Elasticity Of A Function
In mathematics, the elasticity or point elasticity of a positive differentiable function f of a positive variable (positive input, positive output) at point x is defined as
or equivalently
It is thus the ratio of the relative (percentage) change in the function's output with respect to the relative change in its input, for infinitesimal changes from a point . Equivalently, it is the ratio of the infinitesimal change of the logarithm of a function with respect to the infinitesimal change of the logarithm of the argument.
The elasticity of a function is a constant if and only if the function has the form for a constant .
The elasticity at a point is the limit of the arc elasticity between two points as the separation between those two points approaches zero.
The concept of elasticity is widely used in economics; see elasticity (economics) for details.
Read more about Elasticity Of A Function: Rules, Estimating Point Elasticities, Semi-elasticity
Famous quotes containing the words elasticity of, elasticity and/or function:
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—Jane Austen (1775–1817)
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—William Howard Taft (1857–1930)
“Uses are always much broader than functions, and usually far less contentious. The word function carries overtones of purpose and propriety, of concern with why something was developed rather than with how it has actually been found useful. The function of automobiles is to transport people and objects, but they are used for a variety of other purposes—as homes, offices, bedrooms, henhouses, jetties, breakwaters, even offensive weapons.”
—Frank Smith (b. 1928)