Arc elasticity of demand

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The arc elasticity of demand is a way of accurately calculating elasticity and is also known as the midpoint method.

Elasticity measures percentage change in one variable (usually quantity demanded) in response to a percentage change in another variable (usually price):

This creates an ambiguity because the same change, in different directions, would yield a different percentage change. For example, suppose that at price 9, 105 widgets are demanded; at price 10, 100 widgets are demanded; and at price 11, 95 units are demanded. Then, if the price rises from 9 to 11,

while the price falling from 11 to 9 yields

Economists resolve this by averaging the endpoints to use the midpoint between the two endpoints; that is,

The elasticity measured from 9 to 11 is then the same as the elasticity measured from 11 to 9.