pairs is treated as the "original" one. The Arc Method removes this asymmetry by measuring elasticity over the ARC (stretch) of the curve between two points, using the AVERAGE of the two prices and the AVERAGE of the two quantities as the base.