Arcelasticitet

Arcelasticitet, or arc elasticity, is a measure of how responsive one variable is to a change in another, evaluated over a finite interval rather than at a single point. It is commonly used to assess the price elasticity of demand or supply between two observed points on a curve. Compared with point elasticity, arc elasticity reduces sensitivity to the choice of the base point and provides a symmetric measure around the interval’s midpoint.

Formally, for two observations with prices P1 and P2 and quantities Q1 and Q2, one widely used form is E_arc = ((Q2 - Q1) / (P2 - P1)) * ((P1 + P2) / (Q1 + Q2)). Equivalently, E_arc = ((Q2 - Q1) / (Q1 + Q2)) / ((P2 - P1) / (P1 + P2)). The result is dimensionless and typically negative for demand and positive for supply; its magnitude indicates the percentage change in Q associated with a one-percent change in P over the interval.

Example: P falls from 10 to 8 and Q rises from 100 to 120. Then ΔQ = 20, ΔP = -2, P̄ = 9, Q̄ = 110. E_arc ≈ (20 / -2) * (9 / 110) = -10 * 0.0818 ≈ -0.818. This suggests demand is relatively inelastic over this price range.

Uses and limitations: arc elasticity helps estimate how revenue changes when prices or other factors change and is useful in pricing strategies and policy analysis. Limitations include dependence on the chosen interval, potential nonlinearity of the underlying curve, and sensitivity to outliers. It provides a useful snapshot rather than a constant measure across all price levels.

See also: price elasticity of demand, price elasticity of supply, point elasticity, revenue.