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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.