In the economic science an elasticity is a measure, which indicates, how a dependent variable reacts to a change of one of its measured variables. For example the price elasticity of the offer shows, how the offer of economic goods changes, if the price of the property changes.

Not completely correctly, but thereby the following question is descriptive: Around how much per cent does a variable change as reaction to in-per cent change other This definition becomes completely correct, if one instead of a in-per cent change one infinitesimally (about: infinitely small) small change regards.

Mathematical representation

In order to seize this verbal definition mathematically, one regards a function y = f (x_1, x_2,"…, x_n) \, which depends on one or more measured variables a x_1, x_2,"…, x_n \. An elasticity \ epsilon_i \, indicates, around which relative amount \ delta changes y/y \, the function value y \, if a measured variable changes for delta around the relative amount \ x_i/x_i \, in the case of a marginally small change. Thus applies

\ epsilon_i (x_i) = \ lim_ {\ delta x_i \ rarr0} {\ delta y/y \ more over \ delta x_i/x_i} = {\ partial y/y \ more over \ partial x_i/x_i} = {x_i \ over y} {\ partial y \ more over \ partial x_i} = {\ partial \ log y \ more over \ partial \ logs x_i},

whereby \ partial a partial derivative and a log a logarithmic function with arbitrary basis designate.

The amount (absolute value) of the result lies in the interval between 0 and infinitely, including the two borders than special cases. A function (or also subrange or one point of a function) with the elasticity 0 is called infinitely or minus infinitely perfectly inelastic, one with the elasticity as perfectly flexible.

Note: A linear function, how it is frequently used in the economic science, has usually like most functions at each point another elasticity (exception: Origin straight line). Functions, which exhibit the same elasticity over their entire definition range, are called ISO-flexible functions. Examples would be as mentioned the function y = {1 \ over x} with the elasticity \ epsilon = -1 \, or an origin straight line y = A x \, with the elasticity \ epsilon = 1 \.

Kinds of

In the economic science the among other things following plays a role:

as a function of argument

• Which influence do price adjustments on supply and demand
• Which influence do price adjustments have with a property on supply and demand at other
• Income elasticity: Which influence do changes of income have on the demand for a
• Which influence have would marketing-wind up on the demand for a

as a function of the market side

• How does the offer react to changes of other
• How does the demand react to changes of other

Linkage

Further economic

• Enterprise elasticity
• Substitution elasticity: , as "“easy"” one indicates a factor of production for a given production function and an output constantly held (e.g. Work) by another (e.g. Principal one) to replace can. (Comparisons for example the CES Produktionsfunktion)
• Scale elasticity, indicates, how strongly the output can be increased, if the quantities required of the inputs are expanded.
• Tax amount elasticity
• Interest elasticity
• Income elasticity

See also

• Amoroso Robinson relation ''

Articles in category "Elasticity (economics)"

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