Point Elasticity vs. Arc Elasticity: Key Differences, Formulas & When to Use
Point elasticity measures responsiveness at a single point on a curve, using the derivative dQ/dP × P/Q; arc elasticity averages two points with (ΔQ/ΔP) × [(P1+P2)/(Q1+Q2)].
People mix them up because both spit out a number called “elasticity,” but one is a snapshot and the other is a movie. A coffee shop owner sees a 1-cent price tweak and grabs point elasticity; a national chain comparing last year’s to this year’s prices reaches for arc elasticity.
Key Differences
Point elasticity needs calculus, gives exact sensitivity at one price, and works best for tiny changes. Arc elasticity uses basic arithmetic, smooths two prices and quantities, and handles bigger jumps without calculus.
Which One Should You Choose?
Pick point elasticity for real-time pricing apps, derivatives, or infinitesimal shifts. Choose arc elasticity when you only have before-and-after data, like quarterly sales reports or A/B tests.
Is point elasticity always more accurate?
Only for infinitesimal changes; for real-world jumps, arc elasticity often yields more reliable averages.
Can arc elasticity ever equal point elasticity?
Yes, if the demand curve is linear and the two points collapse into one, the formulas converge.