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
Famous quotes containing the word formula:
“I take it that what all men are really after is some form or perhaps only some formula of peace.”
—Joseph Conrad (1857–1924)
“Beauty, like all other qualities presented to human experience, is relative; and the definition of it becomes unmeaning and useless in proportion to its abstractness. To define beauty not in the most abstract, but in the most concrete terms possible, not to find a universal formula for it, but the formula which expresses most adequately this or that special manifestation of it, is the aim of the true student of aesthetics.”
—Walter Pater (1839–1894)
“Given for one instant an intelligence which could comprehend all the forces by which nature is animated and the respective positions of the beings which compose it, if moreover this intelligence were vast enough to submit these data to analysis, it would embrace in the same formula both the movements of the largest bodies in the universe and those of the lightest atom; to it nothing would be uncertain, and the future as the past would be present to its eyes.”
—Pierre Simon De Laplace (1749–1827)