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Line 1: − + − There is an ambiguity in calculating the percentage change in price or quantity in calculating elasticity of demand. What should be used as the denominator in deriving the percentages? If $100 increases to $110, then the percent change could be described as $10/$100 x 100% or $10/$110 x 100%. Above we used the initial price and quantity as the denominator, but we could have used the final price and quantity as the denominator instead.+ − + + + + + + + + + + + + + + + + + + + +
Arc elasticity of demand (view source)
Revision as of 23:18, January 5, 2012
, 23:18, January 5, 2012Expanded
The '''arc elasticity of demand''' calculates the elasticity by using the average overall values for [[price]] and [[quantities]] as the respective denominator in calculating the elasticities. The arc elasticity may also be referred to, as in Mankiw's text, as the price elasticity of demand calculated using the '''midpoint method'''.
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):
Economists resolve this by typically using the “arc elasticity” because it is a more accurate depiction of the “arc” or curve of demand. That is, rather than using 100 or 110 as the denominator, the average (or midpoint) would be used - the elasticity would be measured (10/105)x100%.
:<math>\frac{% \Delta Q}{% \Delta P} = \frac{\frac{Q_{new}-Q_{old}}{Q_{old}}}{\frac{P_{new}-P_{old}}{P_{old}}}</math>
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,
<math>Elasticity = \frac{\frac{95-105}{95}}{\frac{11-9}{9}} = \frac{\frac{-10}{95}}{\frac{2}{9}} = \frac{-9}{19} \approx -.47</math>
while the price falling from 11 to 9 yields
<math>Elasticity = \frac{\frac{105-95}{105}}{\frac{9-11}{11}} = \frac{\frac{10}{105}}{\frac{-2}{11}} = \frac{11}{-21} \approx -.52</math>
Economists resolve this by averaging the endpoints to use the midpoint between the two endpoints; that is,
<math>Elasticity = \frac{\frac{105-95}{\frac{95+105}{2}}}{\frac{9-11}{\frac{9+11}{2}}} = \frac{\frac{10}{100}}{\frac{-2}{10}} = \frac{-1}{2} = -.5</math>
The elasticity measured from 9 to 11 is then the same as the elasticity measured from 11 to 9.
[[Category:Economics]]
[[Category:Economics]]