17:
862:
In contrast, if the percentage change in quantity demanded were measured against the initial value, the calculated percentage change would be (120-80)/80= 50%. The percent change for the reverse sequence of observations, 120 units to 80 units, would be (80-120)/120 = -33.3%. The midpoint formula has
858:
Suppose the quantity of hot dogs demanded at halftime of football games is measured at two different games at which two different prices are charged: at one measurement the quantity demanded is 80 units, and at the other measurement it is 120 units. The percent change, measured against the average,
392:
The arc elasticity is used when there is not a general function for the relationship of two variables, but two points on the relationship are known. In contrast, calculation of the point elasticity requires detailed knowledge of the functional relationship and can be calculated wherever the function
48:
Like the point elasticity, the arc elasticity can vary in value depending on the starting point. For example, the arc elasticity of supply of a product with respect to the product's price could be large when the starting and ending prices are both low, but could be small when they are both
388:
refers to its price, due to the following properties: (1) it is symmetric with respect to the two prices and quantities, (2) it is independent of the units of measurement, and (3) it yields a value of unity if the total revenues (price times quantity) at the two points are equal.
509:
853:
875:
of the price elasticity as simply price elasticity, since for a normal (decreasing) demand curve the elasticity is always negative and so the "minus" part can be made implicit. Thus the arc price elasticity demand of the football fans is 0.4.
136:
866:
Suppose that the change in the price of hot dogs, which led to this change in quantity demanded from 80 to 120, was from $ 3 to $ 1. The percent change in price measured against the midpoint would be (1-3)/2 = -100%, so the
40:
of one variable with respect to another between two given points. It is the ratio of the percentage change of one of the variables between the two points to the percentage change of the other variable. It contrasts with the
357:
250:
580:
16:
410:
689:
45:, which is the limit of the arc elasticity as the distance between the two points approaches zero and which hence is defined at a single point rather than for a pair of points.
859:
would be (120-80)/((120+80)/2))=40%. If the measurements were taken in reverse sequence (first 120 and then 80), the absolute value of the percentage change would be the same.
680:
634:
519:
The arc elasticity of quantity demanded (or quantity supplied) Q with respect to price P, also known as the arc price elasticity of demand (or supply), is calculated as
71:
258:
151:
525:
362:
The use of the midpoint arc elasticity formula (with the midpoint used for the base of the change, rather than the initial point (
955:
682:, are known. (Nothing else might be known about the demand curve.) Then the arc elasticity is obtained using the formula
504:{\displaystyle E_{x,y}={\frac {\partial x}{\partial y}}\cdot {\frac {y}{x}}={\frac {\partial \ln x}{\partial \ln y}}}
976:
863:
the benefit that a percentage change from A to B is measured in absolute value as the same as one from B to A.
848:{\displaystyle E_{p}={\frac {\frac {Q_{2}-Q_{1}}{(Q_{1}+Q_{2})/2}}{\frac {P_{2}-P_{1}}{(P_{1}+P_{2})/2}}}.}
911:
868:
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639:
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37:
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376:) which is used in almost all other contexts for calculating percentages) was advocated by
8:
928:
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920:
131:{\displaystyle E_{x,y}={\frac {\%{\mbox{ change in }}x}{\%{\mbox{ change in }}y}}}
145:
in going from point 1 to point 2 is usually calculated relative to the midpoint:
377:
352:{\displaystyle \%{\mbox{ change in }}y={\frac {y_{2}-y_{1}}{(y_{2}+y_{1})/2}}.}
245:{\displaystyle \%{\mbox{ change in }}x={\frac {x_{2}-x_{1}}{(x_{2}+x_{1})/2}};}
970:
25:
946:
Parkin, Michael; Powell, Melanie; Matthews, Kent (2014). "Elasticity".
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29:
924:
909:
Allen, R. G. D. (1933). "The
Concept of Arc Elasticity of Demand".
575:{\displaystyle (\%{\mbox{ change in }}Q)/(\%{\mbox{ change in }}P)}
384:
refers to the quantity of a good demanded or supplied and
950:(9th European ed.). Harlow: Pearson. p. 82.
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is 40%/(-100%) or -0.4. It is common to refer to the
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912:Review of Economic Studies
869:price elasticity of demand
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886:Elasticity of a function
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891:Elasticity (economics)
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919:(3): 226–229.
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34:arc elasticity
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361:
140:
62:
58:
56:
47:
42:
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26:mathematics
897:References
141:where the
38:elasticity
948:Economics
787:−
721:−
557:%
533:%
493:
487:∂
479:
473:∂
454:⋅
445:∂
437:∂
292:−
263:%
185:−
156:%
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98:%
30:economics
971:Category
880:See also
933:2967486
586:Example
53:Formula
36:is the
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929:JSTOR
952:ISBN
636:and
57:The
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699:p
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