Elasticity (economics)
In economics, elasticity is a measure that indicates the relative change of a dependent variable to a relative change one of its independent variables. Not quite correct, but clearly is the following question: By what percentage change of a variable y in response to the one-percent change in another variable x? One calls this the elasticity of the relative change of y with respect to x or x - y of elasticity.
Consider for example the relative change in demand at a relative change in the price, which is about the price or the price elasticity of demand, also briefly called price elasticity of demand elasticity.
- 4.1 Alternative notations
- 4.2 Special features of the elasticity 4.2.1 Example of an isoelastic function
- 5.1 elasticity with respect to the independent variable,
- 5.2 link
- 5.3 Further economic elasticities
- 6.1 Example of a linear function
Motivation
The motivation for the use of elasticities arises from the fact that the absolute change in the dependent variable not well informed on the structure of a reaction.
There is, for example, a product considered, the price is increased by 1 €, after which the rate decreases to 10,000. Based on the absolute sizes little will be seen over the range of the change in demand. There is a lack of a benchmark: Fraud of the price in base 10 or 100 €? If the sales dropped from 50,000 to 40,000 or 1,000,000 to 990,000 pieces? A useful measure of the effect of an instrument, however, is the elasticity that comes from relative changes. Since the elasticity of no dimension ( such as " € " or "piece" ) contains, it enables the comparability of similar values.
Mathematical representation
An independent variable x
To summarize this verbal definition mathematically, we consider a function.
Analogous to the concept of the difference quotient as an introduction to the differential quotient is first assumed that the so-called arc elasticity. One considers a finite small change of variables and the variables, so that there are the relative changes and. The average relative change of y with respect to a relative change of the sheet is elastic
Of. If you let go, is obtained as infinitesimal considers the elasticity function of y with respect to x
- That even when
Can be represented, for all the values of y where no zero point exists and where the function is differentiable. We call this elasticity as a point elasticity.
It can also show that the elasticity can also be represented as
Several independent variables
Is considered a function which is dependent on one or more factors. An elasticity indicates the extent to which the relative amount ceteris paribus, the function value changes when changes an influencing factor to the relative amount. Thus results for the arc elasticity
And infinitesimal consideration
Where a partial derivative referred.
Mathematical properties of elasticity
The elasticity is dimensionless. Your range is the set of real numbers.
Economic properties of elasticity
The elasticity is a measure of the degree of responsiveness of a function with respect to a change in the abscissa. A negative elasticity means that the function in the area in question falls.
It can be in resilience following conclusions may be drawn:
Alternative notations
An elasticity with a value of 1 is called a proportional elastic or fluid. In the literature such as in the widely used textbook by Varian "Principles of Microeconomics " is also found the term " unit elastic" for an elasticity with the absolute value 1 Lower values are as disproportionately referred elastic or inelastic, are referred to as values above elastic than proportional or elastic.
Special features of the elasticity
Perfectly inelastic and perfectly elastic, special idealized cases.
A linear function, as it is widely used in economics, has generally like most of the functions at each point a different elasticity (except through the origin ). Functions having over its entire domain, the same elasticity, are referred to as isoelastic functions.
Example of an isoelastic function
The elasticity is a function of isoelastic, because it is
Could be interpreted as a model of price sales function. In this context, one could say something casually that in all areas of the marketing function, price, demand falls by 1 % when the price increases by 1%.
Another example of isoelasticity is a line through the origin with the elasticity. A useful application would be a revenue function in polypolistic provider model.
Selected elasticities
In economics, among others, the following elasticities play a role:
Elasticity with respect to the independent variable,
- Price elasticities: The impact of price changes on supply and demand?
- Cross-price elasticities: The impact of changes in price of a commodity on supply and demand for other goods?
- Dynamic price elasticities: What influence has a current price change on future sales?
- Income elasticities: The impact of changes in income on the demand for a good?
- Sales value elasticities: The impact of marketing efforts on the demand for a good?
A distinction as the dependent variable, for example, at the price and cross- price elasticity nor between supply and demand.
Link
The micro-economic concept of price elasticity of demand and / or the Offer can be operationally not only use there always exquisite, where appropriate in-house data material obtained, but also transferred to other independent variables as prizes. Above all trading companies with its own ERP system and scanner checkouts open up numerous opportunities for performance analysis by means of elasticity ratios. For example, the demand or sales change - even for a single species - are related as the dependent variable on independent variables such as advertising activities, advertising intensity, change of price optics, change of placement, introduction of a double placement or other commercial psychological measures. In principle, for commercial establishments ", the elasticity measure applicable to all instruments of trade marketing and all market participants: service elasticity, elasticity of retail space, front track elasticity or placement elasticity of suppliers, competitors and customers, etc. with corresponding cross elasticities. "
More economic elasticities
- Elasticity of substitution: specifies how can replace " easy " one for a given production function and output is kept constant, a factor of production (eg labor ) by another (eg capital ). (See, for example, the CES production function)
- Scale elasticity, indicates how much the output can be increased when the amounts of the inputs be extended.
- Amount of tax elasticity measures the response of tax revenue in a change in the tax base.
- Interest elasticity indicates how an interest rate position in a relative change in the interest rate responding.
- Production elasticity indicates approximately how much percent of the output ( production ) of a company or an economy changed when the use of a factor of production is increased by one percent.
Examples
For example a linear function
A line that does not go out from the origin, has at each point a different elasticity, as the following practical example.
Where is the linear function. It is to be examined at the point of the elasticity, that is, the percent change of y when x is incremented by one percent.
For part of the function value.
X is increased by 1 %. So we obtain for.
After the 1 % increase of x the y value has grown from 200 to 201. It has absolutely increased by 1, which corresponds to a percentage change of 0.5%.
Using the elastic function for a straight line can be expressed as
- ,
Would result for the example
It being noted that the elastic function for a positive slope of the line is positive and increases with the absolute term. When she falls monotonically from to of and strives with growing against 1
Is the elasticity is now calculated for the point that corresponds to the function value. x is increased by 1 %, that is absolutely second to follows. The percentage change is here, so 0.667 %.
The determination of the elasticity function results here