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June 26, 2016 

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VARIABLE FACTOR OF PRODUCTION: An input whose quantity can be changed in the time period under consideration. This usually goes by the shorter term fixed input and should be immediately compared and contrasted with fixed factor of production, which goes by the shorter term fixed input. The most common example of a variable factor of production is labor. A variable factor of production provides the extra inputs that a firm needs to expand short-run production. In contrast, a fixed factor of production, like capital, provides the capacity constraint in production. As larger quantities of a variable factor of production, like labor, are added to a fixed factor of production like capital, the variable factor of production becomes less productive.

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ARC ELASTICITY:

The average elasticity for discrete changes in two variables. The distinguishing characteristic of arc elasticity is that percentage changes are calculated based on the average of initial and ending values of each variable, rather than initial values. Arc elasticity is generally calculated using the midpoint elasticity formula. The contrast to arc elasticity is point elasticity. For infinitesimally small changes in two variables, arc elasticity is the same as point elasticity.
Arc elasticity is best considered the average elasticity over a range of values for a relation. Like any average, some values within the range are likely to be greater and some less. However, it provides a quick approximation of elasticity when more precise and sophisticated calculation techniques are not possible.

Working Through an Example

A Standard Demand Curve
Demand Curve
The demand curve displayed to the right can be used to illustrate the measurement of arc elasticity using the midpoint elasticity formula. If the price declines from $12 to $8, the quantity demanded increases from 4 to 6, from point X to point Z. Using this midpoint formula (with price designated as P and quantity designated as Q) average price elasticity of demand is:
midpoint
elasticity
=(Q[Z] - Q[X])
(Q[Z] + Q[X])/2
÷(P[Z] - P[X])
(P[Z] + P[X])/2

midpoint
elasticity
=(6 - 4)
(6 + 4)/2
÷(8 - 12)
(8 + 12)/2
=(2)
(5)
÷(-4)
(10)

midpoint
elasticity
=0.4÷-0.4=-1.0

Ignoring the minus sign, the price elasticity of demand over this segment of the demand curve from X to Z is 1.0.

An Average Value

This value of 1.0 is actually an average for the entire range between points X and Z. Precise estimates of point elasticity shows that the elasticity is 0.67 at point X and 1.5 at point Z. Moreover, the elasticity is different at each point on a straight line demand curve such as this one. The only point in which the elasticity is exactly equal to 1.0 is at point Y, the midpoint between X and Z.

This last observation is worth emphasizing. The midpoint elasticity formula effectively estimates the point elasticity at the very midpoint of the overall segment. This means that the elasticity of any point on a demand curve (point elasticity) can be obtained by calculating the arc elasticity with the midpoint elasticity formula such that the desired point is dead center in the middle, the midpoint of the arc.

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Recommended Citation:

ARC ELASTICITY, AmosWEB Encyclonomic WEB*pedia, http://www.AmosWEB.com, AmosWEB LLC, 2000-2016. [Accessed: June 26, 2016].


Check Out These Related Terms...

     | point elasticity | coefficient of elasticity | midpoint elasticity formula | endpoint elasticity formula | point elasticity |


Or For A Little Background...

     | elasticity | price elasticity of demand | price elasticity of supply | income elasticity of demand | cross elasticity of demand |


And For Further Study...

     | elasticity and demand slope | elasticity and supply intercept | demand elasticity and total expenditure | elasticity alternatives | elasticity determinants |


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