Formula
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 rather than the initial point (x1, y1) used 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.
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.
For comparison, the y point elasticity of x is given by
Read more about this topic: Arc Elasticity
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