<P> The use of the midpoint arc elasticity formula (with the midpoint used for the base of the change, rather than the initial point (x, y) which is used in almost all other contexts for calculating percentages) was advocated by R.G.D. Allen for use when x refers to the quantity of a good demanded or supplied and y refers to its price, due to the following properties: (1) it is symmetric with respect to the two prices and quantities, (2) it is independent of the units of measurement, and (3) it yields a value of unity if the total revenues (price times quantity) at the two points are equal . </P> <P> The arc elasticity is used when there is not a general function for the relationship of two variables, but two points on the relationship are known . in contrast, calculation of the point elasticity requires detailed knowledge of the functional relationship and can be calculated wherever the function is defined . </P> <P> For comparison, the y point elasticity of x is given by </P> <Dl> <Dd> E x, y = ∂ x ∂ y ⋅ y x = ∂ ln ⁡ x ∂ ln ⁡ y (\ displaystyle E_ (x, y) = (\ frac (\ partial x) (\ partial y)) \ cdot (\ frac (y) (x)) = (\ frac (\ partial \ ln x) (\ partial \ ln y))) </Dd> </Dl>

Explain how to measure elasticity using the arc method