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

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.

<= AMERICAN ECONOMIC ASSOCIATION

ASSUMPTION =>

ARC ELASTICITY, AmosWEB Encyclonomic WEB*pedia, http://www.AmosWEB.com, AmosWEB LLC, 2000-2014. [Accessed: April 24, 2014].

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

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

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

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