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 a 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. Generalisations to multi-input-multi-output cases also exist in the literature. 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 and Metabolic Control Analysis; see elasticity (economics) and Elasticity coefficient respectively for details. Rules for finding the elasticity of products and quotients are simpler than those for derivatives. Let f, g be differentiable. Then The derivative can be expressed in terms of elasticity as Let a and b be constants. Then In economics, the price elasticity of demand refers to the elasticity of a demand function Q(P), and can be expressed as (dQ/dP)/(Q(P)/P) or the ratio of the value of the marginal function (dQ/dP) to the value of the average function (Q(P)/P). This relationship provides an easy way of determining whether a demand curve is elastic or inelastic at a particular point. First, suppose one follows the usual convention in mathematics of plotting the independent variable (P) horizontally and the dependent variable (Q) vertically. Then the slope of a line tangent to the curve at that point is the value of the marginal function at that point. The slope of a ray drawn from the origin through the point is the value of the average function.

About this result

This page is automatically generated and may contain information that is not correct, complete, up-to-date, or relevant to your search query. The same applies to every other page on this website. Please make sure to verify the information with EPFL's official sources.

Related concepts (3)

Related courses (35)

Related lectures (204)

MSE-669: Thin film and small scale mechanics

The course focuses on mechanics of solid thin films and small scale structures and on state-of-the-art experimental techniques employed for evaluation and extraction of thin films and small scale stru

MSE-203: Continuum mechanics

Dans ce cours, les outils qui permettent de décrire les matériaux non pas au niveau atomique mais au niveau d'un continuum sont présentés. Les tenseurs des contraintes et des déformations, les lois de

CIVIL-705: Selected Topics on Advanced Composites in Engineering Structures

The course focuses on the current investigations in the fields of fatigue and fracture of composite materials and composite structural components, like adhesively-bonded joints. Students would be able

Elasticity of a function

Elasticity (economics)

In economics, elasticity measures the responsiveness of one economic variable to a change in another. If the price elasticity of the demand of something is -2, a 10% increase in price causes the quantity demanded to fall by 20%. Elasticity in economics provides an understanding of changes in the behavior of the buyers and sellers with price changes. There are two types of elasticity for demand and supply, one is inelastic demand and supply and other one is elastic demand and supply.

Price elasticity of demand

A good's price elasticity of demand (, PED) is a measure of how sensitive the quantity demanded is to its price. When the price rises, quantity demanded falls for almost any good, but it falls more for some than for others. The price elasticity gives the percentage change in quantity demanded when there is a one percent increase in price, holding everything else constant. If the elasticity is −2, that means a one percent price rise leads to a two percent decline in quantity demanded.

Elasticity: Constitutive Modelling in Geomechanics CIVIL-402: Geomechanics

Explores constitutive equations in geomechanics, stress-strain behavior, and practical applications in engineering.

Snow Mechanics: Avalanche Release and Crack Propagation ENV-525: Physics and hydrology of snow

Explores snow mechanics, focusing on avalanche release and crack propagation mechanisms, including stress redistribution and safety considerations.

Elasticity: Constitutive Modelling in Geomechanics CIVIL-402: Geomechanics

Explores constitutive modelling in geomechanics, focusing on stress-strain behavior and the application of elastic models in analytical and numerical methods.