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Definition – What is midpoint elasticity (also known as arc elasticity)?
Midpoint elasticity, also known as arc elasticity, measures the average responsiveness of quantity demanded or supplied to changes in price between two points. Unlike traditional elasticity, midpoint elasticity provides more consistent results by using the average of the initial and final values.
- If midpoint elasticity > 1, the good is elastic, meaning quantity is highly responsive to price changes.
- If midpoint elasticity < 1, the good is inelastic, meaning quantity responds weakly to price changes.
- If midpoint elasticity = 1, the good has unit elasticity, meaning quantity changes proportionally to price.
This method gives a more accurate understanding of how price changes impact demand or supply over a range of values.
Formula – How to calculate Arc Elasticity
The formula for midpoint elasticity is:
Midpoint Elasticity = (ΔQuantity ÷ Average Quantity) ÷ (ΔPrice ÷ Average Price)
Where:
- Δ Quantity is the change in quantity demanded or supplied.
- Δ Price is the change in price.
- Average Quantity and Average Price are the averages of the initial and final values of quantity and price, respectively.
Example
Suppose the price of a product increases from $10 to $12, and the quantity demanded decreases from 200 to 180 units. The midpoint formula is applied as follows:
- Average Price: (10 + 12) ÷ 2 = 112
- Average Quantity: (200 + 180) ÷ 2=190
- Change in Price (ΔP): 12 − 10 = 2
- Change in Quantity (ΔQ): 200 − 180 = 20
Plugging these values into the formula:
Midpoint Elasticity = (20 ÷ 190) ÷ (2 ÷ 11) = 0.105 ÷ 0.182 ≈ 0.58
This result indicates that demand is inelastic, as the elasticity is less than 1.
Why Midpoint Elasticity Matters
The midpoint method provides a more accurate measure of elasticity over a range, which is particularly useful when there are significant changes in price or quantity. Traditional elasticity can yield different results depending on the direction of change, but midpoint elasticity solves this problem by using averages, making it a more reliable tool for businesses and economists when analyzing price sensitivity.
Midpoint Elasticity vs. Regular Elasticity
Midpoint elasticity calculates the average elasticity between two points, using the midpoint formula for consistency, while regular elasticity measures the responsiveness based on the initial point, which can lead to different results depending on where the price change starts.
Sources and more resources
- Wikipedia contributors. (2024e, June 19). Arc elasticity. Wikipedia. https://en.wikipedia.org/wiki/Arc_elasticity
- Pindyck, R., & Rubinfeld, D., Microeconomics (8th ed.), (2013). United States of America: Pearson. ISBN 13: 978-0-13-285712-3. Page 36.
- Greenlaw, S., & Shapiro, D., Principles of Microeconomics 2e. (2018). Houston: Rice University OpenStax. ISBN 13: 978-1-947172-35-7. Page 109.