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 feel like a white granular mass of amorphous crystals—my formula appears to be isomeric with Spasmotoxin. My aurochloride precipitates into beautiful prismatic needles. My Platinochloride develops octohedron crystals,—with a fine blue florescence. My physiological action is not indifferent. One millionth of a grain injected under the skin of a frog produced instantaneous death accompanied by an orange blossom odor.”
—Lafcadio Hearn (1850–1904)
“I take it that what all men are really after is some form or perhaps only some formula of peace.”
—Joseph Conrad (1857–1924)
“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)