Arc Elasticity Calculator

Formula

To calculate the Arc Elasticity (\(E_p\)):

\[ E_p = \frac{(Q_2 - Q_1) / (Q_2 + Q_1)}{(P_2 - P_1) / (P_2 + P_1)} \]

Where:

\(E_p\) is the Arc Elasticity
\(Q_1\) is the Initial Quantity
\(Q_2\) is the Final Quantity
\(P_1\) is the Initial Price
\(P_2\) is the Final Price

What is Arc Elasticity?

Arc elasticity measures how the relationship between the demand and price of a good or service changes over time with a change in either of those metrics.

Example Calculation

Let's assume the following values:

Initial Quantity (\(Q_1\)) = 100
Final Quantity (\(Q_2\)) = 80
Initial Price (\(P_1\)) = 10
Final Price (\(P_2\)) = 12

Using the formula:

\[ E_p = \frac{(80 - 100) / (80 + 100)}{(12 - 10) / (12 + 10)} = \frac{-20 / 180}{2 / 22} = \frac{-1/9}{1/11} = -\frac{11}{9} \approx -1.22 \]

The Arc Elasticity is approximately -1.22.