Arc elasticity is the elasticity of one variable with respect to another between two given points. It is useful when the relationship between the variables lacks a constant rate, defining elasticity between two points on a curve.
The concept finds applications in both economics and mathematics. In economics, it is primarily used to gauge changes between the quantity of goods demanded and their prices.
Key Insights
- Arc elasticity measures the elasticity of one variable with respect to another between two defined points.
- The concept spans both economics and mathematics.
- Commonly used to assess changes in the quantity of goods demanded in relation to their prices.
- Two primary methods to calculate elasticity: price (or point) elasticity of demand and arc elasticity of demand.
Grasping Arc Elasticity
In economics, arc elasticity aligns with the law of demand, measuring percentage shifts between goods’ quantity demanded and their prices.
Two methodologies exist for calculating elasticity—price (or point) elasticity of demand and arc elasticity of demand. Price elasticity of demand assesses how responsive quantity demanded is to price alterations, either at a specific point on the demand curve or between two points. However, arc elasticity of demand utilizes a midpoint between the two chosen points.
Formula for Price (Point) Elasticity of Demand
𝑃𝐸_𝑑 = \frac{\text{\% Change in Quantity}}{\text{\% Change in Price}}
Example Calculation
If the price of a product decreases from $10 to $8, causing an increase in quantity demanded from 40 to 60 units, the price elasticity of demand is calculated as:
- % change in quantity demanded = (Qd2 - Qd1) / Qd1 = (60 - 40) / 40 = 0.5
- % change in price = (P2 - P1) / P1 = (8 - 10) / 10 = -0.2
- Thus, PEd= 0.5 / -0.2 = 2.5
Since price elasticity concerns absolute values, the negative sign is disregarded. Hence, the price elasticity when the price drops from $10 to $8 is 2.5.
Arc Elasticity of Demand
A shortcoming of the price elasticity of demand formula is that it varies based on whether the price rises or falls. For instance, if the price increased from $8 to $10 and the quantity demanded fell from 60 to 40, PEd will be:
- % change in quantity demanded = (40 - 60) / 60 = -0.33
- % change in price = (10 - 8) / 8 = 0.25
- PEd = -0.33 / 0.25 = 1.32, differing considerably from 2.5
Calculating Arc Elasticity of Demand
Arc elasticity mitigates this issue by measuring at the midpoint between the selected points on the demand curve, using the following formula:
- Arc Ed = [(Qd2 - Qd1) / midpoint Qd] ÷ [(P2 - P1) / midpoint P]
Following the earlier example:
- Midpoint Qd = (Qd1 + Qd2) / 2 = (40 + 60) / 2 = 50
- Midpoint Price = (P1 + P2) / 2 = (10 + 8) / 2 = 9
- % change in quantity demanded = (60 - 40) / 50 = 0.4
- % change in price = (8 - 10) / 9 = -0.22
- Arc Ed = 0.4 / -0.22 = 1.82
Using arc elasticity ensures identical values for elasticity irrespective of whether prices rise or fall, making it beneficial when price changes are considerable.
More About Elasticity
What Is Elasticity in Economics?
In economics, elasticity measures the change in quantity demanded for a product in response to price fluctuations. A product is deemed elastic if demand significantly alters with price changes.
Understanding the Law of Demand
The law of demand is a core economic principle stating that an increase in price results in a decrease in the demand for a good or service.
Benefits of Arc Elasticity of Demand
Arc elasticity, by using a midpoint approach, effectively measures elasticity between two points, particularly valuable when price change is substantial.
Conclusion
Arc elasticity is widely employed in economics to gauge percentage changes between the demand for goods and their prices. Elasticity can be computed via price elasticity of demand or arc elasticity of demand, with the latter being more pertinent when facing significant price changes.
Related Terms: Elasticity, Demand Curve, Law of Demand, Price Elasticity.
References
- Federal Reserve Bank of St. Louis. “Elasticity of Demand - The Economic Lowdown Podcast Series”.
- University of Minnesota. “The Price Elasticity of Demand”.
