Arc elasticity

The y arc elasticity of x is defined as: where the percentage change in going from point 1 to point 2 is usually calculated relative to the midpoint: The use of the midpoint arc elasticity formula (with the midpoint used for the base of the change, rather than the initial point (x1, y1) 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.

For comparison, the y point elasticity of x is given by The arc elasticity of quantity demanded (or quantity supplied) Q with respect to price P, also known as the arc price elasticity of demand (or supply), is calculated as [2] Suppose that two points on a demand curve,

Then the arc elasticity is obtained using the formula Suppose the quantity of hot dogs demanded at halftime of football games is measured at two different games at which two different prices are charged: at one measurement the quantity demanded is 80 units, and at the other measurement it is 120 units.

If the measurements were taken in reverse sequence (first 120 and then 80), the absolute value of the percentage change would be the same.

The midpoint formula has the benefit that a percentage change from A to B is measured in absolute value as the same as one from B to A.

Thus the arc price elasticity demand of the football fans is 0.4.